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If square roots are too high try changing % the lines describing /radical and /radicalex to, % % /radical [0 -75 550 0] % /radicalex [-50 -75 500 0] % % Move braceleftbt a bit - default PostScript character is off a bit. % /Sdefs [ /bracketlefttp [201 500] /bracketleftbt [201 500] /bracketrighttp [-81 380] /bracketrightbt [-83 380] /braceleftbt [203 490] /bracketrightex [220 -125 500 0] /radical [0 0 550 0] /radicalex [-50 0 500 0] /parenleftex [-20 -170 0 0] /integral [100 -50 500 0] /infinity [10 -75 730 0] ] def /S1defs [ /underscore [0 80 500 0] /endash [7 90 650 0] ] def % % Tries to round clipping path dimensions, as stored in array pagebbox, so they % match one of the known sizes in the papersizes array. Lower left coordinates % are always set to 0. % /roundpagebbox { 7 dict begin /papersizes [8.5 inch 11 inch 14 inch 17 inch] def /mappapersize { /val exch def /slop .5 inch def /diff slop def /j 0 def 0 1 papersizes length 1 sub { /i exch def papersizes i get val sub abs dup diff le {/diff exch def /j i def} {pop} ifelse } for diff slop lt {papersizes j get} {val} ifelse } def pagebbox 0 0 put pagebbox 1 0 put pagebbox dup 2 get mappapersize 2 exch put pagebbox dup 3 get mappapersize 3 exch put end } bind def %%EndProlog %%BeginSetup mark /xoffset 0 def /yoffset 0 def /#copies 1 store /magnification 1 def %%FormsPerPage: 1 /formsperpage 1 def /landscape false def /resolution 720 def setup 2 setdecoding %%EndSetup %%Page: 1 1 /saveobj save def mark 1 pagesetup 10 R f (AT&T Bell Laboratories)2 993 1 2203 1560 t (Murray Hill, NJ 07974)3 916 1 2242 1680 t (Computing Science Technical Report No. 136)5 1848 1 1776 2853 t 12 B f (Pictures of Karmarkar's Linear Programming Algorithm)5 2958 1 1221 3147 t 10 I f (David M. Gay)2 568 1 2416 3411 t 10 R f (January 1987)1 535 1 2432 5871 t cleartomark showpage saveobj restore %%EndPage: 1 1 %%Page: 1 2 /saveobj save def mark 2 pagesetup 12 B f (Pictures of Karmarkar's Linear Programming Algorithm)5 2958 1 1401 1230 t 10 I f (David M. Gay)2 568 1 2596 1470 t 10 R f (AT&T Bell Laboratories)2 993 1 2383 1650 t (Murray Hill, New Jersey 07974)4 1267 1 2246 1770 t 10 I f (ABSTRACT)2643 2150 w 10 R f ( by)1 165(Karmarkar's linear programming algorithm handles inequality constraints)6 3185 2 1330 2410 t ( equally distant; it moves in the steepest-)7 1651(changing variables to make all constraints about)6 1949 2 1080 2530 t ( variants of)2 489( paper summarizes four)3 996( This)1 247(descent direction seen by the new variables.)6 1868 4 1080 2650 t ( algorithm \(primal affine, primal projective, dual affine,)7 2264(Karmarkar's linear programming)2 1336 2 1080 2770 t ( and presents pic-)3 740(and dual projective\), discusses depicting polytopes \(feasible regions\),)7 2860 2 1080 2890 t ( give an algorithm's eye view of)6 1316( pictures)1 346( These)1 293(tures illustrating the latter three variants.)5 1645 4 1080 3010 t (the variable changes and provide visual verification of some theoretical results.)10 3163 1 1080 3130 t 10 B f (Introduction)720 3490 w 10 R f ( linear programming)2 849(This paper shows an algorithm's eye view of several variants of Karmarkar's)11 3221 2 970 3646 t ( use changes of variables to bring the current iterate to the center of the feasible region and)17 3774(problem. All)1 546 2 720 3766 t ( considering problems having)3 1233( By)1 183( the changed variables.)3 962(move in the steepest-descent direction seen by)6 1942 4 720 3886 t ( before and after the variable changes, thus)7 1802(three degrees of freedom, we can depict the feasible regions)9 2518 2 720 4006 t (graphically illustrating their effect.)3 1392 1 720 4126 t ( primal)1 336( variants of Karmarkar's linear programming algorithm:)6 2390(We begin by summarizing four)4 1344 3 970 4282 t ( we discuss)2 489( Then)1 272( projective, dual affine, and dual projective; the last is apparently new.)11 2998(affine, primal)1 561 4 720 4402 t ( the feasible regions of the linear programming problems, and present pictures that)12 3333(depicting polytopes, i.e.,)2 987 2 720 4522 t ( irrelevant reasons, these)3 1016( \(For)1 232( dual projective, and primal projective algorithms.)6 2063(illustrate the dual affine,)3 1009 4 720 4642 t (three variants happened to be the most convenient to illustrate.\))9 2535 1 720 4762 t ( choice, used in most of our pictures, the views we)10 2119( the right)2 379( With)1 259(The choice of variables matters.)4 1313 4 970 4918 t ( Unfortu-)1 401( projective algorithms.)2 906(obtain are unique up to rotations, and they illustrate some properties of the)12 3013 3 720 5038 t ( discuss these)2 550( We)1 191( are from a seemingly natural but ``wrong'' choice of variables.)10 2570(nately, the pictures in [9])4 1009 4 720 5158 t (variables at the end and show how differently things look from their perspective.)12 3225 1 720 5278 t (The norms)1 430 1 970 5434 t 10 S f (||)1425 5434 w 10 R f (.)1473 5404 w 10 S f (||)1506 5434 w 10 R f ( usual,)1 262( As)1 162( are Euclidean.)2 597(used below)1 452 4 1571 5434 t 10 I f (I)3070 5434 w 10 R f (denotes an identity matrix,)3 1069 1 3129 5434 t 10 B f (0)4249 5434 w 10 R f (a matrix or vector)3 715 1 4325 5434 t (of zeros,)1 346 1 720 5554 t 10 I f (e)1094 5554 w 7 I f (k)1149 5574 w 10 R f (denotes the)1 454 1 1215 5554 t 10 I f (k)1696 5554 w 10 R f (th standard unit vector, and)4 1098 1 1740 5554 t 10 I f (e)2865 5554 w 10 S f (=)2958 5554 w 15 S f (S)3078 5584 w 7 I f (k)3194 5604 w 10 I f (e)3241 5554 w 7 I f (k)3296 5574 w 10 R f (denotes a vector of ones, all of dimension)7 1678 1 3362 5554 t ( notation is defined as needed below.)6 1478( Other)1 277(dictated by context.)2 785 3 720 5704 t 10 B f (The Problem)1 558 1 720 5944 t 10 R f ( a vector)2 397( Find)1 261( in standard form:)3 794(Linear programming \(LP\) problems can always be expressed)7 2618 4 970 6100 t 10 I f (x)720 6220 w 10 S f (\316)805 6220 w 10 I f (I R)1 78 1 917 6220 t 7 I f (n)1000 6180 w 10 R f (\(of length)1 391 1 1068 6220 t 10 I f (n)1484 6220 w 10 R f (\) to)1 136 1 1534 6220 t (\(1a\) minimize)1 2233 1 720 6400 t 10 I f (c)3027 6400 w 7 R f (T)3082 6360 w 10 I f (x)3141 6400 w 10 R f (subject to)1 386 1 720 6580 t (\(1b\))720 6760 w 10 I f (Ax)2726 6760 w 10 S f (=)2880 6760 w 10 I f (b)2984 6760 w 10 R f (and)720 6940 w (\(1c\))720 7120 w 10 I f (x)2748 7120 w 10 S f (\263)2833 7120 w 10 B f (0)2929 7120 w 10 R f (,)2987 7120 w (where)720 7300 w 10 I f (A)1017 7300 w 10 S f (\316)1119 7300 w 10 I f (I R)1 78 1 1231 7300 t 7 I f (m)1314 7260 w 7 S f (\264)1369 7260 w 7 I f (n)1413 7260 w 10 R f ( given \(real)2 514(is a)1 165 2 1510 7300 t 10 I f (m)2244 7300 w 10 S f (\264)2348 7300 w 10 I f (n)2435 7300 w 10 R f (\) matrix,)1 374 1 2485 7300 t 10 I f (b)2914 7300 w 10 S f (\316)3005 7300 w 10 I f (I R)1 78 1 3117 7300 t 7 I f (m)3200 7260 w 10 R f (, and superscript T means ``transposed''.)5 1782 1 3258 7300 t (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 1 2 %%Page: 2 3 /saveobj save def mark 3 pagesetup 10 R f (- 2 -)2 166 1 2797 480 t ( with \(1\) is the)4 615( Associated)1 496( omitted when vectors are spelled componentwise.\))6 2097(\(Superscript T will be)3 901 4 720 840 t 10 I f (dual)4862 840 w (problem)720 960 w 10 R f (\(2a\) maximize)1 2238 1 720 1140 t 10 I f (b)3032 1140 w 7 R f (T)3093 1100 w 10 I f (y)3152 1140 w 10 R f (subject to)1 386 1 720 1320 t (\(2b\))720 1500 w 10 I f (A)2702 1500 w 7 R f (T)2774 1460 w 10 I f (y)2833 1500 w 10 S f (\243)2918 1500 w 10 I f (c)3014 1500 w 10 R f (\(with no sign constraints on)4 1111 1 720 1680 t 10 I f (y)1856 1680 w 10 R f ( simplicity, we assume)3 911(\). For)1 247 2 1900 1680 t 10 I f (A)3083 1680 w 10 R f (has full rank \()3 557 1 3169 1680 t 10 I f (m)3726 1680 w 10 R f (\).)3798 1680 w (The hard part about \(1\) is determining which components of)9 2446 1 970 1836 t 10 I f (x)3445 1836 w 10 R f ( in solutions to)3 608(can be strictly positive)3 914 2 3518 1836 t ( be satisfied as equalities in solu-)6 1321( is equivalent to determining which components of \(2b\) can only)10 2596(\(1\). \(This)1 403 3 720 1956 t ( of)1 111( set algorithms, such as the simplex method, repeatedly update an estimate of a set)14 3318( Active)1 318(tions to \(2\).\))2 501 4 720 2076 t 10 I f (x)4996 2076 w 10 R f (components that may be positive; in effect, they only allow a few \(at most)13 3028 1 720 2196 t 10 I f (m)3778 2196 w 10 R f ( of)1 112(\) components)1 546 2 3850 2196 t 10 I f (x)4537 2196 w 10 R f (to be posi-)2 430 1 4610 2196 t ( has all com-)3 516( algorithm, on the other hand, works with a solution estimate that)11 2607( Karmarkar's)1 553(tive at one time.)3 644 4 720 2316 t ( the changed)2 522( repeatedly changes variables, computes the steepest descent direction in)9 2989( It)1 121(ponents positive.)1 688 4 720 2436 t ( and translates the resulting point back to the original vari-)10 2366(variables, moves some distance in that direction,)6 1954 2 720 2556 t (ables.)720 2676 w ( can)1 175( One)1 228( make its changes of variables.)5 1285(Karmarkar's paper [15] uses projective transformations to)6 2382 4 970 2832 t ( Karmarkar's algorithm \(references)3 1432(also use a linear change of variables; the resulting ``affine variant'' of)11 2888 2 720 2952 t ( the affine)2 426( Although)1 438(for which are given below\) is a bit easier to describe than the ``projective variant''.)14 3456 3 720 3072 t (variant is appealing for its simplicity, stronger convergence results are known for the projective variant.)14 4142 1 720 3192 t 10 B f (Affine Variant)1 624 1 720 3432 t 10 R f (In the affine variant of Karmarkar's LP algorithm, we proceed from iterate)11 2980 1 970 3588 t 10 I f (x)3975 3588 w 7 I f (k)4030 3548 w 10 R f (to)4094 3588 w 10 I f (x)4197 3588 w 7 I f (k)4252 3548 w 7 S f (+)4299 3548 w 7 R f (1)4349 3548 w 10 R f ( We)1 189(as follows.)1 434 2 4417 3588 t (start with the change of variables)5 1322 1 720 3713 t 10 I f (x)2067 3713 w 11 R f (\303)2073 3708 w 10 S f (=)2160 3713 w 10 I f (D)2264 3713 w 7 S f (-)2347 3673 w 7 R f (1)2397 3673 w 10 I f (x)2448 3713 w 10 R f (, where)1 293 1 2492 3713 t (\(3\))720 3893 w 10 I f (D)2452 3893 w 10 S f (=)2573 3893 w 10 I f (D)2677 3893 w 7 I f (k)2760 3853 w 10 S f (=)2848 3893 w 10 R f (diag \()1 213 1 2952 3893 t 10 I f (x)3173 3893 w 7 I f (k)3228 3853 w 10 R f (\))3275 3893 w (is the diagonal matrix whose \()5 1237 1 720 4073 t 10 I f (i)1965 4073 w 10 R f (,)2001 4073 w 10 I f (i)2034 4073 w 10 R f (\) entry is)2 367 1 2070 4073 t 10 I f (x)2468 4073 w 7 I f (i)2517 4092 w (k)2517 4033 w 10 R f (, the)1 178 1 2556 4073 t 10 I f (i)2766 4073 w 10 R f (th component of the current iterate)5 1418 1 2794 4073 t 10 I f (x)4244 4073 w 7 I f (k)4299 4033 w 10 R f ( constraints)1 465(. The)1 237 2 4338 4073 t (\(1b,c\) become)1 585 1 720 4198 t 10 I f (A)1344 4198 w 11 R f (\303)1362 4168 w 10 I f (x)1405 4198 w 11 R f (\303)1411 4193 w 10 S f (=)1498 4198 w 10 I f (b)1602 4198 w 10 R f (and)1691 4198 w 10 I f (x)1874 4198 w 11 R f (\303)1880 4193 w 10 S f (\263)1959 4198 w 10 B f (0)2055 4198 w 10 R f (, where)1 307 1 2105 4198 t 10 I f (A)2451 4198 w 11 R f (\303)2469 4168 w 10 S f (=)2561 4198 w 10 I f (AD)2665 4198 w 10 R f (, and the objective \(1a\) becomes)5 1361 1 2798 4198 t 10 I f (c)4198 4198 w 11 R f (\303)4204 4193 w 7 R f (T)4253 4129 w 10 I f (x)4312 4198 w 11 R f (\303)4318 4193 w 10 R f (, where)1 307 1 4356 4198 t 10 I f (c)4702 4198 w 11 R f (\303)4708 4193 w 10 S f (=)4795 4198 w 10 I f (Dc)4899 4198 w 10 R f (.)5015 4198 w (Note that the current iterate)4 1105 1 720 4323 t 10 I f (x)1852 4323 w 7 I f (k)1907 4283 w 10 R f (transforms into a vector of ones \(denoted)6 1653 1 1973 4323 t 10 I f (e)3653 4323 w 10 R f (\):)3697 4323 w 10 I f (x)3811 4323 w 11 R f (\303)3817 4318 w 7 I f (k)3866 4254 w 10 R f (:)3946 4323 w 10 S f (=)3990 4323 w 10 I f (D)4094 4323 w 7 S f (-)4177 4283 w 7 R f (1)4227 4283 w 10 I f (x)4278 4323 w 7 I f (k)4333 4283 w 10 S f (=)4421 4323 w 10 I f (e)4525 4323 w 10 R f ( \(con-)1 238(. The)1 233 2 4569 4323 t (strained\) steepest descent direction is then)5 1683 1 720 4443 t (\(4\))720 4628 w 10 I f (p)2635 4628 w 11 R f (\303)2644 4623 w 10 S f (= -)1 167 1 2734 4628 t 10 I f (P)2917 4628 w 7 I f (A)2989 4648 w 8 R f (\303)3003 4620 w 10 I f (c)3048 4628 w 11 R f (\303)3054 4623 w 10 R f (,)3100 4628 w (where)720 4808 w 10 I f (P)988 4808 w 7 I f (B)1060 4828 w 10 R f ( matrix)1 287(denotes projection onto the orthogonal complement of the row space of a)11 2920 2 1136 4808 t 10 I f (B)4369 4808 w 10 R f ( step in this)3 462(. A)1 148 2 4430 4808 t (direction to)1 462 1 720 4933 t 10 I f (x)1211 4933 w 11 R f (\303)1217 4928 w 7 I f (k)1266 4864 w 7 S f (+)1313 4864 w 7 R f (1)1363 4864 w 10 S f (=)1455 4933 w 10 I f (x)1559 4933 w 11 R f (\303)1565 4928 w 7 I f (k)1614 4864 w 10 S f (+ a)1 167 1 1702 4933 t 11 R f (\303)1820 4928 w 10 I f (p)1877 4933 w 11 R f (\303)1886 4928 w 10 R f (translates into the step)3 903 1 1956 4933 t 10 I f (x)2888 4933 w 7 I f (k)2943 4893 w 7 S f (+)2990 4893 w 7 R f (1)3040 4893 w 10 S f (=)3132 4933 w 10 I f (x)3236 4933 w 7 I f (k)3291 4893 w 10 S f (+ a)1 167 1 3379 4933 t 10 I f (p)3554 4933 w 10 S f (=)3653 4933 w 10 I f (x)3757 4933 w 7 I f (k)3812 4893 w 10 S f (- a)1 167 1 3900 4933 t 10 I f (DP)4075 4933 w 7 I f (AD)4219 4953 w 10 I f (Dc)4328 4933 w 10 R f (in the original)2 567 1 4473 4933 t (variables, where)1 654 1 720 5058 t 10 S f (a = a)2 279 1 1400 5058 t 11 R f (\303)1630 5053 w 10 S f (>)1728 5058 w 10 R f (0 is small enough that)4 882 1 1832 5058 t 10 I f (x)2740 5058 w 7 I f (k)2795 5018 w 7 S f (+)2842 5018 w 7 R f (1)2892 5018 w 10 S f (>)2984 5058 w 10 R f (0 \(i.e., that all components of)5 1176 1 3088 5058 t 10 I f (x)4290 5058 w 10 R f (remain positive\).)1 679 1 4361 5058 t (People often choose)2 804 1 720 5178 t 10 S f (a)1549 5178 w 10 R f ( 0. 9)2 141(in the range [)3 529 2 1637 5178 t 10 S f (a)2315 5178 w 7 I f (max)2383 5138 w 7 R f (,)2504 5138 w 10 R f (0. 99)1 183 1 2571 5178 t 10 S f (a)2762 5178 w 7 R f (max)2830 5138 w 10 R f (], where)1 326 1 2967 5178 t 10 S f (a)3318 5178 w 7 R f (max)3386 5138 w 10 S f (=)3564 5178 w 10 R f (max)3668 5178 w 10 I f ({)3848 5178 w 10 S f (t >)1 148 1 3896 5178 t 10 R f (0 :)1 86 1 4093 5178 t 10 I f (x)4220 5178 w 7 I f (k)4275 5138 w 10 S f (+ t)1 148 1 4363 5178 t 10 I f (p)4519 5178 w 10 S f (\263)4610 5178 w 10 B f (0)4706 5178 w 10 I f (})4764 5178 w 10 R f (.)4804 5178 w ( other people or)3 653( Several)1 357( in late 1984.)3 546(I first learned about the primal affine variant from Karmarkar)9 2514 4 970 5334 t ( 5, 7, 25].)3 356(groups appear to have proposed this variant independently, including [3,)9 2893 2 720 5454 t 10 B f (Projective Variant)1 789 1 720 5694 t 10 R f (In [15], Karmarkar assumed the optimal value of)7 2021 1 970 5850 t 10 I f (c)3027 5850 w 7 R f (T)3082 5810 w 10 I f (x *)1 102 1 3141 5850 t 10 R f (to be zero, that)3 626 1 3279 5850 t 10 I f (b)3941 5850 w 7 I f (i)4002 5870 w 10 S f (=)4079 5850 w 10 R f (0 for)1 202 1 4183 5850 t 10 I f (i)4421 5850 w 10 S f (<)4498 5850 w 10 I f (m)4602 5850 w 10 R f (and that)1 330 1 4710 5850 t 10 I f (A)720 5970 w 7 I f (m)792 5990 w 7 R f (,)847 5990 w 7 I f (j)876 5990 w 10 S f (=)953 5970 w 10 R f (1 for all)2 342 1 1057 5970 t 10 I f (j)1437 5970 w 10 R f ( are various)2 489( There)1 294( always transform a problem to this form.)7 1743(; he showed that one can)5 1049 4 1465 5970 t ( and)1 177( 8, 13, 14, 16, 19, 21, 22, 24],)8 1111( this transformation or relax these assumptions; see, e.g., [2,)9 2469(ways to make)2 563 4 720 6090 t ( making pictures it seems most convenient to do things as in [10].)12 2624( For)1 189(the Concluding Remarks below.)3 1288 3 720 6210 t (This version of the algorithm computes a sequence of pairs \()10 2418 1 970 6366 t 10 I f (x)3396 6366 w 7 I f (k)3451 6326 w 10 R f (,)3498 6366 w 10 S f (b)3555 6366 w 7 I f (k)3615 6326 w 10 R f (\) that maintain)2 583 1 3662 6366 t (\(5a\))720 6546 w 10 I f (Ax)2684 6546 w 7 I f (k)2800 6506 w 10 S f (=)2888 6546 w 10 I f (b)2992 6546 w 10 R f (,)3050 6546 w (\(5b\))720 6726 w 10 I f (x)2715 6726 w 7 I f (k)2770 6686 w 10 S f (>)2858 6726 w 10 B f (0)2962 6726 w 10 R f (,)3020 6726 w (and)720 6906 w (\(5c\))720 7086 w 10 S f (b)2598 7086 w 7 I f (k)2658 7046 w 10 S f (\263 -)1 159 1 2738 7086 t 10 I f (c)2913 7086 w 7 R f (T)2968 7046 w 10 I f (x *)1 102 1 3027 7086 t 10 R f (,)3137 7086 w (where)720 7266 w 10 I f (c)988 7266 w 7 R f (T)1043 7226 w 10 I f (x *)1 102 1 1102 7266 t 10 R f (is the optimal objective function value \(1a\), and that always reduce the ``potential function'')13 3693 1 1229 7266 t (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 2 3 %%Page: 3 4 /saveobj save def mark 4 pagesetup 10 R f (- 3 -)2 166 1 2797 480 t (\(6\))720 890 w 10 S f (f)1874 890 w 10 R f (\()1934 890 w 10 I f (x)1975 890 w 10 R f (,)2027 890 w 10 S f (b)2060 890 w 10 R f (\) :)1 110 1 2123 890 t 10 S f (=)2249 890 w 10 R f (\()2353 890 w 10 I f (n)2394 890 w 10 S f (+)2484 890 w 10 R f ( \()1 41( log)1 144(1 \))1 91 3 2579 890 t 10 I f (c)2863 890 w 7 R f (T)2918 850 w 10 I f (x)2977 890 w 10 S f (+ b)1 159 1 3070 890 t 10 R f (\))3237 890 w 10 S f (-)3327 890 w 7 I f (i)3431 990 w 7 S f (=)3467 990 w 7 R f (1)3517 990 w 15 S f (S)3447 920 w 7 I f (n)3474 790 w 10 R f (log \()1 169 1 3584 890 t 10 I f (x)3761 890 w 7 I f (i)3816 910 w 10 R f (\))3852 890 w (by at least a constant amount:)5 1200 1 720 1190 t 10 S f (f)1973 1190 w 10 R f (\()2033 1190 w 10 I f (x)2074 1190 w 7 I f (k)2129 1150 w 7 S f (+)2176 1150 w 7 R f (1)2226 1150 w 10 R f (,)2277 1190 w 10 S f (b)2310 1190 w 7 I f (k)2370 1150 w 7 S f (+)2417 1150 w 7 R f (1)2467 1150 w 10 R f (\))2518 1190 w 10 S f (\243 f)1 148 1 2600 1190 t 10 R f (\()2756 1190 w 10 I f (x)2797 1190 w 7 I f (k)2852 1150 w 10 R f (,)2899 1190 w 10 S f (b)2932 1190 w 7 I f (k)2992 1150 w 10 R f (\))3039 1190 w 10 S f (-)3129 1190 w 10 R f (5)3258 1260 w (1)3258 1130 w 10 S1 f (_ _)1 80 1 3243 1160 t 10 R f ( forces)1 272(. This)1 256 2 3333 1190 t 7 I f (k)3890 1260 w 7 S f (\256 \245)1 125 1 3926 1260 t 10 R f (lim)3903 1190 w 10 S f (f)4082 1190 w 10 R f (\()4142 1190 w 10 I f (x)4183 1190 w 7 I f (k)4238 1150 w 10 R f (,)4285 1190 w 10 S f (b)4318 1190 w 7 I f (k)4378 1150 w 10 R f (\))4425 1190 w 10 S f ( \245)1 89(= -)1 167 2 4515 1190 t 10 R f (; if the)2 269 1 4771 1190 t ( bounded, this forces)3 847(feasible region is)2 694 2 720 1360 t 10 S f (-)2291 1360 w 7 I f (k)2362 1430 w 7 S f (\256 \245)1 125 1 2398 1430 t 10 R f (lim)2375 1360 w 10 S f (b)2554 1360 w 7 I f (k)2614 1320 w 10 S f (=)2702 1360 w 7 I f (k)2806 1430 w 7 S f (\256 \245)1 125 1 2842 1430 t 10 R f (lim)2819 1360 w 10 I f (c)2998 1360 w 7 R f (T)3053 1320 w 10 I f (x)3112 1360 w 7 I f (k)3167 1320 w 10 S f (=)3255 1360 w 10 I f (c)3359 1360 w 7 R f (T)3414 1320 w 10 I f (x *)1 102 1 3473 1360 t 10 R f ( we discuss obtaining)3 873(. Later)1 290 2 3575 1360 t 10 I f (x)4768 1360 w 7 R f (0)4823 1320 w 10 R f (and)4896 1360 w 10 S f (b)720 1530 w 7 R f (0)780 1490 w 10 R f (; for now assume them known.)5 1232 1 823 1530 t ( \()1 59(Given iterate)1 518 2 970 1686 t 10 I f (x)1555 1686 w 7 I f (k)1610 1646 w 10 R f (,)1657 1686 w 10 S f (b)1690 1686 w 7 I f (k)1750 1646 w 10 R f (\), we define)2 475 1 1797 1686 t 10 I f (D)2298 1686 w 10 R f ( time we use the projective change of vari-)8 1709( This)1 229(, as before, by \(3\).)4 732 3 2370 1686 t (ables)720 1806 w 10 I f (x)2029 2071 w 11 R f (\303)2035 2066 w 10 S f (= y)1 173 1 2122 2071 t 10 R f (\()2303 2071 w 10 I f (x)2344 2071 w 10 R f (\) :)1 110 1 2396 2071 t 10 S f (=)2522 2071 w 10 R f (\()2626 2071 w 10 I f (e)2667 2071 w 7 R f (T)2722 2031 w 10 I f (D)2781 2071 w 7 S f (-)2864 2031 w 7 R f (1)2914 2031 w 10 I f (x)2965 2071 w 10 S f (+)3058 2071 w 10 R f (1 \))1 91 1 3162 2071 t 7 S f (-)3264 2031 w 7 R f (1)3314 2031 w 10 S f (\351)3373 1984 w (\357)3373 2084 w (\353)3373 2184 w 10 R f (1)3512 2136 w 10 I f (D)3423 2036 w 7 S f (-)3506 1996 w 7 R f (1)3556 1996 w 10 I f (x)3607 2036 w 10 S f (\371)3651 1984 w (\357)3651 2084 w (\373)3651 2184 w 10 R f (,)3705 2071 w (whose inverse is)2 660 1 720 2356 t 10 I f (x)2307 2541 w 10 S f (= y)1 173 1 2400 2541 t 7 S f (-)2584 2501 w 7 R f (1)2634 2501 w 10 R f (\()2685 2541 w 10 I f (x)2726 2541 w 11 R f (\303)2732 2536 w 10 R f (\))2778 2541 w 10 S f (=)2868 2541 w 10 I f (x)2972 2541 w 11 R f (\303)2978 2536 w 7 I f (n)3021 2560 w 7 S f (+)3072 2560 w 7 R f (1)3122 2560 w 7 S f (-)3021 2473 w 7 R f (1)3071 2473 w 10 I f (Dx)3173 2541 w 11 R f (\303)3251 2536 w 7 R f (1..)3300 2561 w 7 I f (n)3376 2561 w 10 R f (,)3427 2541 w (where)720 2726 w 10 I f (x)988 2726 w 11 R f (\303)994 2721 w 7 R f (1..)1043 2746 w 7 I f (n)1119 2746 w 10 R f (stands for the first)3 724 1 1187 2726 t 10 I f (n)1936 2726 w 10 R f (components of)1 591 1 2011 2726 t 10 I f (x)2627 2726 w 11 R f (\303)2633 2721 w 10 R f ( constraints \(1b,c\) become)3 1053(. The)1 230 2 2671 2726 t (\(7a\))720 2991 w 10 S f (\351)2499 2904 w (\357)2499 3004 w (\353)2499 3104 w 10 I f (e)2562 3051 w 7 R f (T)2617 3011 w 10 I f (AD)2549 2941 w 10 R f (1)2791 3041 w 10 S f (-)2756 2941 w 10 I f (b)2827 2941 w 10 S f (\371)2877 2904 w (\357)2877 3004 w (\373)2877 3104 w 10 I f (x)2915 2991 w 11 R f (\303)2921 2986 w 10 S f (=)3008 2991 w (\354)3120 2954 w (\356)3120 3054 w 10 R f (1)3169 3051 w 10 B f (0)3169 2951 w 10 S f (\374)3219 2954 w (\376)3219 3054 w 10 R f (\(7b\))720 3281 w 10 I f (x)2748 3281 w 11 R f (\303)2754 3276 w 10 S f (\263)2833 3281 w 10 B f (0)2929 3281 w 10 R f (,)2987 3281 w (and)720 3461 w 10 S f (f)889 3461 w 10 R f (becomes)966 3461 w 10 S f (f)1669 3776 w 11 R f (\303)1677 3746 w 10 R f (\()1729 3776 w 10 I f (x)1770 3776 w 11 R f (\303)1776 3771 w 10 R f (,)1822 3776 w 10 S f (b)1855 3776 w 10 R f (\))1918 3776 w 10 S f (=)2008 3776 w 7 I f (i)2119 3876 w 7 S f (=)2155 3876 w 7 R f (1)2205 3876 w 15 S f (S)2135 3806 w 7 I f (n)2111 3676 w 7 S f (+)2162 3676 w 7 R f (1)2212 3676 w 10 R f (log)2279 3776 w 10 S f (\354)2423 3639 w (\357)2423 3739 w (\357)2423 3839 w (\356)2423 3939 w 10 I f (x)2843 3871 w 11 R f (\303)2849 3866 w 7 I f (i)2898 3891 w 10 I f (c)2497 3696 w 7 R f (T)2552 3656 w 10 I f (Dx)2611 3696 w 11 R f (\303)2689 3691 w 7 R f (1..)2738 3716 w 7 I f (n)2814 3716 w 10 S f (+ b)1 159 1 2906 3696 t 10 I f (x)3073 3696 w 11 R f (\303)3079 3691 w 7 I f (n)3128 3716 w 7 S f (+)3179 3716 w 7 R f (1)3229 3716 w 10 S1 f (_ ________________)1 805 1 2482 3746 t 10 S f (\374)3297 3639 w (\357)3297 3739 w (\357)3297 3839 w (\376)3297 3939 w (-)3419 3776 w 10 R f (log \( det \()3 340 1 3547 3776 t 10 I f (D)3895 3776 w 10 R f (\) \))1 74 1 3975 3776 t 10 I f (.)4065 3776 w 10 R f (Let)720 4116 w 10 I f (A)878 4116 w 10 S1 f (_ _)1 51 1 888 4023 t 10 R f (:)980 4116 w 10 S f (=)1024 4116 w 10 R f (\()1128 4116 w 10 I f (AD)1169 4116 w 10 R f (,)1310 4116 w 10 S f (-)1375 4116 w 10 I f (b)1446 4116 w 10 R f (\),)1504 4116 w (\(8a\))720 4331 w 10 I f (u)2559 4331 w 10 R f (:)2650 4331 w 10 S f (=)2694 4331 w 10 I f (P)2798 4331 w 7 I f (A)2870 4351 w 7 S1 f (_ _)1 36 1 2879 4279 t 10 S f (\354)2945 4294 w (\356)2945 4394 w 10 R f (0)3027 4391 w 10 I f (Dc)2994 4291 w 10 S f (\374)3110 4294 w (\376)3110 4394 w 10 R f (,)3175 4331 w (\(8b\))720 4601 w 10 I f (v)2595 4601 w 10 R f (:)2680 4601 w 10 S f (=)2724 4601 w 10 I f (P)2828 4601 w 7 I f (A)2900 4621 w 7 S1 f (_ _)1 36 1 2909 4549 t 10 S f (\354)2975 4564 w (\356)2975 4664 w 10 R f (1)3024 4661 w 10 B f (0)3024 4561 w 10 S f (\374)3074 4564 w (\376)3074 4664 w 10 R f (,)3139 4601 w (and)720 4836 w (\(9\))720 5016 w 10 S f (m)1986 5016 w 10 R f (\()2052 5016 w 10 S f (b)2093 5016 w 10 R f (\) :)1 110 1 2156 5016 t 10 S f (=)2282 5016 w 10 R f (min)2386 5016 w 10 I f ({)2550 5016 w 10 R f (\()2598 5016 w 10 I f (u)2639 5016 w 10 S f (+ b)1 159 1 2738 5016 t 10 I f (v)2905 5016 w 10 R f (\))2957 5016 w 7 I f (i)3001 5036 w 10 R f (: 1)1 119 1 3037 5016 t 10 S f (\243)3197 5016 w 10 I f (i)3293 5016 w 10 S f (\243)3362 5016 w 10 I f (n)3458 5016 w 10 S f (+)3548 5016 w 10 R f (1)3643 5016 w 10 I f (} .)1 73 1 3701 5016 t 10 R f (The convergence theory requires)3 1327 1 720 5196 t 10 S f (b)2078 5196 w 7 I f (k)2138 5156 w 7 S f (+)2185 5156 w 7 R f (1)2235 5156 w 10 R f (to satisfy both \(5c\) and)4 945 1 2309 5196 t 10 S f (m)3286 5196 w 10 R f (\()3352 5196 w 10 S f (b)3393 5196 w 7 I f (k)3453 5156 w 7 S f (+)3500 5156 w 7 R f (1)3550 5156 w 10 R f (\))3601 5196 w 10 S f (\243)3683 5196 w 10 R f (0. Either)1 376 1 3779 5196 t 10 S f (m)4187 5196 w 10 R f (\()4253 5196 w 10 S f (b)4294 5196 w 7 I f (k)4354 5156 w 10 R f (\))4401 5196 w 10 S f (\243)4483 5196 w 10 R f (0, in which)2 461 1 4579 5196 t (case)720 5316 w 10 S f (b)919 5316 w 7 I f (k)979 5276 w 7 S f (+)1026 5276 w 7 R f (1)1076 5276 w 10 R f (:)1160 5316 w 10 S f (= b)1 159 1 1204 5316 t 7 I f (k)1368 5276 w 10 R f (suffices, or else we can choose)5 1244 1 1435 5316 t 10 S f (b)2707 5316 w 7 I f (k)2767 5276 w 7 S f (+)2814 5276 w 7 R f (1)2864 5276 w 10 S f (< b)1 159 1 2956 5316 t 7 I f (k)3120 5276 w 10 R f (with)3187 5316 w 10 S f (m)3393 5316 w 10 R f (\()3459 5316 w 10 S f (b)3500 5316 w 7 I f (k)3560 5276 w 7 S f (+)3607 5276 w 7 R f (1)3657 5276 w 10 R f (\))3708 5316 w 10 S f (=)3798 5316 w 10 R f ( case duality the-)3 685(0, in which)2 453 2 3902 5316 t (ory implies)1 453 1 720 5441 t 10 S f (b)1198 5441 w 7 I f (k)1258 5401 w 7 S f (+)1305 5401 w 7 R f (1)1355 5401 w 10 S f (\263 -)1 159 1 1439 5441 t 10 I f (c)1614 5441 w 7 R f (T)1669 5401 w 10 I f (x *)1 102 1 1728 5441 t 10 R f ( steepest-descent direction for)3 1194( The)1 205( [10] for details.)3 643(: see)1 205 4 1830 5441 t 10 S f (f)4102 5441 w 11 R f (\303)4110 5411 w 10 R f (in the)1 225 1 4179 5441 t 10 I f (x)4429 5441 w 11 R f (\303)4435 5436 w 10 R f (variables is)1 452 1 4498 5441 t 10 I f (p)1834 5706 w 11 R f (\303)1843 5701 w 10 S f (= -)1 167 1 1933 5706 t 10 I f (P)2116 5706 w 7 I f (B)2188 5726 w 10 S f (\354)2255 5619 w (\357)2255 5719 w (\356)2255 5819 w (b)2304 5766 w 7 I f (k)2364 5726 w 7 S f (+)2411 5726 w 7 R f (1)2461 5726 w 10 I f (Dc)2346 5656 w 10 S f (\374)2504 5619 w (\357)2504 5719 w (\376)2504 5819 w (= -)1 167 1 2602 5706 t 10 R f (\()2785 5706 w 10 I f (I)2826 5706 w 10 S f (-)2908 5706 w 10 I f (n)3037 5776 w 10 S f (+)3127 5776 w 10 R f (1)3222 5776 w 10 I f (ee)3080 5646 w 7 R f (T)3179 5606 w 10 S1 f (_ _____)1 265 1 3023 5676 t 10 R f (\) \()1 74 1 3306 5706 t 10 I f (u)3388 5706 w 10 S f (+ b)1 159 1 3487 5706 t 7 I f (k)3651 5666 w 7 S f (+)3698 5666 w 7 R f (1)3748 5666 w 10 I f (v)3799 5706 w 10 R f (\) ,)1 74 1 3851 5706 t (where)720 6076 w 10 I f (B)988 6076 w 10 S f (=)1098 6076 w (\351)1210 5989 w (\357)1210 6089 w (\353)1210 6189 w 10 I f (e)1273 6136 w 7 R f (T)1328 6096 w 10 I f (AD)1260 6026 w 10 R f (1)1502 6126 w 10 S f (-)1467 6026 w 10 I f (b)1538 6026 w 10 S f (\371)1588 5989 w (\357)1588 6089 w (\373)1588 6189 w 10 R f ( step)1 186(. The)1 230 2 1626 6076 t 10 I f (x)2067 6076 w 11 R f (\303)2073 6071 w 7 I f (k)2122 6007 w 7 S f (+)2169 6007 w 7 R f (1)2219 6007 w 10 S f (=)2311 6076 w 10 I f (x)2415 6076 w 11 R f (\303)2421 6071 w 7 I f (k)2470 6007 w 10 S f (+ a)1 167 1 2558 6076 t 11 R f (\303)2676 6071 w 10 I f (p)2733 6076 w 11 R f (\303)2742 6071 w 10 R f (translates back to)2 693 1 2808 6076 t 10 I f (x)3526 6076 w 7 I f (k)3581 6036 w 7 S f (+)3628 6036 w 7 R f (1)3678 6036 w 10 S f (=)3770 6076 w 10 I f (x)3874 6076 w 7 I f (k)3929 6036 w 10 S f (+ a)1 134 1 3992 6076 t 7 I f (k)4131 6036 w 10 I f (p)4170 6076 w 7 I f (k)4231 6036 w 10 R f (, where)1 293 1 4270 6076 t (\(10\))720 6366 w 10 I f (p)2397 6366 w 7 I f (k)2458 6326 w 10 S f (=)2546 6366 w 10 I f (Dp)2650 6366 w 11 R f (\303)2731 6361 w 7 R f (1..)2783 6386 w 7 I f (n)2859 6386 w 10 S f (-)2951 6366 w 10 I f (p)3055 6366 w 11 R f (\303)3064 6361 w 7 I f (n)3116 6386 w 7 S f (+)3167 6386 w 7 R f (1)3217 6386 w 10 I f (x)3268 6366 w 7 I f (k)3323 6326 w 10 R f (and)720 6611 w 10 S f (a)892 6611 w 7 I f (k)960 6571 w 10 S f (=)1048 6611 w 10 R f (\()1177 6706 w 10 I f (n)1218 6706 w 10 S f (+)1292 6706 w 10 R f (1 \))1 91 1 1363 6706 t 7 S f (-)1465 6666 w 7 R f (1)1515 6666 w 10 S f (+ a)1 167 1 1607 6706 t 11 R f (\303)1725 6701 w 10 I f (p)1782 6706 w 11 R f (\303)1791 6701 w 7 I f (n)1843 6726 w 7 S f (+)1894 6726 w 7 R f (1)1944 6726 w 10 S f (a)1551 6551 w 11 R f (\303)1565 6546 w 10 S1 f (_ ________________)1 840 1 1163 6581 t 10 R f ( a fixed choice of)4 704(. Although)1 456 2 2013 6611 t 10 S f (a)3201 6611 w 11 R f (\303)3215 6606 w 10 R f (, e.g.)1 197 1 3264 6611 t 10 S f (a)3489 6611 w 11 R f (\303)3503 6606 w 10 S f (=)3601 6611 w 10 R f (1)3705 6611 w 10 I f (/)3763 6611 w 10 R f ( for the convergence)3 828(3, suffices)1 413 2 3799 6611 t (theory, in practice one gets much faster convergence by choosing)9 2799 1 720 6826 t 10 S f (a = a)2 279 1 3565 6826 t 7 I f (k)3849 6786 w 10 R f (to minimize)1 501 1 3934 6826 t 10 S f (f)4480 6826 w 10 R f (\()4540 6826 w 10 I f (x)4581 6826 w 7 I f (k)4636 6786 w 10 S f (+ a)1 167 1 4724 6826 t 10 I f (p)4899 6826 w 7 I f (k)4960 6786 w 10 R f (\))5007 6826 w (approximately.)720 6946 w (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 3 4 %%Page: 4 5 /saveobj save def mark 5 pagesetup 10 R f (- 4 -)2 166 1 2797 480 t 10 B f (Dual Affine Algorithm)2 966 1 720 840 t 10 R f ( More-)1 308(The algebra works out nicely when we apply the above algorithms to the dual problem \(2\).)15 3762 2 970 996 t ( there are considerable errors in the projections. This variant)9 2450(over, the dual affine variant works even when)7 1870 2 720 1116 t (appears to have been proposed independently in [1] and [20].)9 2444 1 720 1236 t ( is useful to convert \(2\) to standard form by introducing slack vari-)12 2752(To derive the dual algorithms, it)5 1318 2 970 1392 t ( define)1 275(ables: we)1 400 2 720 1512 t 10 I f (s)1420 1512 w 10 S f (\316)1500 1512 w 10 I f (I R)1 78 1 1612 1512 t 7 I f (n)1695 1472 w 10 R f (by)1763 1512 w 10 I f (s)1888 1512 w 10 S f (=)1976 1512 w 10 I f (c)2080 1512 w 10 S f (-)2173 1512 w 10 I f (A)2277 1512 w 7 R f (T)2349 1472 w 10 I f (y)2408 1512 w 10 R f ( we shall compute with)4 927(. Although)1 453 2 2452 1512 t 10 I f (y)3857 1512 w 10 R f (, it is useful to eliminate)5 967 1 3901 1512 t 10 I f (y)4893 1512 w 10 R f (in)4962 1512 w ( do this, let)3 499( To)1 178(deriving the dual algorithm.)3 1167 3 720 1632 t 10 I f (A)2607 1632 w 7 S f (+)2679 1592 w 10 R f (be any generalized inverse of)4 1240 1 2769 1632 t 10 I f (A)4052 1632 w 10 R f (, i.e., any matrix with)4 927 1 4113 1632 t 10 I f (A)720 1752 w 10 S f (=)830 1752 w 10 I f (AA)934 1752 w 7 S f (+)1067 1712 w 10 I f (A)1130 1752 w 10 R f ( choice of)2 409(. \(The)1 271 2 1191 1752 t 10 I f (A)1904 1752 w 7 S f (+)1976 1712 w 10 R f (is irrelevant, since)2 745 1 2056 1752 t 10 I f (A)2834 1752 w 7 S f (+)2906 1712 w 10 R f ( we're)1 259( Since)1 280(will not appear in the final formulae.)6 1515 3 2986 1752 t (assuming)720 1872 w 10 I f (A)1125 1872 w 10 R f (to have full rank, in fact)5 974 1 1213 1872 t 10 I f (AA)2215 1872 w 7 S f (+)2348 1832 w 10 S f (=)2452 1872 w 10 I f (I)2556 1872 w 10 R f (.\) Then)1 316 1 2589 1872 t 10 I f (y)2933 1872 w 10 S f (=)3026 1872 w 10 I f (A)3130 1872 w 7 S f (+)3202 1832 w 7 R f (T)3252 1832 w 10 R f (\()3311 1872 w 10 I f (c)3352 1872 w 10 S f (-)3436 1872 w 10 I f (s)3531 1872 w 10 R f (\), so maximizing)2 681 1 3578 1872 t 10 I f (b)4287 1872 w 7 R f (T)4348 1832 w 10 I f (y)4407 1872 w 10 R f (is the same as)3 561 1 4479 1872 t (minimizing)720 1992 w 10 I f (b)1207 1992 w 7 R f (T)1268 1952 w 10 I f (A)1327 1992 w 7 S f (+)1399 1952 w 7 R f (T)1449 1952 w 10 R f (\()1508 1992 w 10 I f (s)1549 1992 w 10 S f (-)1628 1992 w 10 I f (c)1723 1992 w 10 R f ( \(2\) is equivalent to)4 777(\). Thus)1 308 2 1775 1992 t ( \()1 107(\(11a\) minimize)1 1898 2 720 2172 t 10 I f (A)2733 2172 w 7 S f (+)2805 2132 w 10 I f (b)2868 2172 w 10 R f (\))2926 2172 w 7 R f (T)2970 2132 w 10 I f (s)3029 2172 w 10 S f (-)3117 2172 w 10 I f (c)3221 2172 w 7 R f (T)3276 2132 w 10 I f (A)3335 2172 w 7 S f (+)3407 2132 w 10 I f (b)3470 2172 w 10 R f (subject to)1 386 1 720 2352 t (\(11b\) \()1 1487 1 720 2532 t 10 I f (I)2215 2532 w 10 S f (-)2297 2532 w 10 I f (A)2401 2532 w 7 R f (T)2473 2492 w 10 I f (A)2532 2532 w 7 S f (+)2604 2492 w 7 R f (T)2654 2492 w 10 R f (\))2713 2532 w 10 I f (s)2762 2532 w 10 S f (=)2850 2532 w 10 R f (\()2954 2532 w 10 I f (I)2995 2532 w 10 S f (-)3077 2532 w 10 I f (A)3181 2532 w 7 R f (T)3253 2492 w 10 I f (A)3312 2532 w 7 S f (+)3384 2492 w 7 R f (T)3434 2492 w 10 R f (\))3493 2532 w 10 I f (c)3542 2532 w 10 R f (and)720 2712 w (\(11c\))720 2892 w 10 I f (s)2750 2892 w 10 S f (\263)2830 2892 w 10 B f (0)2926 2892 w 10 R f (,)2984 2892 w (where)720 3072 w 10 I f (I)988 3072 w 10 R f (denotes the identity matrix of appropriate dimension \(i.e.,)7 2303 1 1046 3072 t 10 I f (n)3374 3072 w 10 S f (\264)3432 3072 w 10 I f (n)3495 3072 w 10 R f (\).)3545 3072 w ( us to compute step direction \(4\), with)7 1955(The affine algorithm requires)3 1355 2 970 3233 t 10 I f (A)4367 3233 w 11 R f (\303)4385 3203 w 10 R f (from \(11b\):)1 525 1 4515 3233 t 10 I f (A)720 3358 w 11 R f (\303)738 3328 w 10 R f (:)822 3358 w 10 S f (=)866 3358 w 10 R f (\()970 3358 w 10 I f (I)1011 3358 w 10 S f (-)1093 3358 w 10 I f (A)1197 3358 w 7 R f (T)1269 3318 w 10 I f (A)1328 3358 w 7 S f (+)1400 3318 w 7 R f (T)1450 3318 w 10 R f (\))1509 3358 w 10 I f (D)1558 3358 w 10 R f (, where)1 302 1 1630 3358 t 10 I f (D)1966 3358 w 10 S f (=)2087 3358 w 10 R f (diag \()1 213 1 2191 3358 t 10 I f (s)2412 3358 w 7 I f (k)2462 3318 w 10 R f (\) and)1 211 1 2509 3358 t 10 I f (s)2754 3358 w 7 I f (k)2804 3318 w 10 R f ( the rows of)3 501( Fortunately,)1 545(is the current iterate.)3 847 3 2877 3358 t 10 I f (AD)4803 3358 w 7 S f (-)4947 3318 w 7 R f (1)4997 3318 w 10 R f ( \()1 229( null space of this constraint matrix:)6 2314(span the)1 475 3 720 3478 t 10 I f (I)3746 3478 w 10 S f (-)3828 3478 w 10 I f (A)3932 3478 w 7 R f (T)4004 3438 w 10 I f (A)4063 3478 w 7 S f (+)4135 3438 w 7 R f (T)4185 3438 w 10 R f (\))4244 3478 w 10 I f (A)4293 3478 w 7 R f (T)4365 3438 w 10 S f (=)4465 3478 w 10 B f (0)4569 3478 w 10 R f (. Thus)1 421 1 4619 3478 t 10 I f (P)720 3598 w 7 I f (A)792 3618 w 8 R f (\303)806 3590 w 10 S f (=)892 3598 w 10 I f (D)996 3598 w 7 S f (-)1079 3558 w 7 R f (1)1129 3558 w 10 I f (A)1180 3598 w 7 R f (T)1252 3558 w 10 R f (\()1311 3598 w 10 I f (AD)1352 3598 w 7 S f (-)1496 3558 w 7 R f (2)1546 3558 w 10 I f (A)1597 3598 w 7 R f (T)1669 3558 w 10 R f (\))1728 3598 w 7 S f (-)1772 3558 w 7 R f (1)1822 3558 w 10 I f (AD)1873 3598 w 7 S f (-)2017 3558 w 7 R f (1)2067 3558 w 10 R f ( constant)1 368(. The)1 241 2 2110 3598 t 10 I f (c)2754 3598 w 7 R f (T)2809 3558 w 10 I f (A)2868 3598 w 7 S f (+)2940 3558 w 10 I f (b)3003 3598 w 10 R f (in \(11a\) is irrelevant to the affine algorithm, so)8 1952 1 3088 3598 t (the)720 3723 w 10 I f (c)868 3723 w 11 R f (\303)874 3718 w 10 R f (of \(4\) is)2 318 1 938 3723 t 10 I f (DA)1282 3723 w 7 S f (+)1426 3683 w 10 I f (b)1489 3723 w 10 R f (; since)1 259 1 1539 3723 t 10 I f (AA)1824 3723 w 7 S f (+)1957 3683 w 10 S f (=)2061 3723 w 10 I f (I)2165 3723 w 10 R f (, the search direction)3 837 1 2198 3723 t 10 I f (p)3062 3723 w 10 S f (=)3161 3723 w 10 I f (Dp)3265 3723 w 11 R f (\303)3346 3718 w 10 R f (boils down to)2 549 1 3414 3723 t 10 I f (p)3990 3723 w 10 S f (= -)1 167 1 4089 3723 t 10 I f (A)4272 3723 w 7 R f (T)4344 3683 w 10 R f (\()4403 3723 w 10 I f (AD)4444 3723 w 7 S f (-)4588 3683 w 7 R f (2)4638 3683 w 10 I f (A)4689 3723 w 7 R f (T)4761 3683 w 10 R f (\))4820 3723 w 7 S f (-)4864 3683 w 7 R f (1)4914 3683 w 10 I f (b)4965 3723 w 10 R f (.)5015 3723 w (But this is a search direction for)6 1486 1 720 3843 t 10 I f (s)2266 3843 w 10 R f (; since)1 293 1 2305 3843 t 10 I f (s)2658 3843 w 10 S f (=)2746 3843 w 10 I f (c)2850 3843 w 10 S f (-)2943 3843 w 10 I f (A)3047 3843 w 7 R f (T)3119 3803 w 10 I f (y)3178 3843 w 10 R f (, adding)1 357 1 3222 3843 t 10 S f (a)3639 3843 w 10 I f (p)3710 3843 w 10 R f (to)3820 3843 w 10 I f (s)3957 3843 w 10 R f (is the same as adding)4 985 1 4055 3843 t 10 S f (a)720 3963 w 10 R f (\()791 3963 w 10 I f (AD)832 3963 w 7 S f (-)976 3923 w 7 R f (2)1026 3923 w 10 I f (A)1077 3963 w 7 R f (T)1149 3923 w 10 R f (\))1208 3963 w 7 S f (-)1252 3923 w 7 R f (1)1302 3923 w 10 I f (b)1353 3963 w 10 R f (to)1428 3963 w 10 I f (y)1531 3963 w 10 R f (.)1575 3963 w (In short, the dual affine variant takes the form)8 1832 1 970 4119 t 10 I f (D)1220 4299 w 10 R f (:)1333 4299 w 10 S f (=)1377 4299 w 10 I f (D)1481 4299 w 7 I f (k)1564 4259 w 10 S f (=)1652 4299 w 10 R f (diag \()1 213 1 1756 4299 t 10 I f (c)1977 4299 w 10 S f (-)2061 4299 w 10 I f (A)2156 4299 w 7 R f (T)2228 4259 w 10 I f (y)2287 4299 w 7 I f (k)2342 4259 w 10 R f (\))2389 4299 w 10 I f (y)1236 4479 w 7 I f (k)1291 4439 w 7 S f (+)1338 4439 w 7 R f (1)1388 4439 w 10 S f (=)1480 4479 w 10 I f (y)1584 4479 w 7 I f (k)1639 4439 w 10 S f (+ a)1 167 1 1727 4479 t 7 I f (k)1899 4439 w 10 R f (\()1946 4479 w 10 I f (AD)1987 4479 w 7 S f (-)2131 4439 w 7 R f (2)2181 4439 w 10 I f (A)2232 4479 w 7 R f (T)2304 4439 w 10 R f (\))2363 4479 w 7 S f (-)2407 4439 w 7 R f (1)2457 4439 w 10 I f (b)2508 4479 w 10 R f (,)2566 4479 w (with)720 4659 w 10 S f (a)923 4659 w 7 I f (k)991 4619 w 10 S f (>)1079 4659 w 10 R f (0 chosen to retain)3 707 1 1183 4659 t 10 I f (c)1915 4659 w 10 S f (-)2008 4659 w 10 I f (A)2112 4659 w 7 R f (T)2184 4619 w 10 I f (y)2243 4659 w 7 I f (k)2298 4619 w 7 S f (+)2345 4619 w 7 R f (1)2395 4619 w 10 S f (>)2487 4659 w 10 B f (0)2591 4659 w 10 R f (.)2641 4659 w 10 B f (Dual Projective Algorithm)2 1131 1 720 4899 t 10 R f ( projective algorithm must compute the)5 2149(The dual)1 466 2 970 5055 t 10 I f (u)3725 5055 w 10 R f (and)3915 5055 w 10 I f (v)4199 5055 w 10 R f (of \(8\) with)2 657 1 4383 5055 t 10 I f (A)720 5180 w 10 S1 f (_ _)1 51 1 730 5087 t 10 S f (=)830 5180 w 10 R f ([ \()1 74 1 934 5180 t 10 I f (I)1016 5180 w 10 S f (-)1098 5180 w 10 I f (A)1202 5180 w 7 R f (T)1274 5140 w 10 I f (A)1333 5180 w 7 S f (+)1405 5140 w 7 R f (T)1455 5140 w 10 R f (\))1514 5180 w 10 I f (D)1563 5180 w 10 R f (,)1643 5180 w 10 S f (-)1717 5180 w 10 R f (\()1788 5180 w 10 I f (I)1829 5180 w 10 S f (-)1911 5180 w 10 I f (A)2015 5180 w 7 R f (T)2087 5140 w 10 I f (A)2146 5180 w 7 S f (+)2218 5140 w 7 R f (T)2268 5140 w 10 R f (\))2327 5180 w 10 I f (c)2376 5180 w 10 R f ( mentioned in [10], the columns of)6 1385(]. As)1 219 2 2428 5180 t 10 I f (Q)2398 5445 w 10 S f (=)2519 5445 w (\351)2631 5358 w (\357)2631 5458 w (\353)2631 5558 w 10 B f (0)2809 5510 w 10 I f (D)2681 5410 w 7 S f (-)2764 5370 w 7 R f (1)2814 5370 w 10 I f (A)2865 5410 w 7 R f (T)2937 5370 w 10 R f (1)3184 5510 w 10 I f (D)3095 5410 w 7 S f (-)3178 5370 w 7 R f (1)3228 5370 w 10 I f (c)3279 5410 w 10 S f (\371)3323 5358 w (\357)3323 5458 w (\373)3323 5558 w 10 R f (span the null space of this)5 1120 1 720 5815 t 10 I f (A)1883 5815 w 10 S1 f (_ _)1 51 1 1893 5722 t 10 R f ( \(8\) becomes)2 551(. Thus)1 293 2 1944 5815 t 10 I f (u)2831 5815 w 10 S f (+ b)1 159 1 2930 5815 t 10 I f (v)3097 5815 w 10 R f (:)3182 5815 w 10 S f (=)3226 5815 w 10 I f (Q)3330 5815 w 10 R f (\()3410 5815 w 10 I f (Q)3451 5815 w 7 R f (T)3534 5775 w 10 I f (Q)3593 5815 w 10 R f (\))3673 5815 w 7 S f (-)3717 5775 w 7 R f (1)3767 5775 w 10 I f (Q)3818 5815 w 7 R f (T)3901 5775 w 10 S f (\354)3976 5728 w (\357)3976 5828 w (\356)3976 5928 w (b)4126 5880 w 10 I f (DA)4025 5780 w 7 S f (+)4169 5740 w 10 I f (b)4232 5780 w 10 S f (\374)4282 5728 w (\357)4282 5828 w (\376)4282 5928 w 10 R f (, except that this)3 709 1 4331 5815 t (ignores constant)1 655 1 720 6040 t 10 I f (c)1403 6040 w 7 R f (T)1458 6000 w 10 I f (A)1517 6040 w 7 S f (+)1589 6000 w 10 I f (b)1652 6040 w 10 R f ( a constant to the objective function effectively)7 1891( shown in [10], adding)4 914( As)1 164(in \(11a\).)1 341 4 1730 6040 t (adds a constant to)3 749 1 720 6245 t 10 S f (b)1507 6245 w 10 R f (, so \(8\) really becomes)4 958 1 1562 6245 t 10 I f (u)2558 6245 w 10 S f (+ b)1 159 1 2657 6245 t 10 I f (v)2824 6245 w 10 R f (:)2909 6245 w 10 S f (=)2953 6245 w 10 I f (Q)3057 6245 w 10 R f (\()3137 6245 w 10 I f (Q)3178 6245 w 7 R f (T)3261 6205 w 10 I f (Q)3320 6245 w 10 R f (\))3400 6245 w 7 S f (-)3444 6205 w 7 R f (1)3494 6205 w 10 I f (Q)3545 6245 w 7 R f (T)3628 6205 w 10 S f (\354)3695 6158 w (\357)3695 6258 w (\356)3695 6358 w (b -)1 159 1 3744 6315 t 10 I f (c)3952 6315 w 7 R f (T)4007 6275 w 10 I f (A)4066 6315 w 7 S f (+)4138 6275 w 10 I f (b)4201 6315 w (DA)3869 6205 w 7 S f (+)4013 6165 w 10 I f (b)4076 6205 w 10 S f (\374)4251 6158 w (\357)4251 6258 w (\376)4251 6358 w 10 R f (; correspondingly,)1 740 1 4300 6245 t (\(6\) becomes)1 490 1 720 6470 t (\(12\))720 6700 w 10 S f (f)1853 6700 w 10 R f (\()1913 6700 w 10 I f (y)1954 6700 w 10 R f (,)2006 6700 w 10 S f (b)2039 6700 w 10 R f (\) :)1 110 1 2102 6700 t 10 S f (=)2228 6700 w 10 R f (\()2332 6700 w 10 I f (n)2373 6700 w 10 S f (+)2463 6700 w 10 R f ( \()1 41( log)1 144(1 \))1 91 3 2558 6700 t 10 S f (b -)1 159 1 2842 6700 t 10 I f (b)3050 6700 w 7 R f (T)3111 6660 w 10 I f (y)3170 6700 w 10 R f (\))3222 6700 w 10 S f (-)3312 6700 w 7 I f (i)3416 6800 w 7 S f (=)3452 6800 w 7 R f (1)3502 6800 w 15 S f (S)3432 6730 w 7 I f (n)3459 6600 w 10 R f (log \()1 169 1 3569 6700 t 10 I f (s)3746 6700 w 7 I f (i)3796 6720 w 10 R f (\) ,)1 74 1 3832 6700 t (\(where)720 7045 w 10 I f (s)1021 7045 w 10 S f (=)1109 7045 w 10 I f (c)1213 7045 w 10 S f (-)1306 7045 w 10 I f (A)1410 7045 w 7 R f (T)1482 7005 w 10 I f (y)1541 7045 w 10 R f (\). But)1 253 1 1585 7045 t 10 I f (Q)1863 7045 w 7 R f (T)1946 7005 w 10 S f (\354)2013 6958 w (\357)2013 7058 w (\356)2013 7158 w (b -)1 159 1 2062 7115 t 10 I f (c)2270 7115 w 7 R f (T)2325 7075 w 10 I f (A)2384 7115 w 7 S f (+)2456 7075 w 10 I f (b)2519 7115 w (DA)2187 7005 w 7 S f (+)2331 6965 w 10 I f (b)2394 7005 w 10 S f (\374)2569 6958 w (\357)2569 7058 w (\376)2569 7158 w (=)2667 7045 w (\354)2787 6958 w (\357)2787 7058 w (\356)2787 7158 w (b)2931 7110 w 10 I f (AA)2836 7010 w 7 S f (+)2969 6970 w 10 I f (b)3032 7010 w 10 S f (\374)3082 6958 w (\357)3082 7058 w (\376)3082 7158 w (=)3188 7045 w (\354)3308 7008 w (\356)3308 7108 w (b)3357 7105 w 10 I f (b)3359 7005 w 10 S f (\374)3412 7008 w (\376)3412 7108 w 10 R f (, and we end up with)5 832 1 3461 7045 t (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 4 5 %%Page: 5 6 /saveobj save def mark 6 pagesetup 10 R f (- 5 -)2 166 1 2797 480 t (\(13\))720 875 w 10 I f (u)2289 875 w 10 S f (+ b)1 159 1 2388 875 t 10 I f (v)2555 875 w 10 R f (:)2640 875 w 10 S f (=)2684 875 w 10 I f (Q)2788 875 w 10 R f (\()2868 875 w 10 I f (Q)2909 875 w 7 R f (T)2992 835 w 10 I f (Q)3051 875 w 10 R f (\))3131 875 w 7 S f (-)3175 835 w 7 R f (1)3225 835 w 10 S f (\354)3284 838 w (\356)3284 938 w (b)3333 935 w 10 I f (b)3335 835 w 10 S f (\374)3388 838 w (\376)3388 938 w 10 I f (.)3445 875 w 10 R f (It is convenient to note that)5 1091 1 720 1110 t (\(14a\) \()1 832 1 720 1375 t 10 I f (Q)1560 1375 w 7 R f (T)1643 1335 w 10 I f (Q)1702 1375 w 10 R f (\))1782 1375 w 7 S f (-)1826 1335 w 7 R f (1)1876 1335 w 10 S f (\354)1935 1338 w (\356)1935 1438 w (b)1984 1435 w 10 I f (b)1986 1335 w 10 S f (\374)2039 1338 w (\376)2039 1438 w (=)2137 1375 w (\354)2257 1288 w (\357)2257 1388 w (\356)2257 1488 w 10 R f (0)2587 1440 w (\()2306 1340 w 10 I f (AD)2347 1340 w 7 S f (-)2491 1300 w 7 R f (2)2541 1300 w 10 I f (A)2592 1340 w 7 R f (T)2664 1300 w 10 R f (\))2723 1340 w 7 S f (-)2767 1300 w 7 R f (1)2817 1300 w 10 I f (b)2868 1340 w 10 S f (\374)2918 1288 w (\357)2918 1388 w (\376)2918 1488 w (+ n)1 156 1 3016 1375 t (\354)3188 1288 w (\357)3188 1388 w (\356)3188 1488 w 10 R f (1)3673 1440 w 10 S f (-)3237 1340 w 10 R f (\()3308 1340 w 10 I f (AD)3349 1340 w 7 S f (-)3493 1300 w 7 R f (2)3543 1300 w 10 I f (A)3594 1340 w 7 R f (T)3666 1300 w 10 R f (\))3725 1340 w 7 S f (-)3769 1300 w 7 R f (1)3819 1300 w 10 I f (AD)3870 1340 w 7 S f (-)4014 1300 w 7 R f (2)4064 1300 w 10 I f (c)4115 1340 w 10 S f (\374)4159 1288 w (\357)4159 1388 w (\376)4159 1488 w 10 R f (,)4216 1375 w (where)720 1660 w (\(14b\))720 1890 w 10 S f (n =)1 156 1 1746 1890 t 10 R f (1)1976 1970 w 10 S f (+)2075 1970 w 10 I f (c)2179 1970 w 7 R f (T)2234 1930 w 10 I f (D)2293 1970 w 7 S f (-)2376 1930 w 7 R f (2)2426 1930 w 10 I f (c)2477 1970 w 10 S f (-)2570 1970 w 10 I f (c)2674 1970 w 7 R f (T)2729 1930 w 10 I f (D)2788 1970 w 7 S f (-)2871 1930 w 7 R f (2)2921 1930 w 10 I f (A)2972 1970 w 7 R f (T)3044 1930 w 10 R f (\()3103 1970 w 10 I f (AD)3144 1970 w 7 S f (-)3288 1930 w 7 R f (2)3338 1930 w 10 I f (A)3389 1970 w 7 R f (T)3461 1930 w 10 R f (\))3520 1970 w 7 S f (-)3564 1930 w 7 R f (1)3614 1930 w 10 I f (AD)3665 1970 w 7 S f (-)3809 1930 w 7 R f (2)3859 1930 w 10 I f (c)3910 1970 w 10 S f (b -)1 159 1 2341 1830 t 10 I f (c)2549 1830 w 7 R f (T)2604 1790 w 10 I f (D)2663 1830 w 7 S f (-)2746 1790 w 7 R f (2)2796 1790 w 10 I f (A)2847 1830 w 7 R f (T)2919 1790 w 10 R f (\()2978 1830 w 10 I f (AD)3019 1830 w 7 S f (-)3163 1790 w 7 R f (2)3213 1790 w 10 I f (A)3264 1830 w 7 R f (T)3336 1790 w 10 R f (\))3395 1830 w 7 S f (-)3439 1790 w 7 R f (1)3489 1790 w 10 I f (b)3540 1830 w 10 S1 f (_ ________________________________________)1 2008 1 1962 1860 t 10 R f (,)3988 1890 w (so that)1 264 1 720 2130 t (\(14c\))720 2445 w 10 I f (u)1310 2445 w 10 S f (+ b)1 159 1 1409 2445 t 10 I f (v)1576 2445 w 10 S f (=)1669 2445 w (\351)1781 2308 w (\357)1781 2408 w (\357)1781 2508 w (\353)1781 2608 w (n)3075 2570 w 10 I f (D)1831 2395 w 7 S f (-)1914 2355 w 7 R f (1)1964 2355 w 10 S f (\354)2023 2358 w (\356)2023 2458 w 10 I f (A)2072 2410 w 7 R f (T)2144 2370 w 10 R f (\()2203 2410 w 10 I f (AD)2244 2410 w 7 S f (-)2388 2370 w 7 R f (2)2438 2370 w 10 I f (A)2489 2410 w 7 R f (T)2561 2370 w 10 R f (\))2620 2410 w 7 S f (-)2664 2370 w 7 R f (1)2714 2370 w 10 I f (b)2765 2410 w 10 S f (+ n)1 156 1 2864 2410 t 10 R f (.)3028 2380 w ([)3061 2410 w 10 I f (c)3102 2410 w 10 S f (-)3195 2410 w 10 I f (A)3299 2410 w 7 R f (T)3371 2370 w 10 R f (\()3430 2410 w 10 I f (AD)3471 2410 w 7 S f (-)3615 2370 w 7 R f (2)3665 2370 w 10 I f (A)3716 2410 w 7 R f (T)3788 2370 w 10 R f (\))3847 2410 w 7 S f (-)3891 2370 w 7 R f (1)3941 2370 w 10 I f (AD)3992 2410 w 7 S f (-)4136 2370 w 7 R f (2)4186 2370 w 10 I f (c)4237 2410 w 10 R f (])4289 2410 w 10 S f (\374)4322 2358 w (\376)4322 2458 w (\371)4371 2308 w (\357)4371 2408 w (\357)4371 2508 w (\373)4371 2608 w 10 I f (.)4425 2445 w 10 R f (Rather than working directly with \(9\), it is convenient to work with)11 2714 1 720 2780 t 10 S f (n)3462 2780 w 10 R f ( we can choose)3 615(: if)1 142 2 3514 2780 t 10 S f (n)4299 2780 w 10 R f (to make the first)3 661 1 4379 2780 t 10 I f (n)720 2900 w 10 R f (components of \(14c\) nonnegative, then)4 2085 1 926 2900 t 10 I f (D)3167 2900 w 7 S f (-)3250 2860 w 7 R f (1)3300 2860 w 10 R f (times these components, i.e.,)3 1542 1 3498 2900 t 10 I f (x)720 3020 w 10 R f (:)805 3020 w 10 S f (=)849 3020 w 10 I f (D)953 3020 w 7 S f (-)1036 2980 w 7 R f (2)1086 2980 w 10 R f ([)1137 3020 w 10 I f (A)1178 3020 w 7 R f (T)1250 2980 w 10 R f (\()1309 3020 w 10 I f (AD)1350 3020 w 7 S f (-)1494 2980 w 7 R f (2)1544 2980 w 10 I f (A)1595 3020 w 7 R f (T)1667 2980 w 10 R f (\))1726 3020 w 7 S f (-)1770 2980 w 7 R f (1)1820 2980 w 10 I f (b)1871 3020 w 10 S f (+ n)1 156 1 1970 3020 t 10 R f (.)2134 2990 w (\()2167 3020 w 10 I f (c)2208 3020 w 10 S f (-)2301 3020 w 10 I f (A)2405 3020 w 7 R f (T)2477 2980 w 10 R f (\()2536 3020 w 10 I f (AD)2577 3020 w 7 S f (-)2721 2980 w 7 R f (2)2771 2980 w 10 I f (A)2822 3020 w 7 R f (T)2894 2980 w 10 R f (\))2953 3020 w 7 S f (-)2997 2980 w 7 R f (1)3047 2980 w 10 I f (AD)3098 3020 w 7 S f (-)3242 2980 w 7 R f (2)3292 2980 w 10 I f (c)3343 3020 w 10 R f ( for \(1\), and)3 878( is feasible)2 693(\) ])1 74 3 3395 3020 t 10 I f (c)720 3140 w 7 R f (T)775 3100 w 10 I f (x)834 3140 w 10 S f (=)927 3140 w 10 I f (b)1031 3140 w 7 R f (T)1092 3100 w 10 R f (\()1151 3140 w 10 I f (AD)1192 3140 w 7 S f (-)1336 3100 w 7 R f (2)1386 3100 w 10 I f (A)1437 3140 w 7 R f (T)1509 3100 w 10 R f (\))1568 3140 w 7 S f (-)1612 3100 w 7 R f (1)1662 3100 w 10 I f (AD)1713 3140 w 7 S f (-)1857 3100 w 7 R f (2)1907 3100 w 10 I f (c)1958 3140 w 10 S f (+ n)1 156 1 2051 3140 t 10 R f (.)2215 3110 w (\()2248 3140 w 10 I f (c)2289 3140 w 7 R f (T)2344 3100 w 10 I f (D)2403 3140 w 7 S f (-)2486 3100 w 7 R f (2)2536 3100 w 10 I f (c)2587 3140 w 10 S f (-)2680 3140 w 10 I f (c)2784 3140 w 7 R f (T)2839 3100 w 10 I f (D)2898 3140 w 7 S f (-)2981 3100 w 7 R f (2)3031 3100 w 10 I f (A)3082 3140 w 7 R f (T)3154 3100 w 10 R f (\()3213 3140 w 10 I f (AD)3254 3140 w 7 S f (-)3398 3100 w 7 R f (2)3448 3100 w 10 I f (A)3499 3140 w 7 R f (T)3571 3100 w 10 R f (\))3630 3140 w 7 S f (-)3674 3100 w 7 R f (1)3724 3100 w 10 I f (AD)3775 3140 w 7 S f (-)3919 3100 w 7 R f (2)3969 3100 w 10 I f (c)4020 3140 w 10 R f ( candidate for)2 660(\) is a)2 308 2 4072 3140 t (updating)720 3260 w 10 S f (b)1108 3260 w 10 R f (: if)1 127 1 1163 3260 t 10 I f (c)1328 3260 w 7 R f (T)1383 3220 w 10 I f (x)1442 3260 w 10 S f (< b)1 159 1 1535 3260 t 10 R f ( we set)2 305(, then)1 235 2 1694 3260 t 10 S f (b)2273 3260 w 10 R f (:)2369 3260 w 10 S f (=)2413 3260 w 10 I f (c)2517 3260 w 7 R f (T)2572 3220 w 10 I f (x)2631 3260 w 10 R f (. Once)1 299 1 2675 3260 t 10 S f (b)3013 3260 w 10 R f (has been updated, the step direction \(10\) for)7 1855 1 3107 3260 t 10 I f (s)5001 3260 w 10 R f (becomes)720 3380 w 10 I f (p)1108 3380 w 10 R f (=)1197 3380 w 10 I f (A)1292 3380 w 7 R f (T)1364 3340 w 10 R f (\()1423 3380 w 10 I f (AD)1464 3380 w 7 S f (-)1608 3340 w 7 R f (2)1658 3340 w 10 I f (A)1709 3380 w 7 R f (T)1781 3340 w 10 R f (\))1840 3380 w 7 S f (-)1884 3340 w 7 R f (1)1934 3340 w 10 R f (\()1985 3380 w 10 I f (b)2026 3380 w 10 S f (- n)1 156 1 2125 3380 t 10 I f (AD)2289 3380 w 7 S f (-)2433 3340 w 7 R f (2)2483 3340 w 10 I f (c)2534 3380 w 10 R f (\))2586 3380 w 10 S f (+ n)1 156 1 2676 3380 t 10 R f (\()2840 3380 w 10 I f (c)2881 3380 w 10 S f (-)2965 3380 w 10 I f (s)3060 3380 w 10 R f (\), with)1 275 1 3107 3380 t 10 S f (n)3421 3380 w 10 R f (from \(14b\); since)2 719 1 3511 3380 t 10 I f (c)4268 3380 w 10 S f (-)4361 3380 w 10 I f (s)4465 3380 w 10 S f (=)4553 3380 w 10 I f (A)4657 3380 w 7 R f (T)4729 3340 w 10 I f (y)4788 3380 w 10 R f (, this)1 208 1 4832 3380 t (boils down to the step direction)5 1258 1 720 3505 t 10 I f (p)2003 3505 w 10 S1 f (_)2005 3437 w 10 S f (=)2102 3505 w 10 R f (\()2206 3505 w 10 I f (AD)2247 3505 w 7 S f (-)2391 3465 w 7 R f (2)2441 3465 w 10 I f (A)2492 3505 w 7 R f (T)2564 3465 w 10 R f (\))2623 3505 w 7 S f (-)2667 3465 w 7 R f (1)2717 3465 w 10 R f (\()2768 3505 w 10 I f (b)2809 3505 w 10 S f (- n)1 156 1 2908 3505 t 10 I f (AD)3072 3505 w 7 S f (-)3216 3465 w 7 R f (2)3266 3465 w 10 I f (c)3317 3505 w 10 R f (\))3369 3505 w 10 S f (+ n)1 156 1 3459 3505 t 10 I f (y)3623 3505 w 10 R f (for)3692 3505 w 10 I f (y)3833 3505 w 10 R f (.)3877 3505 w ( given)1 275(To summarize, the dual projective algorithm works as follows:)8 2535 2 970 3661 t 10 S f (b)3808 3661 w 7 I f (k)3868 3621 w 10 S f (\263)3948 3661 w 10 I f (c)4044 3661 w 7 R f (T)4099 3621 w 10 I f (x *)1 102 1 4158 3661 t 10 R f (\()4288 3661 w 10 S f (=)4321 3661 w 10 I f (b)4425 3661 w 7 R f (T)4486 3621 w 10 I f (y *)1 102 1 4545 3661 t 10 R f ( opti-)1 218(, the)1 175 2 4647 3661 t (mal objective function value\) and)4 1394 1 720 3781 t 10 I f (y)2152 3781 w 7 I f (k)2207 3741 w 10 R f (rendering)2284 3781 w 10 I f (s)2704 3781 w 7 I f (k)2754 3741 w 10 R f (:)2834 3781 w 10 S f (=)2878 3781 w 10 I f (c)2982 3781 w 10 S f (-)3075 3781 w 10 I f (A)3179 3781 w 7 R f (T)3251 3741 w 10 I f (y)3310 3781 w 7 I f (k)3365 3741 w 10 S f (>)3453 3781 w 10 B f (0)3557 3781 w 10 R f (, let)1 163 1 3607 3781 t 10 I f (D)3807 3781 w 10 R f (:)3920 3781 w 10 S f (=)3964 3781 w 10 I f (D)4068 3781 w 7 I f (k)4151 3741 w 10 S f (=)4239 3781 w 10 R f (diag \()1 213 1 4343 3781 t 10 I f (s)4564 3781 w 7 I f (k)4614 3741 w 10 R f (\); if such)2 379 1 4661 3781 t (exists, let)1 378 1 720 3901 t 10 S f (n)1123 3901 w 7 I f (k)1180 3861 w 10 R f (be the minimal)2 600 1 1244 3901 t 10 S f (n)1869 3901 w 10 R f (for which)1 385 1 1946 3901 t 10 I f (A)1657 4081 w 7 R f (T)1729 4041 w 10 R f (\()1788 4081 w 10 I f (AD)1829 4081 w 7 S f (-)1973 4041 w 7 R f (2)2023 4041 w 10 I f (A)2074 4081 w 7 R f (T)2146 4041 w 10 R f (\))2205 4081 w 7 S f (-)2249 4041 w 7 R f (1)2299 4041 w 10 I f (b)2350 4081 w 10 S f (+ n)1 156 1 2449 4081 t 10 R f (\()2613 4081 w 10 I f (c)2654 4081 w 10 S f (-)2747 4081 w 10 I f (A)2851 4081 w 7 R f (T)2923 4041 w 10 R f (\()2982 4081 w 10 I f (AD)3023 4081 w 7 S f (-)3167 4041 w 7 R f (2)3217 4041 w 10 I f (A)3268 4081 w 7 R f (T)3340 4041 w 10 R f (\))3399 4081 w 7 S f (-)3443 4041 w 7 R f (1)3493 4041 w 10 I f (AD)3544 4081 w 7 S f (-)3688 4041 w 7 R f (2)3738 4041 w 10 I f (c)3789 4081 w 10 R f (\))3841 4081 w 10 S f (\263)3923 4081 w 10 B f (0)4019 4081 w 10 R f (,)4077 4081 w (and if)1 230 1 720 4261 t 10 S f (b)1413 4441 w 7 I f (k)1473 4401 w 10 S f (>)1561 4441 w 10 I f (c)1665 4441 w 7 R f (T)1720 4401 w 10 I f (D)1779 4441 w 7 S f (-)1862 4401 w 7 R f (2)1912 4401 w 10 R f ([)1963 4441 w 10 I f (A)2004 4441 w 7 R f (T)2076 4401 w 10 R f (\()2135 4441 w 10 I f (AD)2176 4441 w 7 S f (-)2320 4401 w 7 R f (2)2370 4401 w 10 I f (A)2421 4441 w 7 R f (T)2493 4401 w 10 R f (\))2552 4441 w 7 S f (-)2596 4401 w 7 R f (1)2646 4401 w 10 I f (b)2697 4441 w 10 S f (+ n)1 156 1 2796 4441 t 7 I f (k)2957 4401 w 10 R f (\()3004 4441 w 10 I f (c)3045 4441 w 10 S f (-)3138 4441 w 10 I f (A)3242 4441 w 7 R f (T)3314 4401 w 10 R f (\()3373 4441 w 10 I f (AD)3414 4441 w 7 S f (-)3558 4401 w 7 R f (2)3608 4401 w 10 I f (A)3659 4441 w 7 R f (T)3731 4401 w 10 R f (\))3790 4441 w 7 S f (-)3834 4401 w 7 R f (1)3884 4401 w 10 I f (AD)3935 4441 w 7 S f (-)4079 4401 w 7 R f (2)4129 4401 w 10 I f (c)4180 4441 w 10 R f ( ,)1 41(\) ])1 74 2 4232 4441 t (then set)1 313 1 720 4621 t 10 S f (b)1063 4621 w 7 I f (k)1123 4581 w 7 S f (+)1170 4581 w 7 R f (1)1220 4581 w 10 R f ( otherwise let)2 550(to this value;)2 527 2 1293 4621 t 10 S f (b)2401 4621 w 7 I f (k)2461 4581 w 7 S f (+)2508 4581 w 7 R f (1)2558 4581 w 10 R f (:)2642 4621 w 10 S f (= b)1 159 1 2686 4621 t 7 I f (k)2850 4581 w 10 R f (, and determine)2 630 1 2889 4621 t 10 S f (n)3550 4621 w 7 I f (k)3607 4581 w 10 R f (from \(14b\) \(with)2 683 1 3677 4621 t 10 S f (b = b)2 263 1 4391 4621 t 7 I f (k)4659 4581 w 10 R f (\). Com-)1 342 1 4698 4621 t (pute)720 4746 w 10 I f (p)921 4746 w 10 S1 f (_)923 4678 w 7 I f (k)982 4677 w 10 R f (:)1062 4746 w 10 S f (=)1106 4746 w 10 R f (\()1210 4746 w 10 I f (AD)1251 4746 w 7 S f (-)1395 4706 w 7 R f (2)1445 4706 w 10 I f (A)1496 4746 w 7 R f (T)1568 4706 w 10 R f (\))1627 4746 w 7 S f (-)1671 4706 w 7 R f (1)1721 4706 w 10 R f (\()1772 4746 w 10 I f (b)1813 4746 w 10 S f (- n)1 156 1 1912 4746 t 7 I f (k)2073 4706 w 10 I f (AD)2112 4746 w 7 S f (-)2256 4706 w 7 R f (2)2306 4706 w 10 I f (c)2357 4746 w 10 R f (\))2409 4746 w 10 S f (+ n)1 156 1 2499 4746 t 7 I f (k)2660 4706 w 10 I f (y)2699 4746 w 7 I f (k)2754 4706 w 10 R f (, choose)1 331 1 2793 4746 t 10 S f (a)3153 4746 w 7 I f (k)3221 4706 w 10 R f (to be a value of)4 631 1 3289 4746 t 10 S f (a)3949 4746 w 10 R f (that approximately mini-)2 1000 1 4040 4746 t (mizes)720 4871 w 10 S f (f)978 4871 w 10 R f (\()1038 4871 w 10 I f (y)1079 4871 w 7 I f (k)1134 4831 w 10 S f (+ a)1 167 1 1222 4871 t 10 I f (p)1397 4871 w 10 S1 f (_)1399 4803 w 7 I f (k)1458 4802 w 10 R f (,)1505 4871 w 10 S f (b)1571 4871 w 7 I f (k)1631 4831 w 7 S f (+)1678 4831 w 7 R f (1)1728 4831 w 10 R f (\), and set)2 363 1 1779 4871 t 10 I f (y)2167 4871 w 7 I f (k)2222 4831 w 7 S f (+)2269 4831 w 7 R f (1)2319 4831 w 10 R f (:)2403 4871 w 10 S f (=)2447 4871 w 10 I f (y)2551 4871 w 7 I f (k)2606 4831 w 10 S f (+ a)1 167 1 2694 4871 t 7 I f (k)2866 4831 w 10 I f (p)2905 4871 w 10 S1 f (_)2907 4803 w 7 I f (k)2966 4802 w 10 R f (.)3005 4871 w ( should be)2 423( It)1 117( algorithms described above assumes exact arithmetic.)6 2207(The theory behind the projective)4 1323 4 970 5027 t ( require)1 312( to develop variants of the projective algorithms that do not)10 2430( 14, 19])2 290(possible to use the ideas in [13,)6 1288 4 720 5147 t ( factorizations to do the necessary linear algebra \(or runs)9 2299( if one computes exact)4 910( However,)1 443(exact arithmetic.)1 668 4 720 5267 t ( conjugate gradients, long enough\), then it seems reasonable to)9 2564(some iterative method, e.g., some flavor of)6 1756 2 720 5387 t ( deserves brief)2 603( this regard, the denominator in \(14b\))6 1555( In)1 143(consider running the algorithms described above.)5 2019 4 720 5507 t ( has the form 1)4 631(discussion: it)1 559 2 720 5632 t 10 S f (+)1959 5632 w 10 I f (c)2063 5632 w 11 R f (\304)2069 5627 w 7 R f (T)2118 5563 w 10 I f (Bc)2177 5632 w 11 R f (\304)2244 5627 w 10 R f (, where)1 301 1 2282 5632 t 10 I f (B)2616 5632 w 10 R f ( we)1 148( If)1 123(is a projection and hence is positive semi-definite.)7 2059 3 2710 5632 t (have a Cholesky factor)3 1010 1 720 5752 t 10 I f (L)1786 5752 w 10 R f (of)1898 5752 w 10 I f (AD)2037 5752 w 7 S f (-)2181 5712 w 7 R f (2)2231 5712 w 10 I f (A)2282 5752 w 7 R f (T)2354 5712 w 10 S f (=)2454 5752 w 10 I f (LL)2558 5752 w 7 R f (T)2681 5712 w 10 R f (, then we can compute the denominator of \(14b\) as)9 2308 1 2732 5752 t (1)720 5872 w 10 S f (+)819 5872 w 10 R f (\()923 5872 w 10 S f (||)964 5872 w 10 I f (D)1012 5872 w 7 S f (-)1095 5832 w 7 R f (1)1145 5832 w 10 I f (c)1196 5872 w 10 S f (||)1248 5872 w 7 R f (2)1299 5892 w 10 S f (+ ||)1 144 1 1391 5872 t 10 I f (L)1543 5872 w 7 S f (-)1610 5832 w 7 R f (1)1660 5832 w 10 I f (AD)1711 5872 w 7 S f (-)1855 5832 w 7 R f (2)1905 5832 w 10 I f (c)1956 5872 w 10 S f (||)2008 5872 w 7 R f (2)2059 5892 w 10 R f (\) \()1 74 1 2110 5872 t 10 S f (||)2192 5872 w 10 I f (D)2240 5872 w 7 S f (-)2323 5832 w 7 R f (1)2373 5832 w 10 I f (c)2424 5872 w 10 S f (||)2476 5872 w 7 R f (2)2527 5892 w 10 S f (- ||)1 144 1 2619 5872 t 10 I f (L)2771 5872 w 7 S f (-)2838 5832 w 7 R f (1)2888 5832 w 10 I f (AD)2939 5872 w 7 S f (-)3083 5832 w 7 R f (2)3133 5832 w 10 I f (c)3184 5872 w 10 S f (||)3236 5872 w 7 R f (2)3287 5892 w 10 R f (\); if ever the computed value of)6 1294 1 3338 5872 t 10 S f (||)4662 5872 w 10 I f (D)4710 5872 w 7 S f (-)4793 5832 w 7 R f (1)4843 5832 w 10 I f (c)4894 5872 w 10 S f (||)4946 5872 w 7 R f (2)4997 5892 w 10 R f (is less than that of)4 722 1 720 5992 t 10 S f (||)1468 5992 w 10 I f (L)1516 5992 w 7 S f (-)1583 5952 w 7 R f (1)1633 5952 w 10 I f (AD)1684 5992 w 7 S f (-)1828 5952 w 7 R f (2)1878 5952 w 10 I f (c)1929 5992 w 10 S f (||)1981 5992 w 7 R f (2)2032 6012 w 10 R f (, the computed quantities are probably too inaccurate to justify continuing)10 2965 1 2075 5992 t (the dual projective algorithm, and it seems reasonable to switch to the affine algorithm.)13 3487 1 720 6112 t 10 B f (Bounds)720 6352 w 10 R f ( \(1c\), one has the upper-)5 984( addition to)2 460( in)1 130(Many problems have simple bounds on some of the variables:)9 2496 4 970 6508 t (bound constraints)1 711 1 720 6628 t 10 I f (x)1459 6628 w 10 S f (\243)1544 6628 w 10 I f (u)1640 6628 w 10 R f ( we can express these constraints in the standard form \(1b,c\) by adding)12 2854( course,)1 313(. Of)1 183 3 1690 6628 t ( this effectively replaces)3 996(slack variables;)1 625 2 720 6833 t 10 I f (A)2374 6833 w 10 R f (by)2468 6833 w 10 I f (A)2601 6833 w 11 R f (\304)2619 6803 w 10 S f (=)2711 6833 w (\351)2831 6796 w (\353)2831 6896 w 10 I f (I)2895 6893 w (A)2881 6793 w (I)3032 6893 w 10 B f (0)3024 6793 w 10 S f (\371)3074 6796 w (\373)3074 6896 w 10 R f (and)3145 6833 w 10 I f (D)3322 6833 w 10 R f (by)3427 6833 w 10 I f (D)3560 6833 w 11 R f (\304)3583 6803 w 10 S f (=)3681 6833 w (\354)3801 6746 w (\357)3801 6846 w (\356)3801 6946 w 10 B f (0)3880 6893 w 10 I f (D)3850 6773 w 7 I f (l)3933 6793 w 10 I f (D)4043 6893 w 7 I f (u)4126 6913 w 10 B f (0)4081 6793 w 10 S f (\374)4169 6746 w (\357)4169 6846 w (\376)4169 6946 w 10 R f (, where \()2 367 1 4218 6833 t 10 I f (D)4593 6833 w 7 I f (l)4676 6853 w 10 R f (\))4712 6833 w 7 I f (ii)4756 6853 w 10 S f (=)4853 6833 w 10 I f (x)4957 6833 w 7 I f (i)5012 6853 w 10 R f (and \()1 206 1 720 7058 t 10 I f (D)934 7058 w 7 I f (u)1017 7078 w 10 R f (\))1068 7058 w 7 I f (ii)1112 7078 w 10 S f (=)1209 7058 w 10 I f (u)1313 7058 w 7 I f (i)1374 7078 w 10 S f (-)1451 7058 w 10 I f (x)1555 7058 w 7 I f (i)1610 7078 w 10 R f ( it increases the size of the linear equation)8 1698( first glance this looks undesirable, as)6 1525(. At)1 179 3 1638 7058 t ( by factoring)2 512( However,)1 441( must be solved.)3 653(systems that)1 492 4 720 7183 t 10 I f (A)2844 7183 w 11 R f (\304)2862 7153 w 10 I f (D)2905 7183 w 11 R f (\304)2928 7153 w 7 S f (-)2988 7114 w 7 R f (2)3038 7114 w 10 I f (A)3089 7183 w 11 R f (\304)3107 7153 w 7 R f (T)3161 7114 w 10 R f (appropriately, we can reduce the linear equa-)6 1802 1 3238 7183 t ( Specifically,)1 552(tions to systems of the same size and sparsity as without upper bounds.)12 2840 2 720 7303 t (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 5 6 %%Page: 6 7 /saveobj save def mark 7 pagesetup 10 R f (- 6 -)2 166 1 2797 480 t (\(15\))720 845 w 10 I f (A)2644 845 w 11 R f (\304)2662 815 w 10 I f (D)2705 845 w 11 R f (\304)2728 815 w 7 S f (-)2788 776 w 7 R f (2)2838 776 w 10 I f (A)2889 845 w 11 R f (\304)2907 815 w 7 R f (T)2961 776 w 10 S f (=)3061 845 w (\354)761 1023 w (\357)761 1123 w (\356)761 1223 w 10 B f (0)820 1185 w 10 I f (I)810 1065 w (I)1378 1185 w (AD)945 1065 w 7 I f (l)1083 1084 w 7 S f (-)1083 1025 w 7 R f (2)1133 1025 w 10 R f (\()1184 1065 w 10 I f (D)1225 1065 w 7 I f (l)1302 1084 w 7 S f (-)1302 1025 w 7 R f (2)1352 1025 w 10 S f (+)1435 1065 w 10 I f (D)1530 1065 w 7 I f (u)1607 1084 w 7 S f (-)1607 1025 w 7 R f (2)1657 1025 w 10 R f (\))1708 1065 w 7 S f (-)1752 1025 w 7 R f (1)1802 1025 w 10 S f (\374)1845 1023 w (\357)1845 1123 w (\376)1845 1223 w (\354)1910 1023 w (\357)1910 1123 w (\356)1910 1223 w 10 B f (0)2538 1170 w 10 I f (AD)1959 1050 w 7 I f (l)2097 1069 w 7 S f (-)2097 1010 w 7 R f (2)2147 1010 w 10 I f (D)2198 1050 w 7 I f (u)2275 1069 w 7 S f (-)2275 1010 w 7 R f (2)2325 1010 w 10 R f (\()2376 1050 w 10 I f (D)2417 1050 w 7 I f (l)2494 1069 w 7 S f (-)2494 1010 w 7 R f (2)2544 1010 w 10 S f (+)2627 1050 w 10 I f (D)2722 1050 w 7 I f (u)2799 1069 w 7 S f (-)2799 1010 w 7 R f (2)2849 1010 w 10 R f (\))2900 1050 w 7 S f (-)2944 1010 w 7 R f (1)2994 1010 w 10 I f (A)3045 1050 w 7 R f (T)3117 1010 w 10 I f (D)3242 1180 w 7 I f (l)3319 1199 w 7 S f (-)3319 1140 w 7 R f (2)3369 1140 w 10 S f (+)3452 1180 w 10 I f (D)3547 1180 w 7 I f (u)3624 1199 w 7 S f (-)3624 1140 w 7 R f (2)3674 1140 w 10 B f (0)3454 1070 w 10 S f (\374)3717 1023 w (\357)3717 1123 w (\376)3717 1223 w (\354)3782 1023 w (\357)3782 1123 w (\356)3782 1223 w 10 R f (\()3831 1170 w 10 I f (D)3872 1170 w 7 I f (l)3949 1189 w 7 S f (-)3949 1130 w 7 R f (2)3999 1130 w 10 S f (+)4082 1170 w 10 I f (D)4177 1170 w 7 I f (u)4254 1189 w 7 S f (-)4254 1130 w 7 R f (2)4304 1130 w 10 R f (\))4355 1170 w 7 S f (-)4399 1130 w 7 R f (1)4449 1130 w 10 I f (D)4500 1170 w 7 I f (l)4577 1189 w 7 S f (-)4577 1130 w 7 R f (2)4627 1130 w 10 I f (A)4678 1170 w 7 R f (T)4750 1130 w 10 I f (I)4299 1060 w (I)4883 1160 w 10 B f (0)4875 1060 w 10 S f (\374)4925 1023 w (\357)4925 1123 w (\376)4925 1223 w 10 R f (,)4982 1110 w (so we end up factoring)4 1249 1 720 1395 t 10 I f (AD)2079 1395 w 7 I f (l)2217 1414 w 7 S f (-)2217 1355 w 7 R f (2)2267 1355 w 10 I f (D)2318 1395 w 7 I f (u)2395 1414 w 7 S f (-)2395 1355 w 7 R f (2)2445 1355 w 10 R f (\()2496 1395 w 10 I f (D)2537 1395 w 7 I f (l)2614 1414 w 7 S f (-)2614 1355 w 7 R f (2)2664 1355 w 10 S f (+)2747 1395 w 10 I f (D)2842 1395 w 7 I f (u)2919 1414 w 7 S f (-)2919 1355 w 7 R f (2)2969 1355 w 10 R f (\))3020 1395 w 7 S f (-)3064 1355 w 7 R f (1)3114 1355 w 10 I f (A)3165 1395 w 7 R f (T)3237 1355 w 10 R f (rather than)1 514 1 3398 1395 t 10 I f (AD)4023 1395 w 7 S f (-)4167 1355 w 7 R f (2)4217 1355 w 10 I f (A)4268 1395 w 7 R f (T)4340 1355 w 10 R f ( that)1 261(. \(Note)1 388 2 4391 1395 t 10 I f (D)720 1515 w 7 I f (l)797 1534 w 7 S f (-)797 1475 w 7 R f (2)847 1475 w 10 I f (D)898 1515 w 7 I f (u)975 1534 w 7 S f (-)975 1475 w 7 R f (2)1025 1475 w 10 R f (\()1076 1515 w 10 I f (D)1117 1515 w 7 I f (l)1194 1534 w 7 S f (-)1194 1475 w 7 R f (2)1244 1475 w 10 S f (+)1327 1515 w 10 I f (D)1422 1515 w 7 I f (u)1499 1534 w 7 S f (-)1499 1475 w 7 R f (2)1549 1475 w 10 R f (\))1600 1515 w 7 S f (-)1644 1475 w 7 R f (1)1694 1475 w 10 R f ( bounds, see \2473 of [6], \2472.4)6 1102( other discussions of simple)4 1123( For)1 192(is a diagonal matrix.\))3 858 4 1765 1515 t (of [11], \2475.1 of [23], \2476 of [25].)7 1272 1 720 1635 t (The primal projective algorithm depicted below imposes simple bounds of 10)10 3113 1 970 1791 t 7 R f (4)4088 1751 w 10 R f (on all variables, using)3 883 1 4157 1791 t ( is an ingredient in the)5 926(\(15\). This)1 426 2 720 1911 t 10 I f (Record)2104 1911 w 10 R f ( dual algorithms depicted)3 1034( \(The)1 245(pictures [9] described at the end.)5 1337 3 2424 1911 t (below also use \(15\), but they can conveniently ignore simple bounds of)11 2852 1 720 2031 t 10 S f (+ \245)1 144 1 3597 2031 t 10 R f (.\))3741 2031 w 10 B f (Pictures of Polytopes)2 893 1 720 2271 t 10 R f (Any)970 2427 w 10 I f (x)1169 2427 w 10 R f (value that satisfies \(1b\) and \(1c\) is called a)8 1723 1 1240 2427 t 10 I f (feasible solution)1 661 1 2990 2427 t 10 R f ( set of)2 250( The)1 208(to the LP problem \(1\).)4 903 3 3679 2427 t (all such)1 312 1 720 2547 t 10 I f (x)1061 2547 w 10 R f (values is a)2 424 1 1134 2547 t 10 I f (polytope)1587 2547 w 10 R f ( any)1 172( Similarly,)1 451( intersection of finitely many half-spaces.)5 1673(, i.e., an)2 324 4 1931 2547 t 10 I f (y)4579 2547 w 10 R f (that satis-)1 389 1 4651 2547 t (fies \(2b\) is a feasible solution to the LP problem \(2\), and the set of all such)16 2988 1 720 2667 t 10 I f (y)3733 2667 w 10 R f (values is a polytope.)3 816 1 3802 2667 t (If)970 2823 w 10 I f (A)1070 2823 w 10 R f (or)1165 2823 w 10 I f (A)1282 2823 w 7 R f (T)1354 2783 w 10 R f (has the right shape \320 two or three more columns than rows \320 then we can depict the)17 3600 1 1440 2823 t ( cases)1 247( The)1 217( as we shall now see.)5 897(polytope of feasible solutions graphically,)4 1731 4 720 2943 t 10 I f (m)3849 2943 w 10 S f (=)3970 2943 w 10 R f (2 and)1 231 1 4074 2943 t 10 I f (n)4342 2943 w 10 S f (=)4441 2943 w 10 I f (m)4545 2943 w 10 S f (+)4666 2943 w 10 R f (2 \(two)1 270 1 4770 2943 t ( columns than rows\) can be misleading, since some things that are true in two dimensions)15 3610(rows or two more)3 710 2 720 3063 t ( the cases)2 396( Moreover,)1 475( to higher dimensions.)3 910(do not carry over)3 708 4 720 3183 t 10 I f (m)3241 3183 w 10 S f (=)3362 3183 w 10 R f (3 and)1 226 1 3466 3183 t 10 I f (n)3724 3183 w 10 S f (=)3823 3183 w 10 I f (m)3927 3183 w 10 S f (+)4048 3183 w 10 R f (3 lead to pictures that)4 888 1 4152 3183 t ( we shall concentrate on the latter cases.)7 1601( Therefore)1 442(have greater visual appeal.)3 1063 3 720 3303 t (If)970 3459 w 10 I f (m)1061 3459 w 10 S f (=)1182 3459 w 10 R f (3, then for)2 413 1 1286 3459 t 10 I f (F)1724 3459 w 10 R f (:)1826 3459 w 10 S f (=)1870 3459 w 10 I f (A)1974 3459 w 7 R f (T)2046 3419 w 10 R f (and)2122 3459 w 10 I f (f)2291 3459 w 10 R f (:)2376 3459 w 10 S f (=)2420 3459 w 10 I f (c)2524 3459 w 10 R f (the feasible region for \(2\) has the form)7 1543 1 2593 3459 t (\(16\))720 3639 w 10 I f ({ z)1 87 1 2473 3639 t 10 S f (\316)2601 3639 w 10 I f (I R)1 78 1 2713 3639 t 7 R f (3)2796 3599 w 10 R f (:)2847 3639 w 10 I f (Fz)2916 3639 w 10 S f (\243)3057 3639 w 10 I f ( .)1 33(f })1 92 2 3161 3639 t 10 R f ( If)1 124(It is easy to visualize such a region.)7 1476 2 720 3819 t 10 I f (F)2353 3819 w 7 I f (i)2425 3839 w 10 R f (denotes the)1 460 1 2486 3819 t 10 I f (i)2980 3819 w 10 R f (th row of)2 384 1 3008 3819 t 10 I f (F)3426 3819 w 10 R f (, then each row)3 636 1 3487 3819 t 10 I f (F)4157 3819 w 7 I f (i)4229 3839 w 10 R f (and corresponding)1 749 1 4291 3819 t (component)720 3939 w 10 I f (f)1208 3939 w 7 I f (i)1247 3959 w 10 R f (of)1319 3939 w 10 I f (f)1446 3939 w 10 R f (define a half-space,)2 815 1 1518 3939 t 10 I f ({ z)1 87 1 2377 3939 t 10 S f (\316)2505 3939 w 10 I f (I R)1 78 1 2617 3939 t 7 R f (3)2700 3899 w 10 R f (:)2751 3939 w 10 I f (F)2820 3939 w 7 I f (i)2892 3959 w 10 I f (z)2928 3939 w 10 S f (\243)3008 3939 w 10 I f (f)3112 3939 w 7 I f (i)3151 3959 w 10 I f (})3187 3939 w 10 R f ( the intersection of these half-)5 1279(, and \(16\) is)3 534 2 3227 3939 t ( one or more)3 519( depict \(16\), we may simply plot the edges of \(16\) that are visible when we look in)17 3352(spaces. To)1 449 3 720 4059 t ( direction, vantage point,)3 1005( discuss the choice of view)5 1093( \(We)1 225(view directions from one or more vantage points.)7 1997 4 720 4179 t (and view angle later.\))3 864 1 720 4299 t (On the other hand, if)4 861 1 970 4455 t 10 I f (n)1865 4455 w 10 S f (=)1964 4455 w 10 I f (m)2068 4455 w 10 S f (+)2189 4455 w 10 R f (3, then it is only slightly harder to visualize the feasible region for)12 2747 1 2293 4455 t ( Assume)1 375( is slightly harder, because it requires a change of variables.)10 2413(\(1\). This)1 372 3 720 4575 t 10 I f (A)3908 4575 w 10 R f ( and let)2 298(has full rank,)2 530 2 3997 4575 t 10 I f (F)4852 4575 w 10 R f (by)4940 4575 w (any matrix whose columns span the null space of)8 2004 1 720 4695 t 10 I f (A)2755 4695 w 10 R f ( assumption,)1 512(. By)1 198 2 2816 4695 t 10 I f (A)3557 4695 w 10 R f (has full rank, so)3 656 1 3649 4695 t 10 I f (F)4336 4695 w 10 R f (has 3 columns;)2 612 1 4428 4695 t 10 I f (F)720 4815 w 10 S f (\316)822 4815 w 10 I f (I R)1 78 1 934 4815 t 7 I f (n)1017 4775 w 7 S f (\264)1057 4775 w 7 R f (3)1101 4775 w 10 R f (can be any rank 3 matrix such that)7 1428 1 1177 4815 t 10 I f (AF)2638 4815 w 10 S f (=)2809 4815 w 10 B f (0)2913 4815 w 10 R f (. If)1 149 1 2963 4815 t 10 I f (x)3145 4815 w 10 S f (\260 \316)1 152 1 3189 4815 t 10 I f (I R)1 78 1 3382 4815 t 7 I f (n)3465 4775 w 10 R f ( for \(1\), then for)4 673(is any feasible point)3 826 2 3541 4815 t (any feasible)1 500 1 720 4935 t 10 I f (x)1266 4935 w 10 R f (there is a unique)3 723 1 1357 4935 t 10 I f (z)2127 4935 w 10 S f (\316)2207 4935 w 10 I f (I R)1 78 1 2319 4935 t 7 R f (3)2402 4895 w 10 R f (such that)1 380 1 2492 4935 t 10 I f (x)2919 4935 w 10 S f (=)3012 4935 w 10 I f (x)3116 4935 w 10 S f (\260 -)1 144 1 3160 4935 t 10 I f (Fz)3353 4935 w 10 R f (, and, conversely, if)3 853 1 3453 4935 t 10 I f (z)4353 4935 w 10 S f (\316)4433 4935 w 10 I f (I R)1 78 1 4545 4935 t 7 R f (3)4628 4895 w 10 R f (satisfies)4718 4935 w 10 I f (Fz)720 5055 w 10 S f (\243)861 5055 w 10 I f (x)957 5055 w 10 S f (\260)1001 5055 w 10 R f (, then)1 232 1 1041 5055 t 10 I f (x)1308 5055 w 10 R f (:)1393 5055 w 10 S f (=)1437 5055 w 10 I f (x)1541 5055 w 10 S f (\260 -)1 144 1 1585 5055 t 10 I f (Fz)1778 5055 w 10 R f ( the feasible region for \(1\) corresponds to \(16\) with)9 2129( Thus)1 259(is feasible for \(1\).)3 739 3 1913 5055 t 10 I f (f)720 5175 w 10 R f (:)805 5175 w 10 S f (=)849 5175 w 10 I f (x)953 5175 w 10 S f (\260)997 5175 w 10 R f (.)1037 5175 w (One complication with this latest choice of \(16\) is that)9 2245 1 970 5331 t 10 I f (F)3248 5331 w 10 R f ( is)1 101( way to say this)4 654( Another)1 385(is not unique.)2 558 4 3342 5331 t ( we could choose some nonsingular)5 1478(that, given \(16\),)2 662 2 720 5451 t 10 I f (G)2896 5451 w 10 S f (\316)3009 5451 w 10 I f (I R)1 78 1 3121 5451 t 7 R f (3)3204 5411 w 7 S f (\264)3244 5411 w 7 R f (3)3288 5411 w 10 R f (and change to the variables)4 1130 1 3367 5451 t 10 I f (w)4533 5451 w 10 R f (:)4641 5451 w 10 S f (=)4685 5451 w 10 I f (G)4789 5451 w 7 S f (-)4872 5411 w 7 R f (1)4922 5411 w 10 I f (z)4973 5451 w 10 R f (;)5012 5451 w (this amounts to replacing)3 1011 1 720 5571 t 10 I f (F)1757 5571 w 10 R f (by)1844 5571 w 10 I f (FG)1970 5571 w 10 R f ( variables can profoundly affect pictures of the)7 1878( a change of)3 487( Such)1 251(in \(16\).)1 295 4 2129 5571 t ( the edges of)3 528( Indeed,)1 353( structure.)1 406(polytope \(drawn as suggested above\), but it does not affect the polytope's)11 3033 4 720 5691 t (\(16\) may be characterized by a set)6 1409 1 720 5811 t 10 I f (S)2161 5811 w 10 S f (=)2260 5811 w 10 I f (S)2364 5811 w 10 R f (\()2422 5811 w 10 I f (F)2463 5811 w 10 R f (,)2532 5811 w 10 I f (f)2573 5811 w 10 R f ( \()1 66(\) of quadruples of distinct integers, such that)7 1830 2 2625 5811 t 10 I f (i)4529 5811 w 10 R f (,)4565 5811 w 10 I f (j)4606 5811 w 10 R f (,)4642 5811 w 10 I f (k)4675 5811 w 10 R f (,)4727 5811 w 10 I f (l)4760 5811 w 10 R f (\))4796 5811 w 10 S f (\316)4878 5811 w 10 I f (S)4990 5811 w 10 R f (corresponds to the edge)3 945 1 720 5931 t (\(17\))720 6111 w 10 I f ({ z)1 87 1 1762 6111 t 10 S f (\316)1890 6111 w 10 I f (I R)1 78 1 2002 6111 t 7 R f (3)2085 6071 w 10 R f (:)2136 6111 w 10 I f (F)2205 6111 w 7 I f (i)2277 6131 w 10 I f (z)2313 6111 w 10 S f (=)2401 6111 w 10 I f (f)2513 6111 w 7 I f (i)2552 6131 w 10 R f (,)2588 6111 w 10 I f (F)2654 6111 w 7 I f (j)2726 6131 w 10 I f (z)2762 6111 w 10 S f (=)2850 6111 w 10 I f (f)2962 6111 w 7 I f (j)3001 6131 w 10 R f (,)3037 6111 w 10 I f (F)3103 6111 w 7 I f (k)3175 6131 w 10 I f (z)3222 6111 w 10 S f (\243)3302 6111 w 10 I f (f)3406 6111 w 7 I f (k)3445 6131 w 10 R f (,)3492 6111 w 10 I f (F)3558 6111 w 7 I f (l)3630 6131 w 10 I f (z)3666 6111 w 10 S f (\243)3746 6111 w 10 I f (f)3850 6111 w 7 I f (l)3889 6131 w 10 I f (} .)1 73 1 3925 6111 t (S)720 6291 w 10 R f (remains the same if we change)5 1227 1 795 6291 t 10 I f (F)2047 6291 w 10 R f (to)2133 6291 w 10 I f (FG)2236 6291 w 10 R f (, i.e.,)1 197 1 2369 6291 t 10 I f (S)2591 6291 w 10 R f (\()2649 6291 w 10 I f (FG)2690 6291 w 10 R f (,)2831 6291 w 10 I f (f)2872 6291 w 10 R f (\))2924 6291 w 10 S f (\272)3006 6291 w 10 I f (S)3102 6291 w 10 R f (\()3160 6291 w 10 I f (F)3201 6291 w 10 R f (,)3270 6291 w 10 I f (f)3311 6291 w 10 R f (\).)3363 6291 w (We can make)2 572 1 970 6447 t 10 I f (F)1582 6447 w 10 R f ( columns be orthonormal, i.e., that)5 1454(unique, modulo rotations, by insisting that its)6 1903 2 1683 6447 t 10 I f (F)720 6567 w 7 R f (T)792 6527 w 10 I f (F)851 6567 w 10 S f (=)961 6567 w 10 I f (I)1065 6567 w 10 R f ( in)1 135( a natural interpretation:)3 983( has the added benefit that the necessary projections then have)10 2563(. This)1 261 4 1098 6567 t (terms of the variables)3 871 1 720 6687 t 10 I f (z)1619 6687 w 10 R f (in \(16\), they are just)4 823 1 1686 6687 t 10 I f (FF)2538 6687 w 7 R f (T)2671 6647 w 10 R f ( most of the pictures shown below,)6 1420(. \(For)1 251 2 2722 6687 t 10 I f (F)4422 6687 w 10 R f (was orthogo-)1 528 1 4512 6687 t ( the stabilized Gram-Schmidt algorithm; for views of the original polytope, e.g., figures 2\26114,)13 3895(nalized by)1 425 2 720 6807 t (and for the)2 432 1 720 6927 t 10 I f (Record)1177 6927 w 10 R f (pictures shown at the end,)4 1040 1 1490 6927 t 10 I f (F)2555 6927 w 10 R f (was)2641 6927 w 10 I f (not)2821 6927 w 10 R f (orthogonalized.\))2974 6927 w (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 6 7 %%Page: 7 8 /saveobj save def mark 8 pagesetup 10 R f (- 7 -)2 166 1 2797 480 t 10 B f (Generating and Viewing Polytopes)3 1481 1 720 840 t 10 R f ( for linear programming problems \(1\))5 1540(To generate 3 dimensional polytopes, i.e., the feasible regions)8 2530 2 970 996 t (or \(2\) with)2 437 1 720 1116 t 10 I f (n)1187 1116 w 10 S f (=)1286 1116 w 10 I f (m)1390 1116 w 10 S f (+)1511 1116 w 10 R f (3 or)1 163 1 1615 1116 t 10 I f (m)1807 1116 w 10 S f (=)1928 1116 w 10 R f (3, it was convenient to select tangents to an ellipsoid about the origin, and)13 3008 1 2032 1116 t ( 1 gives the resulting)4 857( Table)1 283(then to jiggle them in or out a little.)8 1468 3 720 1236 t 10 I f (A)3359 1236 w 10 R f (,)3420 1236 w 10 I f (b)3477 1236 w 10 R f (, and)1 201 1 3527 1236 t 10 I f (c)3760 1236 w 10 R f (defining the dual problem \(2\))4 1204 1 3836 1236 t (we shall consider below.)3 987 1 720 1356 t 8 S f (_ ______________________________________________________________________________________________________)1 4115 1 822 1426 t 8 I f (i A)1 348 1 891 1526 t 5 R f (1 ,)1 42 1 1247 1542 t 5 I f (i)1293 1542 w 8 I f (A)1670 1526 w 5 R f (2 ,)1 42 1 1727 1542 t 5 I f (i)1773 1542 w 8 I f (A)2150 1526 w 5 R f (3 ,)1 42 1 2207 1542 t 5 I f (i)2253 1542 w 8 I f (c)2640 1526 w 5 I f (i)2683 1542 w 8 I f (i A)1 386 1 2971 1526 t 5 R f (1 ,)1 42 1 3365 1542 t 5 I f (i)3411 1542 w 8 I f (A)3805 1526 w 5 R f (2 ,)1 42 1 3862 1542 t 5 I f (i)3908 1542 w 8 I f (A)4265 1526 w 5 R f (3 ,)1 42 1 4322 1542 t 5 I f (i)4368 1542 w 8 I f (c)4735 1526 w 5 I f (i)4778 1542 w 8 S f (_ ______________________________________________________________________________________________________)1 4115 1 822 1546 t 8 R f ( 2.64)1 300( \2610.891049)1 540( 1.1329)1 455( 0.776419)1 460( 48)1 420( 0 10)2 960( 0)1 500(1 1)1 240 8 902 1646 t ( 2.64)1 300( \2610.696962)1 540( 1.1012)1 455( 0.683382)1 460( 49)1 420( 0 10)2 960( 0)1 500(2 \2611)1 240 8 902 1746 t ( 2.64)1 300( \2610.392579)1 460( 0.993245)1 535( 0.516868)1 460( 50)1 420( 0 10)2 960( 1)1 500(3 0)1 240 8 902 1846 t ( 2.64)1 300( \2610.305981)1 460( 0.952607)1 535( 0.465984)1 460( 51)1 420( \2611 0 10)3 1460(4 0)1 240 7 902 1946 t ( 2.64)1 300( \2610.106338)1 460( 0.844541)1 535( 0.343589)1 460( 52)1 420( 1 10)2 960( 0)1 500(5 0)1 240 8 902 2046 t ( 0.118341 2.64)2 760( 0.700211)1 575( 0.19781)1 420( 53)1 420( 10)1 500( \2611)1 460( 0)1 500(6 0)1 240 8 902 2146 t ( 0.361075 2.64)2 760( 0.517064)1 495( 0.0306888)1 500( 2.64 54)2 700( \2610.55927)1 420( 0.326798)1 500(7 \2610.948109)1 500 7 902 2246 t ( \2611.03499 2.64)2 840( 1.1356)1 455( 0.892578)1 460( 55)1 320( 2.64)1 340( \2610.459551)1 460( 0.457124)1 500(8 \2610.959071)1 500 8 902 2346 t ( \2610.883178 2.64)2 800( 1.13888)1 495( 0.825649)1 460( 56)1 200( 2.63736)1 460( \2610.356824)1 460( 0.539314)1 500(9 \2610.920668)1 500 8 902 2446 t ( \2610.685394 2.64)2 800( 1.10255)1 495( 0.723153)1 460( 57)1 200( 2.64132)1 460( \2610.248836)1 460( 0.594019)1 500(10 \2610.850045)1 540 8 862 2546 t ( \2610.525279 2.64)2 800( 1.05054)1 495( 0.631666)1 460( 58)1 320( 2.64)1 340( \2610.109757)1 460( 0.630421)1 500(11 \2610.726585)1 540 8 862 2646 t ( 2.64)1 300( \2610.333092)1 460( 0.967662)1 535( 0.514144)1 460( 59)1 200( 0.0683571 2.63472)2 920( 0.630806)1 500(12 \2610.524343)1 540 8 862 2746 t ( 2.64)1 300( \2610.155221)1 460( 0.873909)1 535( 60 0.398956)2 700( 2.6136)1 420( 0.241176)1 460( 0.582318)1 500(13 \2610.281476)1 540 8 862 2846 t ( 2.64)1 260( 0.0256707)1 500( 0.763148)1 535( 0.276002)1 460( 61)1 320( 2.64)1 340( \2610.910721)1 460( 0.649988)1 500(14 \2610.277238)1 540 9 862 2946 t ( 2.64)1 340( \2611.27827)1 460( 1.02965)1 535( 1.21797)1 420( 62)1 320( 2.64)1 340( \2610.760027)1 460( 0.808338)1 500(15 \2610.273845)1 540 9 862 3046 t ( \2610.985681 2.64)2 800( 1.16083)1 575( 1.1142)1 380( 63)1 320( 2.64)1 340( \2610.684334)1 460( 0.841367)1 540(16 \2610.26471)1 500 8 862 3146 t ( \2610.624873 2.64)2 800( 1.09433)1 495( 0.877339)1 460( 64)1 320( 2.64)1 340( \2610.431214)1 460( 0.867007)1 500(17 \2610.220614)1 540 8 862 3246 t ( 2.64)1 300( \2610.302028)1 460( 0.956773)1 535( 0.628164)1 460( 65)1 320( 2.64)1 340( \2610.261174)1 460( 0.838421)1 500(18 \2610.183672)1 540 9 862 3346 t ( 0.247611 2.64)2 760( 0.606655)1 535( 0.148637)1 460( 66)1 320( \2610.0980917 2.64)2 840( 0.78565)1 460(19 \2610.144191)1 540 7 862 3446 t ( 2.64)1 340( \2611.11092)1 460( 1.14455)1 535( 1.33984)1 420( 67)1 320( 2.64)1 340( 0.652504 0.166939)2 920(20 \2610.0724596)1 580 8 862 3546 t ( 2.64)1 340( \2610.93779)1 460( 1.15942)1 535( 1.23592)1 420( 68)1 320( 2.64)1 340( 0.566164 0.295867)2 920(21 \2610.0341189)1 580 8 862 3646 t ( \2610.799053 2.64)2 800( 1.14113)1 535( 69 1.13625)2 660( 2.6532)1 420( \2610.772093)1 460(22 0.0403285 0.955243)2 1040 6 862 3746 t ( 2.64)1 340( \2610.62453)1 460( 1.09404)1 495( 70 0.997802)2 700( 2.6268)1 420( \2610.435773)1 460(23 0.0312882 0.935653)2 1040 7 862 3846 t ( \2610.41278 2.64)2 840( 1.0102)1 455( 0.815322)1 460( 71)1 320( 2.64)1 340( \2610.110836)1 460( 0.817498)1 540(24 0.02042)1 500 8 862 3946 t ( 2.64)1 300( \2610.165629)1 460( 0.882642)1 535( 72 0.586217)2 700( 2.6664)1 420( \2610.589586)1 460(25 0.0934504 0.977023)2 1040 7 862 4046 t ( 2.64)1 260( 0.0876082)1 500( 0.722656)1 535( 0.335572)1 460( 73)1 320( 2.64)1 340( \2610.292568)1 460(26 0.0695163 0.900807)2 1040 8 862 4146 t ( 0.337626 2.64)2 760( 0.536115)1 495( 0.0725957)1 500( 74)1 200( 2.63208)1 420( 0.0683491)1 540(27 0.0356949 0.72303)2 1000 7 862 4246 t ( 2.64)1 340( \2611.12758)1 460( 1.08863)1 535( 1.64933)1 420( 2.64 75)2 700( \2611.15598)1 420( 0.898464)1 500(28 0.434916)1 540 8 862 4346 t ( \2610.834403 2.63736)2 920( 1.12276)1 535( 1.43556)1 420( 76)1 320( 2.64)1 340( \2610.982135)1 500( 1.03648)1 460(29 0.421701)1 540 8 862 4446 t ( 2.6532)1 380( \2610.409256)1 460( 0.998721)1 615( 1.0079)1 380( 77)1 320( 2.64)1 340( \2610.877737)1 500( 1.05712)1 460(30 0.401872)1 540 9 862 4546 t ( 2.63208)1 420( 0.142344)1 500( 0.68317)1 495( 0.348205)1 460( 78)1 320( 2.64)1 340( \2610.655343)1 500( 1.04371)1 460(31 0.348666)1 540 9 862 4646 t ( 2.64)1 340( \2611.01482)1 460( 1.13218)1 535( 1.53321)1 420( 79)1 320( 2.64)1 340( \2610.471783)1 460( 0.995979)1 500(32 0.297745)1 540 9 862 4746 t ( \2610.843658 2.63472)2 920( 1.13052)1 535( 1.39856)1 420( 80)1 320( 2.64)1 340( \2610.253538)1 460( 0.908603)1 500(33 0.231351)1 540 8 862 4846 t ( \2610.641492 2.64264)2 920( 1.08733)1 535( 1.21252)1 420( 81)1 320( 0.0574528 2.64)2 800( 0.736479)1 500(34 0.127643)1 540 7 862 4946 t ( 2.64)1 300( \2610.152374)1 460( 0.871521)1 535( 0.689548)1 460( 82)1 320( 2.64)1 340(35 0.0380502 0.561958 0.304447)3 1500 7 862 5046 t ( 2.64)1 340( \2611.07123)1 420( 0.970384)1 575( 1.89625)1 420( 83)1 320( 2.64)1 340( \2610.995647)1 500( 1.11609)1 460(36 0.733312)1 540 9 862 5146 t ( \2610.968253 2.64)2 800( 1.02483)1 535( 1.83863)1 420( 84)1 320( 2.64)1 340( \2610.891662)1 500( 1.12071)1 460(37 0.695319)1 540 8 862 5246 t ( \2610.759851 2.64)2 800( 1.04786)1 535( 1.64847)1 420( 85)1 320( 2.64)1 340( \2610.774384)1 500( 1.10863)1 500(38 0.64696)1 500 8 862 5346 t ( \2610.499665 2.64)2 800( 0.99948)1 535( 1.34597)1 420( 86)1 320( 1.0851 \2610.664601 2.64)3 1300(39 0.597801)1 540 6 862 5446 t ( 2.64)1 300( \2610.205429)1 460( 0.882985)1 535( 0.951747)1 460( 87)1 320( 2.64)1 340( \2610.527407)1 500( 1.04265)1 460(40 0.532214)1 540 9 862 5546 t ( 0.102808 2.64)2 760( 0.706316)1 535( 0.492661)1 460( 88)1 320( 2.64)1 340( \2610.361111)1 460( 0.975156)1 500(41 0.447604)1 540 8 862 5646 t ( 2.63736)1 420( \2610.834525)1 460( 0.842735)1 575( 2.01458)1 420( 89)1 320( 2.64)1 340( \2610.209721)1 460( 0.900473)1 500(42 0.366364)1 540 9 862 5746 t ( 2.64264)1 420( \2610.661818)1 460( 0.902107)1 655( 1.854)1 340( 90)1 320( 2.64)1 340( \2610.077384)1 460( 0.825726)1 500(43 0.292333)1 540 9 862 5846 t ( 2.64)1 340( \2610.44401)1 420( 0.900002)1 575( 1.56706)1 420( 91)1 320( 2.64)1 300( 0.72715 0.0779788)2 1000(44 0.201976)1 540 8 862 5946 t ( 2.64528)1 420( \2610.195943)1 460( 0.836564)1 575( 1.17334)1 420( 2.64 92)2 700( \2611.28126)1 420( 0.904507)1 500(45 0.860133)1 540 8 862 6046 t ( 2.63472)1 380( 0.0654775)1 500( 0.716115)1 535( 0.699656)1 460( 2.64 93)2 700( \2611.22401)1 460( 1.02706)1 460(46 0.879349)1 540 8 862 6146 t ( 0.404038 2.63208)2 880( \2617.13499e\26116 0.481514)2 995( 94)1 320( 2.64)1 460( \2611.012)1 380( 1.12981)1 460(47 0.826318)1 540 7 862 6246 t 8 S f ( \347)1 -4115(_ ______________________________________________________________________________________________________)1 4115 2 822 6266 t (\347)822 6226 w (\347)822 6146 w (\347)822 6066 w (\347)822 5986 w (\347)822 5906 w (\347)822 5826 w (\347)822 5746 w (\347)822 5666 w (\347)822 5586 w (\347)822 5506 w (\347)822 5426 w (\347)822 5346 w (\347)822 5266 w (\347)822 5186 w (\347)822 5106 w (\347)822 5026 w (\347)822 4946 w (\347)822 4866 w (\347)822 4786 w (\347)822 4706 w (\347)822 4626 w (\347)822 4546 w (\347)822 4466 w (\347)822 4386 w (\347)822 4306 w (\347)822 4226 w (\347)822 4146 w (\347)822 4066 w (\347)822 3986 w (\347)822 3906 w (\347)822 3826 w (\347)822 3746 w (\347)822 3666 w (\347)822 3586 w (\347)822 3506 w (\347)822 3426 w (\347)822 3346 w (\347)822 3266 w (\347)822 3186 w (\347)822 3106 w (\347)822 3026 w (\347)822 2946 w (\347)822 2866 w (\347)822 2786 w (\347)822 2706 w (\347)822 2626 w (\347)822 2546 w (\347)822 2466 w (\347)822 2386 w (\347)822 2306 w (\347)822 2226 w (\347)822 2146 w (\347)822 2066 w (\347)822 1986 w (\347)822 1906 w (\347)822 1826 w (\347)822 1746 w (\347)822 1666 w (\347)822 1586 w (\347)822 1506 w (\347)2872 6266 w (\347)2872 6226 w (\347)2872 6146 w (\347)2872 6066 w (\347)2872 5986 w (\347)2872 5906 w (\347)2872 5826 w (\347)2872 5746 w (\347)2872 5666 w (\347)2872 5586 w (\347)2872 5506 w (\347)2872 5426 w (\347)2872 5346 w (\347)2872 5266 w (\347)2872 5186 w (\347)2872 5106 w (\347)2872 5026 w (\347)2872 4946 w (\347)2872 4866 w (\347)2872 4786 w (\347)2872 4706 w (\347)2872 4626 w (\347)2872 4546 w (\347)2872 4466 w (\347)2872 4386 w (\347)2872 4306 w (\347)2872 4226 w (\347)2872 4146 w (\347)2872 4066 w (\347)2872 3986 w (\347)2872 3906 w (\347)2872 3826 w (\347)2872 3746 w (\347)2872 3666 w (\347)2872 3586 w (\347)2872 3506 w (\347)2872 3426 w (\347)2872 3346 w (\347)2872 3266 w (\347)2872 3186 w (\347)2872 3106 w (\347)2872 3026 w (\347)2872 2946 w (\347)2872 2866 w (\347)2872 2786 w (\347)2872 2706 w (\347)2872 2626 w (\347)2872 2546 w (\347)2872 2466 w (\347)2872 2386 w (\347)2872 2306 w (\347)2872 2226 w (\347)2872 2146 w (\347)2872 2066 w (\347)2872 1986 w (\347)2872 1906 w (\347)2872 1826 w (\347)2872 1746 w (\347)2872 1666 w (\347)2872 1586 w (\347)2872 1506 w (\347)2892 6266 w (\347)2892 6226 w (\347)2892 6146 w (\347)2892 6066 w (\347)2892 5986 w (\347)2892 5906 w (\347)2892 5826 w (\347)2892 5746 w (\347)2892 5666 w (\347)2892 5586 w (\347)2892 5506 w (\347)2892 5426 w (\347)2892 5346 w (\347)2892 5266 w (\347)2892 5186 w (\347)2892 5106 w (\347)2892 5026 w (\347)2892 4946 w (\347)2892 4866 w (\347)2892 4786 w (\347)2892 4706 w (\347)2892 4626 w (\347)2892 4546 w (\347)2892 4466 w (\347)2892 4386 w (\347)2892 4306 w (\347)2892 4226 w (\347)2892 4146 w (\347)2892 4066 w (\347)2892 3986 w (\347)2892 3906 w (\347)2892 3826 w (\347)2892 3746 w (\347)2892 3666 w (\347)2892 3586 w (\347)2892 3506 w (\347)2892 3426 w (\347)2892 3346 w (\347)2892 3266 w (\347)2892 3186 w (\347)2892 3106 w (\347)2892 3026 w (\347)2892 2946 w (\347)2892 2866 w (\347)2892 2786 w (\347)2892 2706 w (\347)2892 2626 w (\347)2892 2546 w (\347)2892 2466 w (\347)2892 2386 w (\347)2892 2306 w (\347)2892 2226 w (\347)2892 2146 w (\347)2892 2066 w (\347)2892 1986 w (\347)2892 1906 w (\347)2892 1826 w (\347)2892 1746 w (\347)2892 1666 w (\347)2892 1586 w (\347)2892 1506 w (\347)4937 6266 w (\347)4937 6226 w (\347)4937 6146 w (\347)4937 6066 w (\347)4937 5986 w (\347)4937 5906 w (\347)4937 5826 w (\347)4937 5746 w (\347)4937 5666 w (\347)4937 5586 w (\347)4937 5506 w (\347)4937 5426 w (\347)4937 5346 w (\347)4937 5266 w (\347)4937 5186 w (\347)4937 5106 w (\347)4937 5026 w (\347)4937 4946 w (\347)4937 4866 w (\347)4937 4786 w (\347)4937 4706 w (\347)4937 4626 w (\347)4937 4546 w (\347)4937 4466 w (\347)4937 4386 w (\347)4937 4306 w (\347)4937 4226 w (\347)4937 4146 w (\347)4937 4066 w (\347)4937 3986 w (\347)4937 3906 w (\347)4937 3826 w (\347)4937 3746 w (\347)4937 3666 w (\347)4937 3586 w (\347)4937 3506 w (\347)4937 3426 w (\347)4937 3346 w (\347)4937 3266 w (\347)4937 3186 w (\347)4937 3106 w (\347)4937 3026 w (\347)4937 2946 w (\347)4937 2866 w (\347)4937 2786 w (\347)4937 2706 w (\347)4937 2626 w (\347)4937 2546 w (\347)4937 2466 w (\347)4937 2386 w (\347)4937 2306 w (\347)4937 2226 w (\347)4937 2146 w (\347)4937 2066 w (\347)4937 1986 w (\347)4937 1906 w (\347)4937 1826 w (\347)4937 1746 w (\347)4937 1666 w (\347)4937 1586 w (\347)4937 1506 w 10 B f (Table 1:)1 353 1 1543 6436 t 10 I f (A)1946 6436 w 10 R f (and)2032 6436 w 10 I f (c)2201 6436 w 10 R f (for \(2\);)1 285 1 2270 6436 t 10 I f (b)2580 6436 w 10 S f (=)2679 6436 w 10 R f ( 881186 ,)2 341( 2.)1 116(\( 3. 305617 ,)3 457 3 2783 6436 t 10 S f (-)3746 6436 w 10 R f (1. 11435 \).)2 399 1 3817 6436 t ( polytope.)1 405(Figure 1 depicts some details of drawing a two-dimensional picture of a three-dimensional)12 3665 2 970 6712 t (Before drawing the polytope, we must choose a viewpoint)8 2399 1 720 6832 t 10 I f (v)3153 6832 w 10 R f (, view direction)2 642 1 3197 6832 t 10 I f (d)3873 6832 w 10 R f (, and angle of view)4 798 1 3923 6832 t 10 S f (a)4755 6832 w 10 R f (. We)1 222 1 4818 6832 t ( the viewpoint and the polytope.)5 1293(then imagine a view screen orthogonal to the direction of view and between)12 3027 2 720 6952 t ( view angle defines)3 779( The)1 232( scale, the exact position of the view screen is immaterial.\))10 2360(\(Because of how things)3 949 4 720 7072 t (a view cone whose vertex is at the viewpoint)8 1855 1 720 7192 t 10 I f (v)2608 7192 w 10 R f (and whose center lies along the view direction)7 1905 1 2685 7192 t 10 I f (d)4623 7192 w 10 R f ( will)1 190(; we)1 177 2 4673 7192 t ( the cone have a circular)5 1001( could let)2 386( [We)1 228(only be able to see parts of the polytope that fall within this cone.)13 2705 4 720 7312 t (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 7 8 %%Page: 8 9 /saveobj save def mark 9 pagesetup 10 R f (- 8 -)2 166 1 2797 480 t ( is more convenient if this)5 1051(cross section, so that its intersection with the view screen would be a circle, but it)15 3269 2 720 840 t ( simplicity we shall insist that this intersection be square, though allowing)11 3049( For)1 197(intersection is rectangular.)2 1074 3 720 960 t ( draw the polytope, we)4 932( To)1 166( matters little.])2 596(separate horizontal and vertical angles of view would complicate)8 2626 4 720 1080 t ( project)1 306( To)1 165( of the next paragraph.)4 916(project its visible edges onto the view screen; ``visibility'' is the subject)11 2933 4 720 1200 t ( the edge's endpoints and draw the segment between their images on the view screen.)14 3524(an edge, we project)3 796 2 720 1320 t (Thus in figure 1, the segment from)6 1396 1 720 1440 t 10 I f (x)2142 1440 w 10 S f (\242)2194 1440 w 10 R f (to)2245 1440 w 10 I f (y)2349 1440 w 10 S f (\242)2401 1440 w 10 R f ( the polytope edge from)4 954(on the view screen is the image of)7 1368 2 2452 1440 t 10 I f (x)4799 1440 w 10 R f (to)4868 1440 w 10 I f (y)4971 1440 w 10 R f (.)5015 1440 w ( on the image screen so that those on the edges of the view cone's intersection)15 3209(Finally, we scale the points)4 1111 2 720 1560 t (with the view screen are at the edge of our picture.)10 2019 1 720 1680 t cleartomark saveobj restore %%BeginGlobal % % Version 3.3 drawing procedures for dpost. Automatically pulled in, but only % when needed. % /inpath false def /savematrix matrix def /Dl { inpath {pop pop neg lineto} {newpath neg moveto neg lineto stroke} ifelse } bind def /De { /y1 exch 2 div def /x1 exch 2 div def /savematrix savematrix currentmatrix def neg exch x1 add exch translate x1 y1 scale 0 0 1 0 360 inpath {1 0 moveto arc savematrix setmatrix} {newpath arc savematrix setmatrix stroke} ifelse } bind def /Da { /dy2 exch def /dx2 exch def /dy1 exch def /dx1 exch def dy1 add neg exch dx1 add exch dx1 dx1 mul dy1 dy1 mul add sqrt dy1 dx1 neg atan dy2 neg dx2 atan inpath {arc} {newpath arc stroke} ifelse } bind def /DA { /dy2 exch def /dx2 exch def /dy1 exch def /dx1 exch def dy1 add neg exch dx1 add exch dx1 dx1 mul dy1 dy1 mul add sqrt dy1 dx1 neg atan dy2 neg dx2 atan inpath {arcn} {newpath arcn stroke} ifelse } bind def /Ds { /y2 exch def /x2 exch def /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 5 x1 mul add 6 div y0 5 y1 mul add -6 div x2 5 x1 mul add 6 div y2 5 y1 mul add -6 div x1 x2 add 2 div y1 y2 add -2 div inpath {curveto} {newpath x0 x1 add 2 div y0 y1 add -2 div moveto curveto stroke} ifelse } bind def %%EndGlobal /saveobj save def mark 10 R f 0.1 setlinewidth 3600 4002 720 4002 Dl 10 I f (d)3647 4022 w 5040 4002 3744 4002 Dl 5040 4002 4968 4020 Dl 5040 4002 4968 3984 Dl 1363 4323 -643 -321 643 -321 Da 10 S f (a)1476 3842 w 10 R f (= view angle)2 516 1 1564 3842 t 2008 4645 -1288 -643 1440 0 Da 10 S f (a)2154 4418 w 10 I f (/)2225 4418 w 10 R f (2)2261 4418 w 7 R f (.)2870 2925 w (.)2870 2963 w (.)2870 3002 w (.)2870 3040 w (.)2870 3079 w (.)2870 3117 w (.)2870 3156 w (.)2870 3195 w 10 R f 0.1 setlinewidth 2880 4434 2880 3192 Dl 7 R f (.)2870 4437 w (.)2870 4473 w (.)2870 4509 w (.)2870 4545 w (.)2870 4581 w (.)2870 4617 w (.)2870 4653 w (.)2870 4689 w (.)2870 4725 w (.)2870 4761 w (.)2870 4797 w (.)2870 4833 w (.)2870 4869 w (.)2870 4905 w (.)2870 4941 w (.)2870 4977 w (.)2870 5013 w (.)2870 5049 w (.)2870 5085 w 10 R f 0.1 setlinewidth 4320 4722 3600 2922 Dl 4860 3462 4320 4722 Dl 3600 2922 4860 3462 Dl 10 I f (x)3578 2870 w (y)4298 4814 w (x)2770 3158 w 10 S f (\242)2822 3158 w 10 I f (y)2770 4526 w 10 S f (\242)2822 4526 w 5040 1842 720 4002 Dl 5039 1842 4983 1890 Dl 5039 1842 4967 1857 Dl 5040 6162 720 4002 Dl 5039 6161 4967 6146 Dl 5039 6161 4983 6113 Dl 753 3990 720 4002 Dl 820 3964 787 3976 Dl 888 3938 855 3950 Dl 956 3913 923 3925 Dl 1023 3888 990 3900 Dl 1092 3863 1059 3875 Dl 1159 3837 1126 3849 Dl 1227 3812 1194 3824 Dl 1295 3786 1262 3798 Dl 1362 3761 1329 3773 Dl 1430 3735 1397 3747 Dl 1498 3710 1465 3722 Dl 1565 3684 1532 3696 Dl 1634 3659 1601 3671 Dl 1701 3634 1668 3646 Dl 1769 3609 1736 3621 Dl 1837 3583 1804 3595 Dl 1905 3558 1872 3570 Dl 1972 3532 1939 3544 Dl 2040 3506 2007 3518 Dl 2108 3481 2075 3493 Dl 2176 3456 2143 3468 Dl 2244 3430 2211 3442 Dl 2311 3405 2278 3417 Dl 2379 3380 2346 3392 Dl 2447 3354 2414 3366 Dl 2514 3329 2481 3341 Dl 2582 3303 2549 3315 Dl 2650 3278 2617 3290 Dl 2718 3252 2685 3264 Dl 2786 3227 2753 3239 Dl 2853 3202 2820 3214 Dl 2921 3177 2888 3189 Dl 2989 3151 2956 3163 Dl 3057 3126 3024 3138 Dl 3124 3100 3091 3112 Dl 3192 3074 3159 3086 Dl 3260 3049 3227 3061 Dl 3328 3024 3295 3036 Dl 3396 2998 3363 3010 Dl 3463 2973 3430 2985 Dl 3531 2948 3498 2960 Dl 3599 2922 3566 2934 Dl 755 4009 720 4002 Dl 826 4023 791 4016 Dl 897 4037 862 4030 Dl 968 4051 933 4044 Dl 1040 4065 1005 4058 Dl 1111 4080 1076 4073 Dl 1182 4094 1147 4087 Dl 1253 4109 1218 4102 Dl 1325 4122 1290 4115 Dl 1396 4137 1361 4130 Dl 1467 4151 1432 4144 Dl 1539 4165 1504 4158 Dl 1610 4180 1575 4173 Dl 1681 4194 1646 4187 Dl 1752 4208 1717 4201 Dl 1824 4222 1789 4215 Dl 1895 4237 1860 4230 Dl 1966 4251 1931 4244 Dl 2038 4265 2003 4258 Dl 2109 4279 2074 4272 Dl 2180 4294 2145 4287 Dl 2251 4308 2216 4301 Dl 2323 4322 2288 4315 Dl 2394 4336 2359 4329 Dl 2465 4351 2430 4344 Dl 2537 4365 2502 4358 Dl 2609 4379 2574 4372 Dl 2680 4394 2645 4387 Dl 2751 4408 2716 4401 Dl 2822 4422 2787 4415 Dl 2894 4436 2859 4429 Dl 2965 4451 2930 4444 Dl 3036 4465 3001 4458 Dl 3107 4479 3072 4472 Dl 3179 4493 3144 4486 Dl 3250 4507 3215 4500 Dl 3321 4522 3286 4515 Dl 3393 4536 3358 4529 Dl 3464 4551 3429 4544 Dl 3535 4564 3500 4557 Dl 3606 4579 3571 4572 Dl 3678 4593 3643 4586 Dl 3749 4608 3714 4601 Dl 3820 4622 3785 4615 Dl 3892 4636 3857 4629 Dl 3963 4650 3928 4643 Dl 4034 4664 3999 4657 Dl 4105 4679 4070 4672 Dl 4177 4693 4142 4686 Dl 4248 4707 4213 4700 Dl 4319 4721 4284 4714 Dl 10 R f (viewpoint)756 3302 w 720 3930 720 3282 Dl 720 3930 702 3858 Dl 720 3930 738 3858 Dl 10 I f (v)698 4108 w 10 R f (view screen)1 473 1 3276 4742 t 2916 4722 3240 4722 Dl 2916 4722 2988 4704 Dl 2916 4722 2988 4740 Dl (image of)1 352 1 3240 3530 t (edge)3240 3650 w 10 I f (e)3453 3650 w 2916 3570 3240 3570 Dl 2916 3570 2988 3552 Dl 2916 3570 2988 3588 Dl 10 R f (polytope edge)1 563 1 3140 4382 t 10 I f (e)3728 4382 w 4158 4362 3780 4362 Dl 4158 4362 4086 4380 Dl 4158 4362 4086 4344 Dl 10 R f (hidden)4192 3530 w (edges)4237 3650 w 4320 3246 4320 3426 Dl 4320 3246 4338 3318 Dl 4320 3246 4302 3318 Dl 4500 4272 4320 3714 Dl 4499 4271 4461 4209 Dl 4499 4271 4494 4197 Dl (Figure 1)1 336 1 2712 6360 t ( we are using a)4 610( Because)1 385( visible.)1 320(Consider now how to tell what portions of which polytope edges are)11 2755 4 970 6756 t ( simply adjoin four view-cone constraints to \(16\) to obtain a)10 2443( we)1 170( easy:)1 234(rectangular view cone, telling this is)5 1473 4 720 6876 t (modified polytope \(16)2 896 1 720 6996 t 10 S f (\242)1616 6996 w 10 R f ( visibility problem to that of deciding whether or not each segment)11 2689(\); this reduces the)3 710 2 1641 6996 t ( \(16)1 167(\(17\) of)1 284 2 720 7116 t 10 S f (\242)1171 7116 w 10 R f ( the viewpoint)2 590( If)1 125(\) is visible.)2 460 3 1196 7116 t 10 I f (v)2405 7116 w 10 R f (is strictly outside the original polytope \(16\), then edge \(17\) of)10 2557 1 2483 7116 t (\(16)720 7236 w 10 S f (\242)853 7236 w 10 R f (\) is visible only if)4 726 1 878 7236 t 10 I f (v)1634 7236 w 10 R f (satisfies)1709 7236 w 10 I f (F)2062 7236 w 7 I f (i)2134 7256 w 10 I f (v)2170 7236 w 10 S f (\263)2255 7236 w 10 I f (f)2359 7236 w 7 I f (i)2398 7256 w 10 R f (or)2457 7236 w 10 I f (F)2571 7236 w 7 I f (j)2643 7256 w 10 I f (v)2679 7236 w 10 S f (\263)2764 7236 w 10 I f (f)2868 7236 w 7 I f (j)2907 7256 w 10 R f ( if)1 92( And)1 228(\(or both\).)1 383 3 2966 7236 t 10 I f (v)3700 7236 w 10 R f (is inside \(16\), then all edges of)6 1265 1 3775 7236 t (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 8 9 %%Page: 9 10 /saveobj save def mark 10 pagesetup 10 R f (- 9 -)2 166 1 2797 480 t (the modified polytope \(16)3 1041 1 720 840 t 10 S f (\242)1761 840 w 10 R f (\) are visible.)2 496 1 1786 840 t ( four)1 204( 2\2615, for example, show)4 1013( Figures)1 362(The view angle can strongly affect a polytope's appearance.)8 2491 4 970 996 t ( the same polytope, with the same view direction but different angles of view \(30)14 3354(views from outside of)3 901 2 720 1116 t 10 S f (\260)4975 1116 w 10 R f (,)5015 1116 w (60)720 1236 w 10 S f (\260)820 1236 w 10 R f (, 90)1 151 1 860 1236 t 10 S f (\260)1011 1236 w 10 R f (, and 120)2 371 1 1051 1236 t 10 S f (\260)1422 1236 w 10 R f ( case was chosen to make the larger of the image's)10 2042( view point in each)4 764(respectively\). The)1 746 3 1488 1236 t ( from details about focusing,)4 1174( \(Aside)1 323( of the viewing window's width and height.)7 1792(width and height be 85%)4 1031 4 720 1356 t (the effect shown in figures 2\2615 is that of decreasing the focal length of a camera's lens.\))16 3516 1 720 1476 t 0.1 setlinewidth 2560 1846 2557 1889 Dl 2557 1889 2548 1963 Dl 2547 1964 2535 2034 Dl 2535 2034 2484 2212 Dl 893 1920 1455 3277 Dl 1455 3278 1496 3350 Dl 1496 3351 1722 3502 Dl 1723 3502 2484 2212 Dl 1107 1789 2310 1789 Dl 1105 1790 1057 1802 Dl 1057 1803 1020 1818 Dl 1020 1817 980 1840 Dl 979 1841 948 1864 Dl 948 1864 892 1919 Dl 2311 1789 2409 1800 Dl 2409 1802 2481 1817 Dl 2483 1817 2544 1837 Dl 2544 1838 2561 1845 Dl 1747 3276 1722 3502 Dl 1807 2933 1748 3276 Dl 1808 2933 2535 2034 Dl (7)2032 2807 w 1804 2868 1802 2915 Dl 1803 2915 1807 2933 Dl 1806 2867 2548 1963 Dl 5 R f (8)2148 2476 w 10 R f 0.1 setlinewidth 1796 2801 1800 2843 Dl 1800 2843 1805 2867 Dl 1796 2800 2557 1889 Dl 5 R f (9)2151 2406 w 10 R f 0.1 setlinewidth 1784 2731 1786 2769 Dl 1787 2770 1797 2800 Dl 1784 2731 2544 1837 Dl 5 R f (10)2133 2339 w 10 R f 0.1 setlinewidth 1759 2646 1764 2679 Dl 1766 2679 1784 2731 Dl 1759 2645 2481 1817 Dl (11)2079 2294 w 1723 2566 1741 2617 Dl 1742 2618 1760 2644 Dl 1724 2565 2409 1800 Dl (12)2031 2241 w 1680 2470 2310 1789 Dl 1706 2555 1674 2501 Dl 1707 2554 1712 2559 Dl 1672 2495 1679 2470 Dl 1674 2500 1672 2496 Dl 1711 2560 1722 2566 Dl (13)1966 2192 w 1748 3053 1748 3276 Dl 1767 2922 1747 3053 Dl 1767 2922 1802 2915 Dl 1760 2858 1760 2907 Dl 1761 2907 1767 2922 Dl 1762 2850 1760 2857 Dl 1763 2850 1800 2843 Dl 1764 2773 1763 2850 Dl 1766 2773 1786 2769 Dl 1747 2742 1753 2762 Dl 1754 2680 1747 2741 Dl 1754 2763 1765 2773 Dl 1754 2681 1764 2679 Dl 1729 2620 1729 2640 Dl 1729 2641 1753 2681 Dl 1728 2619 1741 2617 Dl 1714 2602 1728 2620 Dl 1712 2560 1714 2602 Dl 1671 2498 1671 2496 Dl 1674 2501 1672 2499 Dl 1672 2496 1 1 De 1664 2472 1679 2470 Dl 1663 2489 1661 2484 Dl 1670 2496 1663 2489 Dl 1662 2483 1663 2473 Dl 1745 2765 1745 2766 Dl 1745 2766 1749 2829 Dl 1749 2829 1760 2857 Dl 1753 2763 1746 2764 Dl 1715 2645 1716 2689 Dl 1716 2689 1743 2740 Dl 1729 2641 1715 2645 Dl 1745 2740 1747 2741 Dl 1687 2557 1687 2561 Dl 1688 2562 1690 2570 Dl 1690 2570 1709 2600 Dl 1706 2554 1688 2556 Dl 1709 2601 1714 2602 Dl 1744 2741 1746 2764 Dl 1708 2601 1702 2627 Dl 1703 2627 1715 2645 Dl 1670 2528 1670 2524 Dl 1670 2505 1672 2499 Dl 1670 2518 1670 2505 Dl 1688 2556 1671 2528 Dl 1669 2524 1669 2519 Dl 1725 2899 1713 2944 Dl 1714 2945 1747 3053 Dl 1759 2907 1725 2899 Dl 1708 2870 1725 2899 Dl 1719 2823 1709 2869 Dl 1749 2829 1720 2822 Dl 1718 2759 1713 2795 Dl 1714 2795 1720 2822 Dl 1744 2765 1718 2759 Dl 1707 2687 1705 2715 Dl 1705 2716 1717 2757 Dl 1717 2757 1718 2759 Dl 1715 2689 1707 2687 Dl 1699 2626 1694 2633 Dl 1696 2634 1702 2677 Dl 1702 2678 1707 2687 Dl 1701 2626 1699 2626 Dl 1685 2589 1685 2594 Dl 1689 2571 1684 2589 Dl 1685 2595 1699 2626 Dl 1668 2524 1668 2520 Dl 1669 2519 1 1 De 1663 2473 1652 2471 Dl 1662 2483 1652 2471 Dl 1699 2838 1704 2867 Dl 1697 2788 1699 2836 Dl 1708 2869 1704 2867 Dl 1712 2795 1697 2789 Dl 1698 2750 1693 2784 Dl 1693 2785 1697 2789 Dl 1716 2756 1697 2749 Dl 1680 2720 1692 2743 Dl 1694 2712 1679 2720 Dl 1692 2743 1697 2749 Dl 1704 2715 1694 2711 Dl 1685 2672 1686 2684 Dl 1687 2685 1694 2711 Dl 1700 2677 1684 2671 Dl 1683 2632 1681 2666 Dl 1681 2667 1684 2671 Dl 1688 2632 1683 2632 Dl 1694 2633 1688 2631 Dl 1676 2600 1676 2602 Dl 1684 2594 1677 2599 Dl 1676 2602 1688 2631 Dl 1665 2569 1665 2571 Dl 1675 2558 1664 2568 Dl 1678 2557 1676 2557 Dl 1683 2589 1665 2571 Dl 1687 2560 1678 2557 Dl 1670 2529 1661 2529 Dl 1678 2557 1661 2529 Dl 1669 2519 1657 2506 Dl 1669 2505 1657 2506 Dl 1589 3042 1496 3350 Dl 1684 2932 1589 3042 Dl 1713 2943 1685 2931 Dl (45)1598 3245 w 1675 2859 1673 2862 Dl 1673 2862 1685 2931 Dl 1704 2866 1675 2858 Dl 1682 2780 1699 2836 Dl 1692 2783 1682 2779 Dl 1692 2743 1682 2779 Dl 1686 2684 1676 2717 Dl 1678 2719 1676 2717 Dl 1662 2605 1662 2615 Dl 1676 2602 1661 2605 Dl 1683 2631 1662 2615 Dl 1665 2571 1665 2577 Dl 1665 2577 1677 2599 Dl 1654 2528 1656 2538 Dl 1660 2529 1653 2527 Dl 1676 2557 1656 2538 Dl 1655 2501 1657 2489 Dl 1656 2505 1655 2501 Dl 1663 2489 1657 2489 Dl 1656 2506 1 1 De 1668 2812 1675 2858 Dl 1679 2778 1667 2811 Dl 1681 2779 1679 2778 Dl 1667 2715 1663 2730 Dl 1664 2730 1679 2778 Dl 1675 2716 1668 2713 Dl 1663 2693 1668 2713 Dl 1672 2663 1662 2692 Dl 1680 2666 1672 2662 Dl 1661 2616 1658 2623 Dl 1658 2623 1672 2662 Dl 1660 2600 1661 2605 Dl 1665 2577 1660 2600 Dl 1657 2539 1657 2558 Dl 1664 2568 1657 2558 Dl 1655 2506 1646 2517 Dl 1653 2526 1646 2517 Dl 1609 2901 1589 3042 Dl 1638 2857 1610 2900 Dl 1672 2860 1638 2857 Dl 1662 2730 1661 2730 Dl 1661 2730 1645 2774 Dl 1646 2775 1667 2811 Dl 1657 2623 1650 2623 Dl 1651 2624 1651 2676 Dl 1652 2676 1662 2692 Dl 1636 2560 1635 2561 Dl 1657 2558 1638 2559 Dl 1659 2600 1635 2561 Dl 1657 2488 1639 2465 Dl 1651 2470 1639 2465 Dl 1635 2768 1625 2796 Dl 1625 2796 1638 2857 Dl 1645 2774 1635 2768 Dl 1635 2713 1626 2740 Dl 1627 2740 1635 2768 Dl 1660 2729 1635 2712 Dl 1633 2664 1627 2671 Dl 1627 2671 1635 2712 Dl 1651 2676 1633 2664 Dl 1628 2609 1633 2664 Dl 1650 2623 1627 2608 Dl 1636 2561 1626 2561 Dl 1627 2608 1627 2607 Dl 1627 2561 1627 2607 Dl 1642 2515 1638 2559 Dl 1646 2516 1642 2514 Dl 1641 2514 1638 2510 Dl 1654 2501 1638 2510 Dl 1652 2470 1630 2456 Dl 1639 2464 1630 2456 Dl 1595 2762 1588 2786 Dl 1589 2786 1610 2900 Dl 1624 2795 1595 2761 Dl 1597 2643 1596 2643 Dl 1596 2644 1594 2717 Dl 1610 2657 1597 2643 Dl 1609 2659 1607 2725 Dl 1608 2724 1594 2717 Dl 1625 2561 1605 2569 Dl 1606 2570 1613 2599 Dl 1626 2606 1613 2599 Dl 1629 2456 1614 2444 Dl 1634 2508 1614 2444 Dl 1637 2510 1635 2508 Dl 1592 2717 1589 2722 Dl 1590 2722 1595 2761 Dl 1625 2740 1607 2725 Dl 1627 2670 1611 2658 Dl 1612 2599 1597 2643 Dl 1624 2506 1616 2512 Dl 1635 2507 1625 2505 Dl 1616 2513 1626 2561 Dl 1557 2753 1455 3277 Dl 1588 2786 1558 2753 Dl 5 R f (83)1512 3059 w 10 R f 0.1 setlinewidth 1561 2693 1552 2705 Dl 1553 2706 1558 2753 Dl 1589 2721 1561 2692 Dl 1573 2621 1558 2633 Dl 1559 2633 1561 2692 Dl 1595 2644 1573 2621 Dl 1591 2556 1573 2560 Dl 1573 2560 1573 2621 Dl 1604 2569 1591 2556 Dl 1616 2511 1591 2504 Dl 1591 2505 1591 2556 Dl 1613 2443 1 1 De 1624 2504 1613 2443 Dl 1551 2705 948 1864 Dl (89)1228 2587 w 1558 2632 980 1840 Dl 5 R f (90)1247 2287 w 10 R f 0.1 setlinewidth 1573 2560 1020 1818 Dl 5 R f (91)1270 2239 w 10 R f 0.1 setlinewidth 1590 2504 1057 1802 Dl 5 R f (92)1296 2196 w 10 R f 0.1 setlinewidth 1612 2443 1106 1789 Dl 5 R f (93)1331 2163 w 10 R f (94)1640 2044 w 20 R f 16 setlinewidth 2736 3654 720 3654 Dl 2736 1638 2736 3654 Dl 720 1638 2736 1638 Dl 720 3654 720 1638 Dl 10 R f 0.1 setlinewidth 4842 1912 4835 1960 Dl 4835 1961 4815 2043 Dl 4814 2044 4788 2122 Dl 4788 2122 4693 2316 Dl 3231 2049 3747 3296 Dl 3747 3297 3785 3363 Dl 3785 3363 3993 3502 Dl 3994 3501 4693 2316 Dl 3291 1789 4634 1789 Dl 3289 1789 3253 1819 Dl 3254 1819 3234 1854 Dl 3233 1854 3221 1902 Dl 3221 1903 3219 1949 Dl 3219 1949 3230 2047 Dl 4634 1789 4731 1816 Dl 4732 1817 4793 1853 Dl 4793 1853 4834 1896 Dl 4835 1897 4843 1912 Dl 4008 3405 3993 3502 Dl 4073 3160 4009 3404 Dl 4074 3160 4788 2122 Dl (7)4282 2919 w 4072 3094 4068 3145 Dl 4068 3145 4073 3160 Dl 4072 3092 4815 2043 Dl 5 R f (8)4392 2661 w 10 R f 0.1 setlinewidth 4060 3014 4065 3065 Dl 4066 3066 4072 3093 Dl 4060 3014 4835 1960 Dl 5 R f (9)4399 2585 w 10 R f 0.1 setlinewidth 4041 2926 4044 2977 Dl 4045 2978 4060 3015 Dl 4040 2925 4834 1896 Dl (10)4356 2517 w 4004 2804 4011 2853 Dl 4012 2854 4040 2926 Dl 4004 2804 4793 1853 Dl (11)4330 2437 w 3946 2686 3975 2764 Dl 3975 2765 4003 2803 Dl 3947 2685 4731 1816 Dl (12)4282 2352 w 3882 2539 4634 1789 Dl 3920 2668 3872 2586 Dl 3922 2669 3929 2676 Dl 3869 2579 3881 2540 Dl 3871 2585 3869 2579 Dl 3930 2677 3947 2686 Dl (13)4209 2270 w 3999 3265 4009 3404 Dl 4019 3157 3999 3265 Dl 4020 3156 4068 3145 Dl 4009 3087 4010 3141 Dl 4011 3142 4020 3157 Dl 4011 3078 4008 3086 Dl 4012 3077 4065 3065 Dl 4012 2985 4012 3078 Dl 4014 2983 4044 2977 Dl 3986 2942 3996 2970 Dl 3994 2858 3985 2942 Dl 3996 2970 4013 2984 Dl 3995 2856 4011 2853 Dl 3956 2769 3957 2798 Dl 3957 2798 3995 2856 Dl 3955 2768 3975 2764 Dl 3932 2741 3954 2769 Dl 3930 2677 3933 2741 Dl 3868 2583 3868 2580 Dl 3871 2586 3868 2583 Dl 3868 2579 3869 2579 Dl 3857 2544 3881 2540 Dl 3856 2569 3854 2561 Dl 3868 2579 3857 2568 Dl 3854 2559 3857 2544 Dl 3985 2972 3984 2974 Dl 3985 2974 3992 3052 Dl 3992 3053 4008 3086 Dl 3995 2970 3985 2972 Dl 3935 2806 3938 2869 Dl 3939 2869 3981 2940 Dl 3955 2799 3934 2805 Dl 3980 2940 3985 2942 Dl 3892 2673 3892 2679 Dl 3892 2679 3895 2692 Dl 3896 2693 3925 2739 Dl 3921 2670 3893 2672 Dl 3926 2739 3933 2741 Dl 3981 2940 3985 2972 Dl 3925 2740 3916 2778 Dl 3916 2779 3934 2805 Dl 3866 2628 3865 2622 Dl 3866 2592 3868 2583 Dl 3864 2613 3865 2593 Dl 3892 2671 3866 2628 Dl 3864 2621 3864 2614 Dl 3962 3128 3950 3168 Dl 3951 3169 3999 3265 Dl 4010 3141 3963 3128 Dl 3939 3094 3963 3128 Dl 3950 3041 3939 3093 Dl 3991 3053 3950 3042 Dl 3945 2965 3940 3008 Dl 3940 3009 3950 3042 Dl 3983 2974 3945 2964 Dl 3925 2866 3924 2904 Dl 3924 2904 3943 2960 Dl 3943 2962 3945 2964 Dl 3937 2868 3925 2865 Dl 3911 2778 3905 2788 Dl 3905 2788 3917 2851 Dl 3917 2852 3925 2865 Dl 3915 2777 3911 2777 Dl 3889 2721 3890 2729 Dl 3895 2692 3888 2720 Dl 3889 2729 3911 2777 Dl 3865 2621 3864 2615 Dl 3864 2615 3864 2614 Dl 3856 2543 3840 2540 Dl 3853 2559 3840 2540 Dl 3925 3056 3933 3090 Dl 3917 2997 3924 3054 Dl 3938 3093 3933 3090 Dl 3940 3008 3917 2998 Dl 3915 2948 3911 2991 Dl 3912 2992 3917 2998 Dl 3943 2960 3915 2948 Dl 3887 2907 3907 2939 Dl 3907 2897 3887 2906 Dl 3907 2939 3915 2948 Dl 3923 2904 3908 2897 Dl 3893 2841 3895 2859 Dl 3896 2860 3908 2897 Dl 3916 2851 3892 2841 Dl 3887 2785 3887 2834 Dl 3887 2835 3892 2841 Dl 3895 2784 3888 2784 Dl 3905 2788 3895 2784 Dl 3878 2737 3877 2740 Dl 3888 2729 3877 2736 Dl 3877 2741 3895 2784 Dl 3858 2690 3859 2693 Dl 3875 2673 3858 2689 Dl 3877 2673 3875 2673 Dl 3887 2720 3859 2693 Dl 3890 2678 3877 2673 Dl 3866 2630 3852 2630 Dl 3877 2673 3852 2630 Dl 3864 2614 3846 2594 Dl 3865 2593 3846 2594 Dl 3821 3208 3785 3363 Dl 3914 3149 3822 3207 Dl 3950 3168 3914 3149 Dl 5 R f (45)3885 3327 w 10 R f 0.1 setlinewidth 3893 3075 3891 3077 Dl 3891 3077 3914 3149 Dl 3933 3089 3894 3074 Dl 3896 2983 3924 3054 Dl 3911 2991 3897 2984 Dl 3906 2940 3896 2983 Dl 3896 2983 1 1 De 3894 2860 3882 2903 Dl 3886 2906 3882 2903 Dl 3855 2745 3856 2759 Dl 3875 2740 3854 2744 Dl 3887 2784 3856 2759 Dl 3859 2693 3859 2702 Dl 3859 2703 3877 2736 Dl 3841 2627 3845 2643 Dl 3851 2628 3841 2626 Dl 3875 2672 3845 2643 Dl 3843 2586 3846 2567 Dl 3844 2593 3843 2586 Dl 3856 2568 3846 2567 Dl 3845 2594 1 1 De 3879 3019 3894 3074 Dl 3891 2981 3879 3018 Dl 3896 2983 3892 2981 Dl 3870 2897 3866 2917 Dl 3867 2917 3892 2981 Dl 3882 2902 3871 2897 Dl 3863 2868 3871 2897 Dl 3873 2827 3862 2867 Dl 3886 2834 3874 2828 Dl 3856 2759 3852 2770 Dl 3852 2771 3874 2828 Dl 3852 2737 3854 2744 Dl 3859 2704 3853 2737 Dl 3844 2644 3846 2673 Dl 3856 2689 3846 2673 Dl 3845 2595 3831 2612 Dl 3841 2627 3831 2612 Dl 3822 3094 3822 3207 Dl 3848 3061 3823 3094 Dl 3891 3076 3848 3061 Dl 3866 2918 3864 2918 Dl 3863 2919 3847 2970 Dl 3848 2970 3879 3018 Dl 3851 2770 3841 2770 Dl 3842 2771 3846 2844 Dl 3846 2843 3862 2867 Dl 3818 2675 3816 2677 Dl 3847 2673 3819 2674 Dl 3852 2736 3816 2677 Dl 3846 2567 3821 2532 Dl 3839 2541 3821 2532 Dl 3834 2959 3824 2989 Dl 3825 2989 3848 3061 Dl 3846 2969 3834 2959 Dl 3828 2891 3820 2923 Dl 3820 2923 3834 2959 Dl 3863 2917 3828 2890 Dl 3820 2825 3813 2833 Dl 3813 2834 3828 2890 Dl 3846 2842 3821 2824 Dl 3809 2746 3821 2824 Dl 3841 2770 3808 2746 Dl 3816 2677 3803 2676 Dl 3808 2745 3807 2743 Dl 3803 2676 3807 2743 Dl 3824 2607 3819 2674 Dl 3829 2611 3823 2607 Dl 3823 2606 3818 2600 Dl 3842 2587 3818 2600 Dl 3840 2540 3808 2520 Dl 3821 2532 3808 2520 Dl 3785 2941 3782 2966 Dl 3783 2966 3823 3094 Dl 3823 2988 3785 2940 Dl 3773 2791 3771 2791 Dl 3771 2791 3777 2886 Dl 3791 2812 3773 2791 Dl 3792 2813 3795 2899 Dl 3795 2898 3777 2886 Dl 3802 2676 3776 2687 Dl 3776 2687 3788 2730 Dl 3806 2742 3788 2730 Dl 3807 2519 3786 2501 Dl 3814 2596 3786 2501 Dl 3818 2600 3814 2597 Dl 3777 2886 3774 2891 Dl 3773 2892 3785 2940 Dl 3819 2922 3795 2899 Dl 3813 2833 3791 2813 Dl 3788 2732 3773 2791 Dl 3798 2592 3787 2602 Dl 3814 2597 3800 2593 Dl 3788 2604 3803 2676 Dl 3745 2918 3747 3296 Dl 3781 2965 3745 2917 Dl 5 R f (83)3754 3154 w 10 R f 0.1 setlinewidth 3738 2848 3731 2860 Dl 3732 2861 3745 2917 Dl 3773 2890 3739 2846 Dl 3743 2757 3728 2770 Dl 3728 2770 3739 2846 Dl 3771 2790 3743 2756 Dl 3757 2666 3737 2671 Dl 3737 2672 3743 2756 Dl 3776 2686 3758 2666 Dl 3788 2602 3755 2592 Dl 3756 2592 3758 2666 Dl 3785 2500 1 1 De 3799 2592 3785 2500 Dl 3731 2859 3219 1949 Dl (89)3495 2689 w 3727 2769 3221 1902 Dl 5 R f (90)3473 2422 w 10 R f 0.1 setlinewidth 3737 2671 3234 1854 Dl 5 R f (91)3479 2350 w 10 R f 0.1 setlinewidth 3754 2591 3253 1819 Dl 5 R f (92)3494 2283 w 10 R f 0.1 setlinewidth 3785 2500 3291 1789 Dl 5 R f (93)3524 2228 w 10 R f (94)3872 2071 w 20 R f 16 setlinewidth 5040 3654 3024 3654 Dl 5040 1638 5040 3654 Dl 3024 1638 5040 1638 Dl 3024 3654 3024 1638 Dl 10 B f (Figure 2:)1 391 1 1220 3852 t 10 R f (view angle 30)2 560 1 1636 3852 t 10 S f (\260)2196 3852 w 10 B f (Figure 3:)1 391 1 3524 3852 t 10 R f (view angle 60)2 560 1 3940 3852 t 10 S f (\260)4500 3852 w 0.1 setlinewidth 2509 4367 2497 4415 Dl 2496 4415 2466 4499 Dl 973 4165 2386 4165 Dl 973 4165 956 4219 Dl 957 4218 960 4277 Dl 961 4278 979 4352 Dl 2387 4166 2468 4214 Dl 2469 4214 2504 4274 Dl 2504 4275 2512 4343 Dl 2511 4343 2509 4366 Dl 1845 5829 1830 5855 Dl 1846 5828 2466 4499 Dl 1840 5780 1841 5817 Dl 1841 5818 1846 5829 Dl 1839 5780 2497 4415 Dl 5 R f (9)2094 5257 w 10 R f 0.1 setlinewidth 1816 5685 1818 5753 Dl 1818 5754 1839 5780 Dl 1815 5685 2512 4343 Dl 5 R f (10)2076 5194 w 10 R f 0.1 setlinewidth 1750 5498 1764 5585 Dl 1764 5585 1815 5685 Dl 1751 5495 2504 4274 Dl (11)2023 5096 w 1626 5266 1690 5428 Dl 1690 5428 1749 5496 Dl 1625 5264 2468 4214 Dl (12)1956 4946 w 1491 4941 2386 4165 Dl 1567 5228 1462 5043 Dl 1568 5229 1586 5245 Dl 1457 5027 1491 4941 Dl 1461 5043 1456 5028 Dl 1586 5245 1625 5264 Dl (13)1842 4772 w 1759 5878 1830 5855 Dl 1746 5851 1746 5875 Dl 1746 5876 1759 5878 Dl 1753 5846 1747 5851 Dl 1754 5845 1841 5817 Dl 1760 5771 1753 5845 Dl 1762 5770 1818 5753 Dl 1711 5722 1729 5757 Dl 1730 5594 1711 5722 Dl 1729 5758 1761 5771 Dl 1731 5594 1764 5585 Dl 1646 5439 1650 5495 Dl 1650 5496 1730 5594 Dl 1645 5439 1690 5428 Dl 1596 5383 1645 5439 Dl 1586 5246 1596 5383 Dl 1454 5035 1453 5028 Dl 1462 5043 1455 5036 Dl 1454 5028 1456 5028 Dl 1438 4950 1491 4941 Dl 1431 5003 1427 4985 Dl 1453 5028 1431 5004 Dl 1428 4984 1438 4950 Dl 1709 5759 1707 5760 Dl 1708 5761 1720 5826 Dl 1721 5826 1747 5851 Dl 1729 5758 1710 5759 Dl 1604 5505 1615 5610 Dl 1616 5611 1702 5719 Dl 1649 5496 1603 5506 Dl 1702 5720 1711 5722 Dl 5 R f (23)1643 5608 w 10 R f 0.1 setlinewidth 1505 5235 1504 5249 Dl 1504 5250 1512 5279 Dl 1513 5279 1579 5379 Dl 1566 5230 1505 5235 Dl 1580 5379 1596 5383 Dl 1703 5720 1710 5759 Dl 1579 5379 1561 5454 Dl 1562 5455 1603 5506 Dl 1448 5137 1446 5122 Dl 1448 5056 1455 5036 Dl 1444 5103 1447 5057 Dl 1504 5234 1448 5136 Dl 1446 5121 1444 5103 Dl 1746 5875 1674 5847 Dl 1635 5820 1674 5847 Dl 1649 5799 1634 5820 Dl 1720 5825 1649 5798 Dl 1634 5734 1629 5768 Dl 1629 5768 1649 5798 Dl 1707 5760 1635 5734 Dl 1589 5602 1590 5653 Dl 1590 5653 1631 5729 Dl 1632 5730 1635 5734 Dl 1614 5611 1589 5602 Dl 1552 5452 1540 5469 Dl 1541 5469 1571 5577 Dl 1572 5578 1589 5602 Dl 1561 5453 1553 5451 Dl 1498 5335 1502 5353 Dl 1512 5279 1498 5335 Dl 1503 5353 1553 5451 Dl 1444 5120 1442 5106 Dl 1444 5106 1444 5103 Dl 1438 4949 1404 4942 Dl 1403 4942 1404 4942 Dl 1426 4984 1402 4943 Dl 1609 5788 1625 5814 Dl 1591 5744 1609 5787 Dl 1633 5820 1625 5814 Dl 1628 5769 1590 5744 Dl 1579 5698 1579 5734 Dl 1580 5735 1590 5744 Dl 1631 5729 1580 5698 Dl 1525 5634 1564 5682 Dl 1559 5635 1524 5634 Dl 1565 5683 1580 5698 Dl 1590 5653 1560 5635 Dl 1523 5549 1530 5577 Dl 1531 5577 1560 5635 Dl 1570 5577 1522 5549 Dl 1507 5456 1512 5536 Dl 1512 5537 1522 5549 Dl 1520 5457 1506 5455 Dl 1540 5468 1520 5458 Dl 1480 5364 1478 5370 Dl 1502 5354 1480 5364 Dl 1478 5371 1520 5458 Dl 1436 5265 1438 5273 Dl 1467 5235 1434 5265 Dl 1473 5234 1468 5234 Dl 1497 5334 1438 5273 Dl 1503 5249 1474 5235 Dl 1448 5137 1419 5137 Dl 1474 5234 1419 5137 Dl 1443 5107 1407 5060 Dl 1447 5058 1407 5060 Dl 1565 5770 1563 5768 Dl 1625 5814 1566 5771 Dl 1555 5717 1609 5787 Dl 1579 5733 1555 5716 Dl 1563 5683 1553 5716 Dl 1554 5717 1553 5716 Dl 1530 5577 1516 5626 Dl 1524 5633 1516 5626 Dl 1437 5371 1442 5397 Dl 1478 5370 1437 5370 Dl 1506 5455 1442 5397 Dl 1438 5273 1439 5292 Dl 1440 5293 1480 5364 Dl 1397 5130 1406 5166 Dl 1418 5136 1396 5129 Dl 1468 5234 1406 5166 Dl 1403 5042 1411 5000 Dl 1404 5057 1402 5042 Dl 1431 5003 1411 5000 Dl 1407 5059 1405 5058 Dl 1536 5725 1566 5771 Dl 1546 5711 1535 5725 Dl 1553 5716 1546 5711 Dl 1496 5611 1494 5629 Dl 1493 5631 1546 5711 Dl 1516 5626 1496 5611 Dl 1476 5568 1496 5611 Dl 1488 5519 1476 5567 Dl 1511 5536 1487 5519 Dl 1441 5397 1436 5415 Dl 1436 5415 1487 5519 Dl 1433 5356 1437 5370 Dl 1439 5292 1432 5356 Dl 1406 5165 1412 5228 Dl 1435 5264 1412 5228 Dl 1404 5059 1376 5096 Dl 1396 5129 1376 5096 Dl 1563 5768 1507 5708 Dl 1492 5629 1490 5627 Dl 1490 5628 1480 5656 Dl 1481 5656 1535 5725 Dl 1436 5414 1419 5408 Dl 1419 5409 1444 5522 Dl 1445 5522 1476 5567 Dl 1362 5224 1359 5228 Dl 1411 5229 1362 5224 Dl 1432 5356 1359 5228 Dl 1411 4999 1368 4924 Dl 1402 4942 1368 4924 Dl 1460 5634 1459 5641 Dl 1459 5642 1507 5708 Dl 1479 5656 1460 5634 Dl 1432 5564 1432 5587 Dl 1432 5588 1460 5634 Dl 1489 5627 1432 5563 Dl 1401 5477 1394 5482 Dl 1394 5481 1432 5563 Dl 1443 5523 1401 5477 Dl 1360 5350 1401 5477 Dl 1417 5408 1360 5349 Dl 1359 5228 1337 5221 Dl 1360 5349 1358 5345 Dl 1337 5222 1358 5345 Dl 1363 5086 1362 5224 Dl 1376 5095 1364 5085 Dl 1363 5085 1354 5071 Dl 1402 5043 1354 5071 Dl 1402 4943 1344 4900 Dl 1367 4925 1344 4900 Dl 1459 5641 1403 5559 Dl 1332 5390 1330 5389 Dl 1330 5391 1373 5505 Dl 1360 5434 1332 5391 Dl 1361 5436 1396 5536 Dl 1396 5536 1373 5505 Dl 1336 5221 1303 5230 Dl 1303 5231 1330 5312 Dl 1358 5344 1330 5312 Dl 1345 4900 1309 4865 Dl 1346 5063 1309 4865 Dl 1353 5070 1346 5063 Dl 1373 5505 1372 5505 Dl 1373 5506 1403 5559 Dl 1431 5586 1396 5536 Dl 1393 5481 1360 5435 Dl 1331 5312 1332 5391 Dl 1322 5053 1305 5071 Dl 1346 5062 1323 5052 Dl 1307 5071 1337 5220 Dl 1371 5505 1329 5420 Dl 1293 5318 1290 5322 Dl 1290 5323 1329 5420 Dl 1329 5389 1293 5317 Dl 1277 5184 1260 5183 Dl 1260 5183 1293 5317 Dl 1303 5230 1278 5184 Dl 1305 5070 1262 5044 Dl 1263 5045 1278 5184 Dl 1309 4864 1308 4862 Dl 1323 5052 1308 4862 Dl 1290 5321 979 4352 Dl 1260 5182 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Dl 3508 4585 3496 4644 Dl 3496 4646 3547 4918 Dl 3542 4209 3541 4209 Dl 3521 4492 3541 4209 Dl 3496 4644 3500 4370 Dl 3541 4209 3506 4313 Dl 20 R f 16 setlinewidth 5040 6030 3024 6030 Dl 5040 4014 5040 6030 Dl 3024 4014 5040 4014 Dl 3024 6030 3024 4014 Dl 10 B f (Figure 4:)1 391 1 1220 6228 t 10 R f (view angle 90)2 560 1 1636 6228 t 10 S f (\260)2196 6228 w 10 B f (Figure 5:)1 391 1 3499 6228 t 10 R f (view angle 120)2 610 1 3915 6228 t 10 S f (\260)4525 6228 w 10 R f ( the polytope of figures 2\2615, looking for interesting viewpoints and view direc-)12 3280(I played some with)3 790 2 970 6384 t ( some-)1 277( 6 shows my favorite perspective, one that my wife and I both liked because it looks)16 3503(tions. Figure)1 540 3 720 6504 t (thing like a dinosaur's head.)4 1129 1 720 6624 t (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 9 10 %%Page: 10 11 /saveobj save def mark 11 pagesetup 10 R f (- 10 -)2 216 1 2772 282 t 0.1 setlinewidth 4472 1418 4460 1503 Dl 4459 1504 4418 1661 Dl 1736 1831 2481 4060 Dl 2482 4060 2552 4211 Dl 2553 4210 2974 4539 Dl 1695 967 1645 1085 Dl 1644 1086 1631 1217 Dl 1633 1217 1640 1386 Dl 1640 1386 1663 1537 Dl 1663 1537 1735 1830 Dl 4257 967 4402 1075 Dl 4403 1076 4464 1211 Dl 4465 1211 4478 1365 Dl 4477 1365 4472 1417 Dl 3097 4483 2974 4539 Dl 3690 4005 3097 4482 Dl 3833 3738 3723 3960 Dl 3722 3961 3690 4006 Dl 3834 3738 4418 1661 Dl 3931 3334 3864 3607 Dl 3865 3608 3834 3738 Dl 3933 3333 4460 1503 Dl 5 R f (9)4087 2784 w 10 R f 0.1 setlinewidth 3969 2780 3939 3101 Dl 3938 3101 3932 3333 Dl 3970 2779 4478 1365 Dl (10)4097 2461 w 3875 1929 3898 2265 Dl 3898 2265 3970 2779 Dl 3875 1928 4464 1211 Dl (11)4079 1971 w 3558 1143 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6576 1401 6571 Dl 1398 6576 1391 6578 Dl 1400 6511 1396 6492 Dl 1393 6533 1401 6511 Dl 1391 6534 1393 6534 Dl 1399 6551 1401 6544 Dl 1402 6544 1393 6534 Dl 1393 6554 1398 6552 Dl 1400 6555 1398 6552 Dl 1395 6566 1401 6555 Dl 1390 6569 1395 6567 Dl 1401 6570 1403 6568 Dl 1402 6568 1395 6567 Dl 1399 6575 1401 6572 Dl 1399 6575 1403 6573 Dl 1443 6400 1468 6242 Dl 1422 6461 1443 6401 Dl 1399 6487 1422 6461 Dl 1403 6544 1403 6543 Dl 1403 6543 1414 6514 Dl 1414 6513 1401 6511 Dl 1404 6568 1408 6565 Dl 1408 6565 1408 6554 Dl 1407 6554 1401 6555 Dl 1416 6565 1 1 De 1403 6573 1414 6566 Dl 1403 6572 1416 6565 Dl 1422 6509 1429 6486 Dl 1429 6485 1422 6461 Dl 1414 6513 1420 6509 Dl 1419 6532 1425 6515 Dl 1425 6514 1420 6509 Dl 1404 6542 1419 6532 Dl 1419 6545 1423 6540 Dl 1423 6539 1419 6532 Dl 1409 6553 1419 6546 Dl 1421 6555 1419 6546 Dl 1409 6564 1422 6555 Dl 1417 6565 1422 6560 Dl 1422 6560 1422 6555 Dl 1448 6475 1453 6452 Dl 1453 6452 1443 6401 Dl 1429 6485 1447 6475 Dl 1442 6525 1442 6524 Dl 1442 6524 1446 6496 Dl 1434 6532 1441 6527 Dl 1433 6531 1437 6505 Dl 1437 6505 1446 6496 Dl 1422 6560 1434 6547 Dl 1434 6547 1430 6548 Dl 1423 6555 1430 6548 Dl 1447 6495 1449 6490 Dl 1449 6489 1447 6475 Dl 1426 6514 1437 6505 Dl 1423 6539 1433 6532 Dl 1431 6548 1441 6527 Dl 1473 6431 1650 5583 Dl 1453 6452 1473 6432 Dl 5 R f (83)1517 6015 w 10 R f 0.1 setlinewidth 1467 6471 1474 6452 Dl 1473 6452 1473 6432 Dl 1449 6489 1467 6471 Dl 1455 6511 1465 6491 Dl 1467 6490 1467 6471 Dl 1443 6525 1455 6511 Dl 1442 6537 1453 6522 Dl 1453 6523 1455 6511 Dl 1435 6546 1442 6538 Dl 1474 6452 1843 5938 Dl (89)1634 5966 w 1467 6491 1811 6005 Dl 1454 6522 1775 6067 Dl 20 R f 16 setlinewidth 2016 6702 720 6702 Dl 2016 5406 2016 6702 Dl 720 5406 2016 5406 Dl 720 6702 720 5406 Dl 10 R f 0.1 setlinewidth 2817 6560 2807 6565 Dl 2806 6566 2778 6574 Dl 2778 6574 2738 6582 Dl 2737 6582 2559 6604 Dl 2583 5503 2409 5771 Dl 2409 5771 2394 5807 Dl 2394 5807 2358 6055 Dl 2359 6055 2559 6604 Dl 2892 5646 2831 5610 Dl 2831 5611 2764 5578 Dl 2763 5577 2585 5503 Dl 2839 6545 2818 6560 Dl 2885 6078 2358 6055 Dl 3291 6113 2885 6079 Dl 3292 6114 2738 6582 Dl (7)2729 6297 w 3335 6110 3310 6110 Dl 3310 6110 3292 6113 Dl 3334 6111 2778 6574 Dl 5 R f (8)3036 6344 w 10 R f 0.1 setlinewidth 3367 6103 3349 6106 Dl 3348 6107 3335 6110 Dl 3367 6103 2807 6565 Dl 3389 6093 3382 6095 Dl 3382 6095 3368 6102 Dl 3388 6094 2839 6545 Dl 3404 6080 3402 6082 Dl 3401 6081 3389 6093 Dl 3407 6068 3404 6078 Dl 3188 6075 2885 6079 Dl 3314 6086 3189 6074 Dl 3314 6087 3310 6110 Dl 3349 6081 3324 6081 Dl 3324 6081 3314 6086 Dl 3352 6081 3350 6080 Dl 3354 6082 3349 6106 Dl 3384 6082 3354 6082 Dl 3384 6083 3382 6095 Dl 3394 6071 3389 6075 Dl 3402 6074 3393 6071 Dl 3387 6075 3384 6082 Dl 3403 6076 3402 6082 Dl 3409 6060 3408 6060 Dl 3407 6059 3402 6074 Dl 3408 6060 3407 6067 Dl 3409 6051 3409 6059 Dl 3387 6070 1 1 De 3387 6071 3362 6073 Dl 3361 6073 3350 6080 Dl 3387 6075 3387 6071 Dl 3407 6052 3401 6052 Dl 3400 6052 3393 6069 Dl 3407 6059 3407 6051 Dl 3393 6069 3393 6071 Dl 3408 6036 3408 6037 Dl 3408 6038 3409 6048 Dl 3409 6049 3409 6051 Dl 3392 6070 3387 6071 Dl 3409 6048 3407 6044 Dl 3407 6044 3407 6051 Dl 3319 6057 3277 6049 Dl 3276 6050 3189 6074 Dl 3324 6081 3319 6058 Dl 3329 6048 3319 6058 Dl 3357 6054 3330 6047 Dl 3362 6072 3358 6054 Dl 3382 6053 3367 6050 Dl 3367 6051 3358 6054 Dl 3386 6070 3383 6054 Dl 3398 6047 3391 6046 Dl 3392 6046 3384 6053 Dl 3383 6054 1 1 De 3400 6051 3399 6046 Dl 3407 6042 3405 6040 Dl 3405 6040 3400 6043 Dl 3399 6044 3399 6046 Dl 3407 6044 3407 6043 Dl 3408 6036 3407 6033 Dl 3407 6036 3407 6043 Dl 3342 6042 3330 6044 Dl 3362 6040 3342 6041 Dl 3330 6046 3330 6044 Dl 3367 6050 3363 6040 Dl 3378 6040 3363 6037 Dl 3363 6038 3363 6040 Dl 3383 6053 3378 6041 Dl 3380 6030 3378 6037 Dl 3388 6038 3381 6029 Dl 3378 6038 3378 6041 Dl 3391 6044 3389 6038 Dl 3395 6034 3393 6034 Dl 3392 6033 3389 6038 Dl 3400 6043 3396 6033 Dl 3401 6032 3395 6031 Dl 3396 6031 3396 6033 Dl 3403 6035 3402 6033 Dl 3405 6039 3404 6036 Dl 3403 6029 1 1 De 3406 6035 3404 6030 Dl 3404 6030 3404 6036 Dl 3404 6030 3402 6023 Dl 3404 6030 3404 6029 Dl 3406 6033 3402 6023 Dl 3407 6035 3405 6030 Dl 3067 5952 2394 5807 Dl 3268 6030 3068 5953 Dl 3275 6049 3268 6030 Dl (45)2684 5996 w 3317 6024 3314 6023 Dl 3313 6023 3268 6030 Dl 3329 6044 3318 6025 Dl 3360 6031 3342 6041 Dl 3362 6036 3360 6030 Dl 3378 6036 3360 6030 Dl 3393 6034 3381 6028 Dl 3381 6030 3381 6028 Dl 3397 6020 1 1 De 3403 6028 3398 6020 Dl 3402 6032 3397 6020 Dl 3402 6023 3404 6030 Dl 3337 6021 3318 6025 Dl 3359 6028 3337 6020 Dl 3360 6030 3360 6028 Dl 3377 6022 3370 6020 Dl 3370 6019 3360 6028 Dl 3380 6028 3378 6023 Dl 3381 6021 3378 6023 Dl 3392 6026 3381 6020 Dl 3395 6031 3393 6026 Dl 3396 6020 3394 6018 Dl 3394 6019 3393 6026 Dl 3401 6022 3398 6020 Dl 3401 6022 3399 6018 Dl 3226 5978 3068 5953 Dl 3287 5999 3227 5978 Dl 3313 6023 3287 6000 Dl 3370 6018 3369 6018 Dl 3369 6018 3340 6007 Dl 3339 6007 3337 6020 Dl 3394 6017 3391 6013 Dl 3391 6013 3380 6013 Dl 3380 6014 3381 6020 Dl 3391 6005 1 1 De 3399 6018 3392 6007 Dl 3398 6018 3391 6005 Dl 3335 5999 3312 5992 Dl 3311 5993 3287 6000 Dl 3339 6007 3335 6001 Dl 3358 6002 3341 5996 Dl 3340 5996 3335 6001 Dl 3368 6017 3358 6002 Dl 3371 6002 3366 5998 Dl 3365 5998 3358 6002 Dl 3379 6012 3372 6002 Dl 3381 6000 3372 6002 Dl 3390 6013 3381 6000 Dl 3391 6005 3386 6000 Dl 3386 5999 3381 5999 Dl 3301 5973 3278 5968 Dl 3278 5968 3227 5978 Dl 3311 5992 3301 5974 Dl 3351 5979 3350 5979 Dl 3350 5979 3322 5975 Dl 3358 5987 3353 5980 Dl 3357 5988 3331 5984 Dl 3331 5984 3322 5975 Dl 3386 5999 3373 5987 Dl 3373 5987 3374 5991 Dl 3381 5998 3374 5991 Dl 3321 5974 3316 5972 Dl 3315 5972 3301 5974 Dl 3340 5995 3331 5984 Dl 3365 5998 3358 5988 Dl 3374 5990 3353 5980 Dl 3257 5948 2409 5771 Dl 3278 5968 3258 5948 Dl 5 R f (83)2806 5889 w 10 R f 0.1 setlinewidth 3297 5954 3278 5947 Dl 3278 5948 3258 5948 Dl 3315 5972 3297 5954 Dl 3337 5966 3317 5956 Dl 3316 5954 3297 5954 Dl 3351 5978 3337 5966 Dl 3363 5979 3348 5968 Dl 3349 5968 3337 5966 Dl 3372 5986 3364 5979 Dl 3278 5947 2764 5578 Dl (89)2722 5757 w 3317 5954 2831 5610 Dl 3348 5967 2893 5646 Dl 20 R f 16 setlinewidth 3528 6702 2232 6702 Dl 3528 5406 3528 6702 Dl 2232 5406 3528 5406 Dl 2232 6702 2232 5406 Dl 10 R f 0.1 setlinewidth 4898 6116 4903 6126 Dl 4904 6127 4912 6155 Dl 4912 6155 4920 6195 Dl 4920 6196 4942 6374 Dl 3841 6350 4109 6524 Dl 4109 6524 4145 6539 Dl 4145 6539 4393 6575 Dl 4393 6574 4942 6374 Dl 3984 6041 3948 6102 Dl 3949 6102 3916 6169 Dl 3915 6170 3841 6348 Dl 4883 6094 4898 6115 Dl 4416 6048 4393 6575 Dl 4451 5642 4417 6048 Dl 4452 5641 4920 6195 Dl (7)4590 6200 w 4448 5598 4448 5623 Dl 4448 5623 4451 5641 Dl 4449 5599 4912 6155 Dl 5 R f (8)4660 5895 w 10 R f 0.1 setlinewidth 4441 5566 4444 5584 Dl 4445 5585 4448 5598 Dl 4441 5566 4903 6126 Dl 4431 5544 4433 5551 Dl 4433 5551 4440 5565 Dl 4432 5545 4883 6094 Dl 4418 5530 4420 5532 Dl 4419 5532 4431 5544 Dl 4406 5526 4416 5529 Dl 4413 5745 4417 6048 Dl 4424 5619 4412 5744 Dl 4425 5619 4448 5623 Dl 4419 5584 4419 5609 Dl 4419 5609 4424 5619 Dl 4419 5581 4418 5583 Dl 4420 5579 4444 5584 Dl 4420 5549 4420 5579 Dl 4421 5549 4433 5551 Dl 4409 5539 4413 5544 Dl 4412 5531 4409 5540 Dl 4413 5546 4420 5549 Dl 4414 5531 4420 5532 Dl 4398 5524 4398 5525 Dl 4397 5526 4412 5531 Dl 4398 5525 4405 5526 Dl 4389 5524 4397 5524 Dl 4408 5546 1 1 De 4409 5546 4411 5571 Dl 4411 5572 4418 5583 Dl 4413 5546 4409 5546 Dl 4390 5526 4390 5532 Dl 4390 5533 4407 5540 Dl 4397 5526 4389 5526 Dl 4407 5540 4409 5540 Dl 4374 5525 4375 5525 Dl 4376 5525 4386 5524 Dl 4387 5524 4389 5524 Dl 4408 5541 4409 5546 Dl 4386 5524 4382 5526 Dl 4382 5526 4389 5526 Dl 4395 5614 4387 5656 Dl 4388 5657 4412 5744 Dl 4419 5609 4396 5614 Dl 4386 5604 4396 5614 Dl 4392 5576 4385 5603 Dl 4410 5571 4392 5575 Dl 4391 5551 4388 5566 Dl 4389 5566 4392 5575 Dl 4408 5547 4392 5550 Dl 4385 5535 4384 5542 Dl 4384 5542 4391 5550 Dl 4392 5550 1 1 De 4389 5533 4384 5534 Dl 4380 5526 4378 5528 Dl 4378 5528 4381 5533 Dl 4382 5534 4384 5534 Dl 4382 5526 4381 5526 Dl 4374 5525 4371 5526 Dl 4374 5526 4381 5526 Dl 4380 5592 4382 5604 Dl 4378 5571 4379 5591 Dl 4384 5604 4382 5604 Dl 4388 5566 4378 5570 Dl 4378 5555 4375 5570 Dl 4376 5570 4378 5570 Dl 4391 5550 4379 5555 Dl 4368 5553 4375 5555 Dl 4376 5545 4367 5552 Dl 4376 5555 4379 5555 Dl 4382 5542 4376 5544 Dl 4372 5538 4372 5540 Dl 4371 5541 4376 5544 Dl 4381 5533 4371 5537 Dl 4370 5532 4369 5538 Dl 4369 5537 4371 5537 Dl 4373 5530 4371 5531 Dl 4377 5528 4374 5529 Dl 4367 5530 1 1 De 4373 5527 4368 5529 Dl 4368 5529 4374 5529 Dl 4368 5530 4361 5532 Dl 4368 5529 4367 5529 Dl 4371 5527 4361 5531 Dl 4373 5526 4368 5528 Dl 4290 5866 4145 6539 Dl 4368 5665 4291 5865 Dl 4387 5658 4368 5665 Dl (45)4264 6219 w 4362 5616 4361 5619 Dl 4361 5620 4368 5665 Dl 4382 5604 4363 5615 Dl 4369 5573 4379 5591 Dl 4374 5571 4368 5573 Dl 4374 5555 4368 5573 Dl 4372 5540 4366 5552 Dl 4368 5552 4366 5552 Dl 4358 5536 1 1 De 4366 5530 4358 5535 Dl 4370 5531 4358 5536 Dl 4361 5531 4368 5529 Dl 4359 5596 4363 5615 Dl 4366 5574 4358 5596 Dl 4368 5573 4366 5573 Dl 4360 5556 4358 5563 Dl 4357 5563 4366 5573 Dl 4366 5553 4361 5555 Dl 4359 5552 4361 5555 Dl 4364 5541 4358 5552 Dl 4369 5538 4364 5540 Dl 4358 5537 4356 5539 Dl 4357 5539 4364 5540 Dl 4360 5532 4358 5535 Dl 4360 5532 4356 5534 Dl 4316 5707 4291 5865 Dl 4337 5646 4316 5706 Dl 4361 5620 4338 5646 Dl 4356 5563 4356 5564 Dl 4356 5564 4345 5593 Dl 4345 5594 4358 5596 Dl 4355 5539 4351 5542 Dl 4351 5542 4351 5553 Dl 4352 5553 4358 5552 Dl 4343 5542 1 1 De 4356 5534 4345 5541 Dl 4356 5535 4343 5542 Dl 4337 5599 4330 5622 Dl 4331 5622 4338 5646 Dl 4345 5594 4339 5598 Dl 4340 5575 4334 5592 Dl 4334 5593 4339 5598 Dl 4355 5565 4340 5575 Dl 4340 5562 4336 5567 Dl 4336 5568 4340 5575 Dl 4350 5554 4340 5561 Dl 4338 5552 4340 5561 Dl 4351 5543 4338 5552 Dl 4343 5542 4338 5547 Dl 4337 5547 4337 5552 Dl 4311 5632 4306 5655 Dl 4306 5655 4316 5706 Dl 4330 5622 4312 5632 Dl 4317 5582 4317 5583 Dl 4317 5583 4313 5611 Dl 4325 5575 4318 5580 Dl 4326 5576 4322 5602 Dl 4322 5602 4313 5611 Dl 4337 5547 4325 5560 Dl 4325 5560 4329 5559 Dl 4336 5552 4329 5559 Dl 4312 5612 4310 5617 Dl 4310 5618 4312 5632 Dl 4333 5593 4322 5602 Dl 4336 5568 4326 5575 Dl 4328 5559 4318 5580 Dl 4286 5676 4109 6524 Dl 4306 5656 4286 5676 Dl 5 R f (83)4192 6112 w 10 R f 0.1 setlinewidth 4292 5636 4285 5655 Dl 4286 5656 4286 5676 Dl 4310 5618 4292 5636 Dl 4304 5596 4294 5616 Dl 4292 5617 4292 5636 Dl 4316 5582 4304 5596 Dl 4317 5570 4306 5585 Dl 4306 5584 4304 5596 Dl 4324 5561 4317 5569 Dl 4285 5655 3916 6169 Dl (89)4025 6182 w 4292 5616 3948 6102 Dl 4305 5585 3984 6040 Dl 20 R f 16 setlinewidth 5040 6702 3744 6702 Dl 5040 5406 5040 6702 Dl 3744 5406 5040 5406 Dl 3744 6702 3744 5406 Dl 10 B f (Fig. 7:)1 272 1 804 6900 t 10 I f (d)1101 6900 w 10 R f (= \(0,0,1\), 30)2 497 1 1176 6900 t 10 S f (\260)1673 6900 w 10 R f (view)1738 6900 w 10 B f (Fig. 8:)1 272 1 2418 6900 t 10 I f (d)2715 6900 w 10 R f (= \(\26110)1 264 1 2790 6900 t 7 R f (\26110)3054 6850 w 10 R f (,0,1\))3159 6900 w 10 B f (Fig. 9:)1 272 1 3805 6900 t 10 R f (Figure 7, rotated 180)3 838 1 4102 6900 t 10 S f (\260)4940 6900 w 10 R f ( do not completely determine our view of a polytope:)9 2182(The viewpoint, view direction, and view angle)6 1888 2 970 7056 t ( Tom Duff's convention of changing coordi-)6 1780( Following)1 462( the view direction.)3 771(we are still free to rotate it about)7 1307 4 720 7176 t (nates so the view direction is a positive multiple of \(0,1,0\), I first rotate things in the \()17 3425 1 720 7296 t 10 I f (x)4153 7296 w 10 R f (,)4205 7296 w 10 I f (y)4262 7296 w 10 R f (\) plane \(i.e., about)3 726 1 4314 7296 t (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 10 11 %%Page: 11 12 /saveobj save def mark 12 pagesetup 10 R f (- 11 -)2 216 1 2772 480 t (the)720 840 w 10 I f (z)870 840 w 10 R f ( first coordinate of the view direction, then rotate things in the \()12 2562(axis\) to zero the)3 649 2 937 840 t 10 I f (y)4156 840 w 10 R f (,)4208 840 w 10 I f (z)4265 840 w 10 R f (\) plane to zero the)4 728 1 4312 840 t ( determines an orthogonal matrix)4 1342( This)1 232( the view direction.)3 783(third coordinate of)2 749 4 720 960 t 10 I f (Q)3855 960 w 10 R f (, the product of two Givens)5 1113 1 3927 960 t (rotations, such that a point)4 1154 1 720 1080 t 10 I f (p)1922 1080 w 10 R f (is transformed to)2 723 1 2020 1080 t 10 I f (p)2791 1080 w 10 S f (\242 =)1 129 1 2849 1080 t 10 I f (Q)3027 1080 w 10 R f (\()3107 1080 w 10 I f (p)3148 1080 w 10 S f (-)3238 1080 w 10 I f (v)3333 1080 w 10 R f ( be visible,)2 482( \(To)1 217(\) before being plotted.)3 956 3 3385 1080 t 10 I f (p)720 1200 w 10 S f (\242 =)1 129 1 778 1200 t 10 R f (\()956 1200 w 10 I f (p)997 1200 w 10 S f (\242)1055 1200 w 7 R f (1)1066 1220 w 10 R f (,)1117 1200 w 10 I f (p)1174 1200 w 10 S f (\242)1232 1200 w 7 R f (2)1243 1220 w 10 R f (,)1294 1200 w 10 I f (p)1351 1200 w 10 S f (\242)1409 1200 w 7 R f (3)1420 1220 w 10 R f (\) must have)2 466 1 1471 1200 t 10 I f (p)1962 1200 w 10 S f (\242)2020 1200 w 7 R f (2)2031 1220 w 10 S f (>)2123 1200 w 10 R f (0 and max)2 416 1 2227 1200 t 10 I f ({)2651 1200 w 10 S f (\357)2691 1200 w 10 I f (p)2739 1200 w 10 S f (\242)2797 1200 w 7 R f (1)2808 1220 w 10 I f (/ p)1 86 1 2859 1200 t 10 S f (\242)2953 1200 w 7 R f (2)2964 1220 w 10 S f (\357)3007 1200 w 10 R f (,)3055 1200 w 10 S f (\357)3113 1200 w 10 I f (p)3161 1200 w 10 S f (\242)3219 1200 w 7 R f (3)3230 1220 w 10 I f (/ p)1 86 1 3281 1200 t 10 S f (\242)3375 1200 w 7 R f (2)3386 1220 w 10 S f (\357)3429 1200 w 10 I f (})3477 1200 w 10 S f (\243)3558 1200 w 10 R f (tan \()1 163 1 3654 1200 t 10 S f (a)3825 1200 w 10 I f (/)3896 1200 w 10 R f (2 \).\))1 149 1 3932 1200 t (The above choice of)3 823 1 970 1356 t 10 I f (Q)1822 1356 w 10 R f ( vertical, i.e., to the)4 791(makes the least possible change to the)6 1544 2 1923 1356 t 10 I f (z)4288 1356 w 10 R f ( the view)2 376(axis. If)1 307 2 4357 1356 t (direction)720 1476 w 10 I f (d)1103 1476 w 10 R f (is nearly parallel to the)4 927 1 1181 1476 t 10 I f (z)2136 1476 w 10 R f (axis, then small changes in)4 1086 1 2203 1476 t 10 I f (d)3317 1476 w 10 R f ( in)1 105(can make big changes)3 887 2 3395 1476 t 10 I f (Q)4414 1476 w 10 R f ( 7\2619)1 177(. Figures)1 377 2 4486 1476 t (illustrate this \(with a 30)4 950 1 720 1596 t 10 S f (\260)1670 1596 w 10 R f (view angle\):)1 496 1 1735 1596 t 10 I f (d)2281 1596 w 10 S f (=)2380 1596 w 10 R f ( no rotation in the \()5 774( in figure 7 \(and I use)6 859(\( 0 , 0 , 1 \))6 314 3 2484 1596 t 10 I f (x)4439 1596 w 10 R f (,)4491 1596 w 10 I f (y)4548 1596 w 10 R f (\) plane\); in)2 440 1 4600 1596 t (figure 8,)1 352 1 720 1716 t 10 I f (d)1111 1716 w 10 S f (=)1210 1716 w 10 R f (\()1314 1716 w 10 S f (-)1363 1716 w 10 R f (10)1434 1716 w 7 S f (-)1545 1676 w 7 R f (10)1595 1676 w 10 R f ( makes the figure turn 90)5 1071(, 0 , 1 \))4 215 2 1681 1716 t 10 S f (\260)2967 1716 w 10 R f (; and rotating figure 7 by 180)6 1255 1 3007 1716 t 10 S f (\260)4262 1716 w 10 R f (\(or, equivalently,)1 699 1 4341 1716 t (choosing)720 1836 w 10 I f (d)1110 1836 w 10 R f (to be, e.g., \()3 486 1 1189 1836 t 10 S f (-)1691 1836 w 10 R f (10)1762 1836 w 7 S f (-)1873 1796 w 7 R f (20)1923 1796 w 10 R f (,)2009 1836 w 10 S f (-)2050 1836 w 10 R f (10)2121 1836 w 7 S f (-)2232 1796 w 7 R f (10)2282 1796 w 10 R f ( view relative to figure 2,)5 1034( gives figure 9, which is the ``right'')7 1481(, 1 \)\))2 157 3 2368 1836 t (as it rotates this figure by 90)6 1138 1 720 1956 t 10 S f (\260)1858 1956 w 10 R f (about its)1 342 1 1923 1956 t 10 I f (x)2290 1956 w 10 R f (axis \(rotating the top away from us, the bottom towards us\).)10 2392 1 2359 1956 t (Given a)1 317 1 970 2112 t 10 I f (Q)1316 2112 w 10 R f (, say)1 187 1 1388 2112 t 10 I f (Q)1604 2112 w 7 R f (\( 1 \))2 91 1 1687 2072 t 10 R f ( direction)1 385(, for a particular view)4 877 2 1786 2112 t 10 I f (d)3078 2112 w 7 R f (\( 1 \))2 91 1 3139 2072 t 10 R f (, and given a second view direction)6 1441 1 3238 2112 t 10 I f (d)4709 2112 w 7 R f (\( 2 \))2 91 1 4770 2072 t 10 R f (, we)1 171 1 4869 2112 t (could choose an orthogonal)3 1110 1 720 2232 t 10 I f (Q)1858 2232 w 7 R f (\( 2 \))2 91 1 1941 2192 t 10 R f (to minimize)1 484 1 2068 2232 t 10 S f (||)2580 2232 w 10 I f (Q)2628 2232 w 7 R f (\( 1 \))2 91 1 2711 2192 t 10 S f (-)2867 2232 w 10 I f (Q)2971 2232 w 7 R f (\( 2 \))2 91 1 3054 2192 t 10 S f (||)3169 2232 w 10 R f (subject to)1 389 1 3237 2232 t 10 I f (Q)3653 2232 w 7 R f (\( 2 \))2 91 1 3736 2192 t 10 I f (d)3851 2232 w 7 R f (\( 2 \))2 91 1 3912 2192 t 10 S f (= ||)1 144 1 4068 2232 t 10 I f (d)4220 2232 w 7 R f (\( 2 \))2 91 1 4281 2192 t 10 S f (||)4396 2232 w 7 R f (2)4447 2252 w 10 R f ( but)1 155( \),)1 66( 0)1 82( ,)1 33( 1)1 82(\( 0 ,)2 124 6 4498 2232 t (it is impossible to make)4 979 1 720 2352 t 10 I f (Q)1731 2352 w 10 R f (a continuous function of)3 995 1 1835 2352 t 10 I f (d)2862 2352 w 10 R f (. \(Choosing)1 499 1 2912 2352 t 10 I f (Q)3443 2352 w 10 R f (\()3523 2352 w 10 I f (d)3564 2352 w 10 R f (\) to be the negative of the obvious)7 1418 1 3622 2352 t (Householder transformation would give us a discontinuity at)7 2423 1 720 2472 t 10 I f (d)3168 2472 w 10 S f (=)3267 2472 w 10 R f (\( 0 ,)2 124 1 3371 2472 t 10 S f (-)3511 2472 w 10 R f (1 , 0 \).\))3 240 1 3582 2472 t ( generally means an extra 180)5 1214( This)1 232(I have tried to rotate the remaining figures sensibly.)8 2098 3 970 2628 t 10 S f (\260)4514 2628 w 10 R f (rotation for)1 457 1 4583 2628 t (figures with view direction)3 1079 1 720 2748 t 10 I f (d)1824 2748 w 10 S f (=)1923 2748 w 10 R f ( and no extra rotation for other directions.)7 1669(\( 0 , 0 , 1 \))6 314 2 2027 2748 t ( a cost vector \()4 607(I choose)1 339 2 970 2904 t 10 I f (c)1916 2904 w 10 R f (in \(1a\) or)2 381 1 1990 2904 t 10 I f (b)2401 2904 w 10 R f (in \(2a\)\) to make the simplex method \(as implemented by XMP)10 2559 1 2481 2904 t ( 10 shows figure 6 with the path fol-)8 1518( Figure)1 319( path, one with several zig-zags.)5 1323([17]\) trace out a picturesque)4 1160 4 720 3024 t ( superimposed; the dotted lines connect vertices visited in phase 1 \(while)11 3081(lowed by the simplex method)4 1239 2 720 3144 t ( phase 2.)2 352(XMP sought a feasible point\), and the heavy solid lines \(19 of them\) connect the vertices visited in)17 3968 2 720 3264 t ( what looks like a piece of)6 1072(The first phase-1 step is off screen, and the last three phase-1 steps coalesce into)14 3248 2 720 3384 t (solid line outside the polytope.)4 1231 1 720 3504 t 10 B f (Pictures of the Dual Affine Algorithm)5 1606 1 720 3744 t 10 R f ( version)1 327( This)1 236( LP algorithm.)2 597(The next several figures deal with a dual affine version of Karmarkar's)11 2910 4 970 3900 t (chooses its step lengths as in [1]:)6 1730 1 720 4020 t 10 I f (x)2544 4020 w 7 I f (k)2599 3980 w 7 S f (+)2646 3980 w 7 R f (1)2696 3980 w 10 S f (=)2788 4020 w 10 I f (x)2892 4020 w 7 I f (k)2947 3980 w 10 S f (+)3035 4020 w 10 R f (0. 99)1 183 1 3139 4020 t 10 S f (a)3330 4020 w 7 I f (k)3398 4039 w 7 R f (max)3398 3980 w 10 I f (p)3535 4020 w 7 I f (k)3596 3980 w 10 R f ( steps and)2 530(for the first 10)3 781 2 3729 4020 t 10 I f (x)720 4140 w 7 I f (k)775 4100 w 7 S f (+)822 4100 w 7 R f (1)872 4100 w 10 S f (=)964 4140 w 10 I f (x)1068 4140 w 7 I f (k)1123 4100 w 10 S f (+)1211 4140 w 10 R f (0. 9)1 133 1 1315 4140 t 10 S f (a)1456 4140 w 7 I f (k)1524 4159 w 7 R f (max)1524 4100 w 10 I f (p)1661 4140 w 7 I f (k)1722 4100 w 10 R f ( iterations, where)2 692(for the remaining)2 693 2 1786 4140 t 10 S f (a)3197 4140 w 7 I f (k)3265 4159 w 7 R f (max)3265 4100 w 10 S f (=)3443 4140 w 10 R f (max)3547 4140 w 10 I f ({)3727 4140 w 10 S f (a)3775 4140 w 10 R f (:)3846 4140 w 10 I f (x)3915 4140 w 7 I f (k)3970 4100 w 10 S f (+ a)1 167 1 4058 4140 t 10 I f (p)4233 4140 w 7 I f (k)4294 4100 w 10 S f (\263)4374 4140 w 10 B f (0)4470 4140 w 10 I f (})4528 4140 w 10 R f (is the max-)2 446 1 4594 4140 t ( when it succeeds in finding a point at which the Karush-Kuhn-Tucker optimal-)12 3190( stops)1 233( It)1 113(imum feasible step.)2 784 4 720 4260 t ( the)1 162( For)1 204( is an interesting detail to be discussed elsewhere\).)8 2136( side computation)2 739( \(This)1 275(ity conditions hold.)2 804 6 720 4380 t (problem at hand, it finds an optimal point during the 19th iteration.)11 2680 1 720 4500 t ( shows figure 6 with the dual affine algorithm's path superim-)10 2590( it)1 117( to figure 10:)3 552(Figure 11 is similar)3 811 4 970 4656 t ( along edges of the polytope, the path in figure 11 lies strictly)12 2468( whereas the path in figure 10 runs)7 1397(posed. But)1 455 3 720 4776 t ( are)1 153(inside the polytope; to understand figure 11, imagine that the path is glowing and the polytope's faces)16 4167 2 720 4896 t (translucent but dark enough that you do not see more polytope edges.)11 2774 1 720 5016 t ( solution path in figure 11 appears to be following polytope edges.)11 2763(Notice that the latter half of the)6 1307 2 970 5172 t ( close to a facet, the corre-)6 1084(This accords with the theory in [18], which says that when an affine iterate lies)14 3236 2 720 5292 t (sponding search direction should be nearly parallel to the facet.)9 2528 1 720 5412 t ( are similar to figure 11, but are drawn from other viewpoints and with a view angle of)17 3494(Figures 12\26114)1 576 2 970 5568 t (30)720 5688 w 10 S f (\260)820 5688 w 10 R f ( figure 11, figures)3 721( Like)1 235( where otherwise noted, all the remaining figures use this view angle.\))11 2836(. \(Except)1 388 4 860 5688 t (12 and 13 are from outside the polytope; figure 14, on the other hand, is a view from inside.)18 3670 1 720 5808 t ( when one sits at the)5 878(The view changes rapidly)3 1064 2 970 5964 t 10 I f (center)2950 5964 w 10 R f (\(1,1,1\) of the affinely transformed polytope)5 1803 1 3237 5964 t 10 I f ({ x)1 92 1 720 6084 t 10 S f (\316)853 6084 w 10 I f (I R)1 78 1 965 6084 t 7 I f (n)1048 6044 w 10 R f (:)1099 6084 w 10 I f (ADx)1168 6084 w 10 S f (=)1394 6084 w 10 I f (b)1498 6084 w 10 R f (,)1556 6084 w 10 I f (x)1622 6084 w 10 S f (\263)1707 6084 w 10 B f (0)1803 6084 w 10 I f (})1861 6084 w 10 R f ( direction)1 381( View)1 267(, i.e., at the image of the current iterate.)8 1579 3 1901 6084 t 10 I f (d)4153 6084 w 10 S f (=)4252 6084 w 10 R f (\()4356 6084 w 10 S f (-)4405 6084 w 10 R f ( proves)1 291(1 , 0 , 0 \))5 273 2 4476 6084 t ( 6, the corresponding view, fig-)5 1266( iteration)1 359( For)1 190( 15\26117 show iterations 2\2614.)4 1112( Figures)1 351(interesting in this context.)3 1042 6 720 6204 t ( sharply by changing the view angle from)7 1689( if we turn the magnification up)6 1295( But)1 200(ure 18, looks much simpler.)4 1136 4 720 6324 t (30)720 6444 w 10 S f (\260)820 6444 w 10 R f (to 0.005)1 334 1 891 6444 t 10 S f (\260)1225 6444 w 10 R f ( 20 shows)2 414( figure)1 295( situation is similar for iteration 8:)6 1409( The)1 212( the view in figure 19.)5 917(, then we get)3 528 6 1265 6444 t (view angle 30)2 560 1 720 6564 t 10 S f (\260)1280 6564 w 10 R f (, whereas figure 21 shows much more detail with view angle 0.01)11 2626 1 1320 6564 t 10 S f (\260)3946 6564 w 10 R f (.)3986 6564 w (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 11 12 %%Page: 12 13 /saveobj save def mark 13 pagesetup 10 R f (- 12 -)2 216 1 2772 282 t 0.1 setlinewidth 2470 921 2465 960 Dl 2464 961 2445 1034 Dl 1195 1113 1542 2153 Dl 1542 2154 1575 2224 Dl 1575 2225 1771 2378 Dl 1175 711 1152 766 Dl 1151 766 1145 827 Dl 1146 827 1149 906 Dl 1150 907 1160 977 Dl 1161 977 1194 1113 Dl 2371 711 2438 761 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1692 Dl 1970 1660 1974 1668 Dl 1937 1490 1970 1660 Dl 1891 1477 1937 1489 Dl 1865 1361 1891 1476 Dl 1862 1299 1864 1360 Dl 1848 1282 1862 1299 Dl 1812 1272 1848 1281 Dl 1756 1105 1810 1272 Dl 1726 1120 1756 1105 Dl 1639 1098 1726 1121 Dl 1637 1094 1639 1098 Dl 1592 1091 1635 1093 Dl 1565 990 1591 1091 Dl 10 R f 0.1 setlinewidth 4774 921 4769 960 Dl 4768 961 4749 1034 Dl 3499 1113 3846 2153 Dl 3846 2154 3879 2224 Dl 3879 2225 4075 2378 Dl 3479 711 3456 766 Dl 3455 766 3449 827 Dl 3450 827 3453 906 Dl 3454 907 3464 977 Dl 3465 977 3498 1113 Dl 4675 711 4742 761 Dl 4743 761 4771 824 Dl 4771 824 4777 896 Dl 4777 896 4775 920 Dl 4132 2352 4075 2378 Dl 4409 2129 4133 2351 Dl 4476 2004 4425 2107 Dl 4425 2108 4410 2128 Dl 4477 2003 4749 1034 Dl 4522 1814 4491 1942 Dl 4490 1943 4476 2003 Dl 4523 1813 4769 960 Dl 4539 1556 4525 1706 Dl 4525 1707 4523 1815 Dl 4541 1556 4777 896 Dl 5 R f (10)4598 1408 w 10 R f 0.1 setlinewidth 4497 1160 4507 1316 Dl 4508 1317 4541 1556 Dl 4496 1158 4771 824 Dl (11)4564 1190 w 4348 793 4430 1023 Dl 4432 1023 4496 1159 Dl 4349 792 4742 761 Dl (12)4498 927 w 4138 560 4674 710 Dl 4276 737 4127 585 Dl 4278 738 4301 758 Dl 4119 575 4137 560 Dl 4127 586 4119 576 Dl 4301 758 4348 792 Dl 5 R f (13)4382 706 w 10 R f 0.1 setlinewidth 4199 2263 4133 2351 Dl 4336 2134 4199 2262 Dl 4337 2134 4425 2107 Dl 4368 1994 4330 2107 Dl 4330 2107 4336 2134 Dl 4382 1973 4368 1993 Dl 4383 1972 4491 1942 Dl 5 R f (15)4382 2047 w 10 R f 0.1 setlinewidth 4454 1722 4382 1972 Dl 4455 1721 4525 1706 Dl 5 R f (16)4440 1853 w 10 R f 0.1 setlinewidth 4408 1594 4420 1679 Dl 4464 1322 4408 1594 Dl 4421 1679 4455 1722 Dl 4466 1321 4507 1316 Dl 5 R f (17)4454 1550 w 10 R f 0.1 setlinewidth 4376 1027 4376 1123 Dl 4376 1123 4465 1321 Dl 4376 1026 4430 1023 Dl 5 R f (18)4418 1174 w 10 R f 0.1 setlinewidth 4315 938 4376 1026 Dl 4302 758 4314 938 Dl 5 R f (19)4330 918 w 10 R f 0.1 setlinewidth 4118 579 4116 575 Dl 4127 585 4118 580 Dl 4117 576 4119 576 Dl 4079 558 4137 560 Dl 4083 567 4074 563 Dl 4115 575 4083 568 Dl 4074 564 4079 558 Dl 4391 1687 4386 1692 Dl 4386 1692 4351 1911 Dl 4351 1912 4368 1993 Dl 4421 1679 4392 1686 Dl 4309 1147 4301 1363 Dl 4301 1363 4396 1587 Dl 4375 1123 4309 1147 Dl 4396 1589 4408 1594 Dl 5 R f (23)4352 1346 w 10 R f 0.1 setlinewidth 4196 748 4194 766 Dl 4195 766 4205 803 Dl 4205 804 4292 932 Dl 4276 738 4196 748 Dl 4293 933 4314 938 Dl 4396 1588 4392 1686 Dl 4292 932 4258 1063 Dl 4258 1063 4309 1147 Dl 5 R f (26)4295 1057 w 10 R f 0.1 setlinewidth 4116 664 4112 652 Dl 4111 598 4118 580 Dl 4109 635 4110 597 Dl 4196 747 4116 664 Dl 4112 652 4109 637 Dl 4227 2074 4167 2135 Dl 4167 2135 4199 2262 Dl 4329 2107 4227 2075 Dl 5 R f (28)4217 2163 w 10 R f 0.1 setlinewidth 4189 2004 4227 2075 Dl 4247 1884 4188 2003 Dl 4351 1911 4248 1883 Dl 5 R f (29)4259 2004 w 10 R f 0.1 setlinewidth 4278 1669 4238 1797 Dl 4239 1797 4248 1883 Dl 4386 1691 4278 1668 Dl 5 R f (30)4286 1798 w 10 R f 0.1 setlinewidth 4261 1358 4241 1489 Dl 4241 1490 4274 1660 Dl 4274 1660 4278 1668 Dl 4300 1362 4262 1357 Dl 5 R f (31)4289 1552 w 10 R f 0.1 setlinewidth 4246 1063 4222 1105 Dl 4221 1105 4240 1315 Dl 4242 1315 4262 1357 Dl 4257 1062 4245 1062 Dl 5 R f (32)4242 1222 w 10 R f 0.1 setlinewidth 4178 899 4182 924 Dl 4204 803 4178 897 Dl 4182 924 4245 1062 Dl 4112 652 4107 640 Dl 4108 640 4109 637 Dl 4080 557 4037 559 Dl 4036 559 4037 559 Dl 4074 564 4035 560 Dl 4171 1917 4176 1994 Dl 4177 1774 4170 1917 Dl 4188 2002 4176 1994 Dl 4238 1797 4179 1774 Dl 4195 1633 4165 1758 Dl 4166 1759 4179 1774 Dl 4274 1658 4196 1632 Dl 4131 1519 4176 1609 Dl 4194 1477 4130 1519 Dl 4176 1609 4196 1632 Dl 4241 1488 4195 1476 Dl 4166 1299 4168 1360 Dl 4169 1361 4195 1476 Dl 4240 1314 4166 1299 Dl 4167 1109 4152 1281 Dl 4152 1282 4166 1299 Dl 4191 1102 4168 1110 Dl 4221 1104 4191 1100 Dl 4144 962 4140 975 Dl 4183 924 4145 961 Dl 4140 975 4191 1100 Dl 4090 836 4093 846 Dl 4142 769 4089 836 Dl 4150 766 4142 768 Dl 4177 897 4093 846 Dl 4194 766 4151 766 Dl 4115 664 4074 682 Dl 4151 765 4074 682 Dl 4107 640 4056 617 Dl 4110 598 4056 617 Dl 3923 2127 3879 2224 Dl 4098 2094 3924 2126 Dl 4166 2135 4098 2094 Dl 5 R f (45)4027 2233 w 10 R f 0.1 setlinewidth 4087 1957 4080 1962 Dl 4080 1963 4098 2094 Dl 4176 1994 4088 1957 Dl 4129 1743 4170 1917 Dl 4165 1757 4129 1742 Dl 4175 1609 4127 1740 Dl 4129 1741 4127 1740 Dl 4167 1361 4118 1510 Dl 4130 1517 4118 1510 Dl 4074 1015 4075 1060 Dl 4140 976 4074 1015 Dl 4167 1109 4075 1060 Dl 4093 847 4092 877 Dl 4093 877 4145 961 Dl 4044 687 4054 725 Dl 4073 682 4043 687 Dl 4142 768 4054 725 Dl 4049 607 4057 574 Dl 4053 616 4048 607 Dl 4083 568 4057 574 Dl 4055 617 4053 617 Dl 4071 1835 4088 1957 Dl 4116 1736 4070 1835 Dl 4126 1740 4116 1735 Dl 5 R f (55)4097 1887 w 10 R f 0.1 setlinewidth 4087 1500 4069 1566 Dl 4068 1566 4116 1735 Dl 4117 1509 4087 1499 Dl 4070 1415 4087 1499 Dl 4114 1273 4070 1415 Dl 4150 1281 4114 1272 Dl 4075 1060 4060 1105 Dl 4060 1105 4114 1272 Dl 4069 995 4074 1015 Dl 4092 877 4069 994 Dl 4054 725 4058 804 Dl 4088 835 4058 804 Dl 4053 617 4014 668 Dl 4042 687 4014 668 Dl 3935 1983 3924 2126 Dl 3988 1929 3935 1983 Dl 4079 1962 3988 1929 Dl 5 R f (62)3983 2043 w 10 R f 0.1 setlinewidth 4067 1566 4062 1568 Dl 4062 1568 4006 1722 Dl 4006 1723 4070 1835 Dl 4060 1106 4030 1121 Dl 4029 1121 4029 1356 Dl 4030 1356 4070 1415 Dl 5 R f (64)4038 1270 w 10 R f 0.1 setlinewidth 3978 858 3972 869 Dl 4058 805 3979 857 Dl 4069 994 3972 869 Dl 4056 573 3988 566 Dl 4034 560 3988 566 Dl 3977 1703 3952 1780 Dl 3952 1780 3988 1929 Dl 4006 1722 3978 1702 Dl 5 R f (67)3992 1853 w 10 R f 0.1 setlinewidth 3976 1520 3951 1617 Dl 3951 1617 3978 1702 Dl 4062 1567 3976 1519 Dl 3966 1329 3947 1365 Dl 3947 1366 3976 1519 Dl 4029 1356 3966 1329 Dl 5 R f (69)3992 1457 w 10 R f 0.1 setlinewidth 3943 1098 3966 1329 Dl 4030 1121 3943 1098 Dl 5 R f (70)3967 1230 w 10 R f 0.1 setlinewidth 3971 869 3935 892 Dl 3941 1097 3939 1093 Dl 3935 893 3939 1093 Dl 5 R f (71)3973 1019 w 10 R f 0.1 setlinewidth 3996 669 3979 857 Dl 4014 667 3996 668 Dl 3995 668 3981 665 Dl 4047 608 3981 665 Dl 4036 559 3955 570 Dl 3988 566 3955 570 Dl 3880 1687 3874 1748 Dl 3874 1749 3935 1983 Dl 3951 1779 3880 1687 Dl 3858 1302 3854 1306 Dl 3855 1306 3866 1560 Dl 3897 1337 3859 1302 Dl 3898 1337 3900 1576 Dl 3900 1575 3866 1560 Dl 3935 893 3869 990 Dl 3869 990 3895 1091 Dl 3938 1093 3895 1091 Dl 3955 571 3905 579 Dl 3969 666 3905 579 Dl 3981 665 3970 666 Dl 3865 1561 3859 1578 Dl 3859 1578 3880 1687 Dl 3951 1616 3900 1576 Dl 3946 1365 3897 1337 Dl 3895 1092 3859 1302 Dl 5 R f (81)3891 1244 w 10 R f 0.1 setlinewidth 3933 688 3903 738 Dl 3969 668 3933 689 Dl 3903 738 3935 892 Dl 3818 1672 3846 2153 Dl 3872 1748 3816 1672 Dl 5 R f (83)3848 1972 w 10 R f 0.1 setlinewidth 3800 1513 3792 1557 Dl 3792 1557 3816 1672 Dl 3859 1577 3801 1512 Dl 3802 1267 3779 1337 Dl 3779 1337 3801 1512 Dl 3854 1306 3802 1266 Dl 5 R f (85)3801 1424 w 10 R f 0.1 setlinewidth 3830 978 3790 1051 Dl 3791 1051 3802 1266 Dl 3869 989 3831 977 Dl 5 R f (86)3815 1144 w 10 R f 0.1 setlinewidth 3902 739 3829 803 Dl 3830 803 3831 977 Dl 5 R f (87)3850 879 w 10 R f 0.1 setlinewidth 3905 580 3903 580 Dl 3933 688 3903 580 Dl 3792 1557 3464 977 Dl (89)3649 1583 w 3779 1336 3453 906 Dl 5 R f (90)3632 1259 w 10 R f 0.1 setlinewidth 3790 1050 3449 827 Dl (91)3607 1089 w 3829 803 3456 766 Dl 5 R f (92)3651 889 w 10 R f 0.1 setlinewidth 3903 580 3479 710 Dl 5 R f (93)3706 718 w 20 R f 16 setlinewidth 5040 2502 3024 2502 Dl 5040 486 5040 2502 Dl 3024 486 5040 486 Dl 3024 2502 3024 486 Dl 3686 1255 4032 1679 Dl 3685 1254 3744 1298 Dl 3686 1255 3717 1321 Dl 3700 1203 3685 1254 Dl 3800 1267 3700 1201 Dl 3801 1261 3800 1267 Dl 3797 1152 3802 1262 Dl 3792 1050 3797 1151 Dl 3797 1037 3792 1049 Dl 3830 978 3798 1037 Dl 3831 978 1 1 De 3854 984 3831 977 Dl 3866 989 3854 985 Dl 3868 990 3867 990 Dl 10 B f (Fig. 10:)1 322 1 1144 2700 t 10 R f (simplex \(XMP\) path)2 822 1 1491 2700 t 10 B f (Fig. 11:)1 322 1 3546 2700 t 10 R f (dual affine path)2 626 1 3893 2700 t 0.1 setlinewidth 2516 3966 2523 3983 Dl 2524 3983 2537 4027 Dl 2538 4028 2550 4090 Dl 2550 4091 2584 4368 Dl 871 4328 1288 4600 Dl 1289 4601 1344 4625 Dl 1345 4624 1730 4680 Dl 1730 4680 2584 4368 Dl 1093 3849 1038 3945 Dl 1038 3945 987 4050 Dl 986 4050 871 4327 Dl 2492 3932 2515 3965 Dl 1766 3861 1730 4680 Dl 1820 3229 1766 3861 Dl 1821 3229 2550 4090 Dl (7)2050 4085 w 1815 3162 1815 3200 Dl 1815 3200 1820 3228 Dl 1816 3161 2537 4027 Dl 5 R f (8)2153 3617 w 10 R f 0.1 setlinewidth 1805 3111 1810 3139 Dl 1811 3140 1816 3161 Dl 1804 3112 2523 3983 Dl 5 R f (9)2142 3561 w 10 R f 0.1 setlinewidth 1790 3077 1792 3088 Dl 1793 3089 1804 3111 Dl 1790 3077 2492 3932 Dl 1766 3054 1771 3058 Dl 1771 3059 1789 3077 Dl 1750 3049 1766 3054 Dl 1759 3388 1766 3861 Dl 1777 3193 1759 3388 Dl 1778 3193 1815 3200 Dl 5 R f (14)1759 3445 w 10 R f 0.1 setlinewidth 1770 3138 1771 3178 Dl 1771 3178 1778 3193 Dl 1771 3132 1769 3137 Dl 1773 3132 1810 3139 Dl 1772 3085 1772 3132 Dl 1772 3084 1792 3088 Dl 1755 3071 1761 3078 Dl 1759 3056 1754 3071 Dl 1761 3079 1772 3084 Dl 1761 3056 1771 3058 Dl 1738 3045 1738 3047 Dl 1738 3048 1761 3056 Dl 1736 3046 1748 3048 Dl 1724 3046 1736 3046 Dl 1753 3080 1 1 De 1754 3081 1758 3119 Dl 1758 3119 1769 3137 Dl 1760 3079 1754 3080 Dl 1724 3049 1725 3059 Dl 1725 3059 1751 3070 Dl 1737 3048 1724 3049 Dl 1752 3071 1754 3071 Dl 1700 3048 1702 3048 Dl 1702 3047 1719 3045 Dl 1719 3045 1723 3045 Dl 1752 3072 1754 3080 Dl 1719 3046 1713 3048 Dl 1714 3049 1724 3049 Dl 1734 3187 1721 3252 Dl 1721 3252 1759 3388 Dl 1771 3178 1735 3186 Dl 1718 3169 1735 3186 Dl 1728 3126 1717 3168 Dl 1757 3119 1728 3126 Dl 1727 3087 1722 3111 Dl 1722 3111 1728 3126 Dl 1753 3081 1728 3086 Dl 1717 3062 1715 3073 Dl 1715 3074 1726 3086 Dl 1727 3086 1728 3086 Dl 1724 3059 1717 3061 Dl 1710 3050 1706 3052 Dl 1707 3052 1712 3060 Dl 1712 3061 1717 3061 Dl 1712 3049 1710 3049 Dl 1697 3050 1 1 De 1702 3048 1697 3050 Dl 1698 3050 1710 3049 Dl 1709 3150 1713 3169 Dl 1707 3117 1709 3150 Dl 1717 3169 1713 3169 Dl 1722 3111 1707 3117 Dl 1707 3094 1702 3117 Dl 1703 3117 1707 3117 Dl 1725 3086 1707 3093 Dl 1690 3090 1702 3093 Dl 1704 3078 1690 3090 Dl 1702 3093 1707 3093 Dl 1714 3073 1704 3077 Dl 1697 3067 1697 3071 Dl 1697 3072 1704 3077 Dl 1711 3061 1696 3067 Dl 1695 3057 1693 3067 Dl 1693 3067 1696 3067 Dl 1699 3055 1695 3057 Dl 1705 3052 1700 3054 Dl 1689 3055 1 1 De 1697 3050 1690 3054 Dl 1690 3054 1700 3054 Dl 1680 3057 1 1 De 1689 3053 1679 3057 Dl 1691 3052 1690 3052 Dl 1697 3051 1680 3057 Dl 1700 3049 1692 3052 Dl 1570 3577 1344 4625 Dl 1691 3265 1571 3576 Dl 1721 3252 1692 3264 Dl (45)1558 4116 w 1682 3188 1680 3193 Dl 1682 3194 1692 3264 Dl 1713 3170 1683 3188 Dl 1693 3122 1709 3150 Dl 1702 3117 1692 3121 Dl 1702 3093 1692 3121 Dl 1696 3071 1686 3090 Dl 1688 3090 1686 3090 Dl 1676 3063 1676 3064 Dl 1689 3055 1676 3062 Dl 1695 3057 1676 3064 Dl 1679 3057 1 1 De 1680 3057 1690 3054 Dl 1676 3159 1683 3188 Dl 1688 3123 1676 3157 Dl 1691 3122 1689 3123 Dl 1678 3094 1674 3106 Dl 1675 3107 1689 3123 Dl 1686 3091 1679 3094 Dl 1675 3089 1679 3094 Dl 1684 3071 1674 3089 Dl 1691 3068 1684 3071 Dl 1675 3064 1672 3068 Dl 1672 3069 1684 3071 Dl 1676 3062 1 1 De 1679 3057 1674 3062 Dl 1679 3057 1673 3060 Dl 1610 3330 1571 3576 Dl 1643 3236 1610 3330 Dl 1679 3194 1643 3235 Dl 1674 3106 1673 3108 Dl 1673 3109 1655 3154 Dl 1656 3154 1676 3157 Dl 1673 3069 1666 3074 Dl 1664 3073 1664 3091 Dl 1664 3091 1674 3089 Dl 1654 3073 1653 3074 Dl 1673 3061 1655 3072 Dl 1674 3064 1653 3074 Dl 1644 3161 1632 3198 Dl 1633 3198 1643 3235 Dl 1654 3154 1645 3160 Dl 1648 3125 1638 3152 Dl 1638 3153 1645 3160 Dl 1672 3109 1648 3125 Dl 1647 3104 1641 3113 Dl 1642 3113 1648 3125 Dl 1665 3092 1648 3103 Dl 1645 3089 1648 3103 Dl 1665 3074 1644 3089 Dl 1653 3074 1644 3081 Dl 1643 3089 1 1 De 1643 3082 1643 3089 Dl 1603 3214 1594 3249 Dl 1595 3249 1610 3330 Dl 1632 3198 1604 3213 Dl 1613 3135 1612 3137 Dl 1611 3137 1605 3181 Dl 1625 3126 1613 3134 Dl 1625 3126 1619 3167 Dl 1619 3167 1605 3181 Dl 1643 3082 1624 3102 Dl 1624 3102 1630 3101 Dl 1642 3090 1630 3101 Dl 1605 3182 1601 3191 Dl 1602 3191 1604 3213 Dl 1637 3152 1619 3167 Dl 1641 3113 1626 3125 Dl 1630 3101 1613 3134 Dl 1563 3281 1288 4600 Dl 1593 3249 1563 3281 Dl (83)1407 3964 w 1573 3220 1562 3250 Dl 1562 3250 1563 3281 Dl 1600 3191 1573 3220 Dl 1591 3160 1575 3190 Dl 1574 3190 1573 3220 Dl 1611 3137 1591 3159 Dl 1611 3116 1594 3140 Dl 1593 3141 1591 3159 Dl 1624 3103 1612 3116 Dl 1562 3250 987 4050 Dl (89)1184 4057 w 1575 3190 1038 3945 Dl 5 R f (90)1278 3602 w 10 R f 0.1 setlinewidth 1593 3141 1093 3849 Dl 20 R f 16 setlinewidth 2736 4878 720 4878 Dl 2736 2862 2736 4878 Dl 720 2862 2736 2862 Dl 720 4878 720 2862 Dl 1502 3304 1663 3381 Dl 1526 3254 1502 3304 Dl 1589 3161 1527 3253 Dl 1591 3158 1590 3160 Dl 1593 3148 1591 3158 Dl 1594 3140 1593 3148 Dl 1596 3135 1594 3139 Dl 1610 3116 1597 3135 Dl 1619 3108 1612 3116 Dl 1624 3103 1620 3107 Dl 10 R f 0.1 setlinewidth 3176 4429 4718 4342 Dl 4719 4341 4785 4336 Dl 4786 4336 4888 4309 Dl 3253 3737 3242 3790 Dl 3241 3790 3231 3859 Dl 3231 3860 3218 3968 Dl 3217 3970 3205 4091 Dl 3205 4090 3175 4428 Dl 4594 3875 4888 4309 Dl 4372 3562 4594 3875 Dl 4260 3414 4371 3561 Dl 4211 3365 4248 3400 Dl 4248 3401 4259 3414 Dl 3958 3252 3957 3252 Dl 3950 3254 3947 3255 Dl 3957 3252 3952 3253 Dl 4143 3309 1 1 De 4143 3310 4189 3347 Dl 4190 3347 4210 3365 Dl 4060 3265 4090 3279 Dl 4090 3281 4125 3299 Dl 3999 3249 4001 3249 Dl 4002 3250 4008 3250 Dl 4009 3250 4029 3255 Dl 4126 3299 4142 3309 Dl 4029 3255 4047 3260 Dl 4048 3260 4060 3265 Dl 3978 3250 3976 3250 Dl 3962 3251 3958 3251 Dl 3971 3250 3962 3250 Dl 3998 3249 3979 3249 Dl 3975 3250 3972 3250 Dl 4244 3402 4281 3453 Dl 4281 3453 4371 3561 Dl 4247 3401 4243 3402 Dl 4222 3384 4243 3402 Dl 4186 3348 4222 3384 Dl 4189 3347 4186 3348 Dl 4140 3310 4165 3332 Dl 4167 3333 4186 3348 Dl 4143 3310 4140 3310 Dl 4089 3280 4109 3292 Dl 4109 3292 4138 3309 Dl 4139 3310 4140 3310 Dl 4089 3280 4088 3280 Dl 4047 3261 4052 3263 Dl 4052 3264 4082 3277 Dl 4082 3278 4088 3280 Dl 4020 3255 4024 3255 Dl 4009 3251 4021 3254 Dl 4025 3255 4047 3260 Dl 3974 3250 3972 3250 Dl 3972 3250 1 1 De 3947 3255 3938 3259 Dl 4197 3366 4219 3384 Dl 4161 3336 4197 3366 Dl 4220 3384 4219 3384 Dl 4166 3333 4162 3335 Dl 4133 3313 4158 3334 Dl 4160 3334 4162 3335 Dl 4138 3310 4133 3312 Dl 4113 3303 4129 3310 Dl 4106 3295 4112 3303 Dl 4129 3311 4133 3312 Dl 4108 3293 4106 3294 Dl 4078 3279 4087 3284 Dl 4088 3285 4106 3294 Dl 4082 3277 4078 3279 Dl 4051 3266 4075 3278 Dl 4076 3279 4078 3279 Dl 4050 3264 4050 3265 Dl 4051 3264 4050 3264 Dl 4028 3259 4029 3259 Dl 4025 3256 4028 3258 Dl 4030 3259 4050 3264 Dl 4006 3255 4008 3255 Dl 3999 3251 4006 3254 Dl 4020 3255 4008 3255 Dl 4001 3250 3999 3250 Dl 3979 3249 3979 3250 Dl 3999 3250 3979 3250 Dl 3972 3250 3963 3252 Dl 3963 3252 1 1 De 4387 3680 4785 4336 Dl 4274 3459 4387 3680 Dl 4280 3453 4273 3458 Dl (45)4560 3991 w 4216 3394 4218 3398 Dl 4218 3398 4273 3458 Dl 4219 3385 4215 3394 Dl 4156 3336 4197 3366 Dl 4157 3334 4155 3335 Dl 4129 3311 4155 3335 Dl 4088 3285 4111 3303 Dl 4112 3303 4111 3303 Dl 4033 3264 4039 3266 Dl 4030 3258 4032 3263 Dl 4050 3266 4039 3266 Dl 4009 3255 4013 3256 Dl 4013 3256 4028 3258 Dl 3978 3252 3985 3252 Dl 3979 3252 3978 3252 Dl 3998 3251 3985 3252 Dl 3959 3253 3951 3254 Dl 3963 3252 3960 3252 Dl 3951 3254 1 1 De 4180 3366 4215 3394 Dl 4155 3337 4180 3365 Dl 4155 3335 1 1 De 4109 3305 4120 3315 Dl 4121 3315 4155 3335 Dl 4110 3303 4108 3304 Dl 4093 3297 4108 3304 Dl 4073 3280 4093 3296 Dl 4074 3279 4072 3280 Dl 4039 3267 4044 3270 Dl 4045 3271 4072 3280 Dl 4029 3263 4032 3263 Dl 4014 3256 4029 3263 Dl 3986 3252 3999 3254 Dl 4006 3254 3999 3254 Dl 3963 3252 3970 3252 Dl 3977 3251 3970 3252 Dl 4257 3495 4387 3680 Dl 4219 3424 4257 3495 Dl 4218 3399 4218 3425 Dl 4120 3315 4120 3316 Dl 4121 3317 4154 3355 Dl 4154 3355 4180 3365 Dl 4044 3270 4044 3273 Dl 4045 3275 4081 3295 Dl 4082 3295 4093 3296 Dl 4000 3263 4001 3263 Dl 4000 3254 4000 3261 Dl 4028 3263 4001 3263 Dl 3951 3255 3934 3262 Dl 3938 3260 3934 3262 Dl 4149 3358 4171 3388 Dl 4172 3389 4218 3425 Dl 4153 3356 4149 3358 Dl 4109 3324 4129 3347 Dl 4129 3348 4149 3358 Dl 4120 3317 4109 3324 Dl 4073 3300 4078 3307 Dl 4079 3308 4109 3324 Dl 4080 3295 4073 3300 Dl 4034 3281 4073 3300 Dl 4044 3274 4034 3280 Dl 4001 3263 4001 3267 Dl 4033 3280 1 1 De 4001 3268 4033 3280 Dl 3970 3254 4000 3261 Dl 3970 3253 3968 3254 Dl 3967 3254 3965 3255 Dl 3960 3253 3965 3255 Dl 3933 3262 3927 3265 Dl 4147 3393 4166 3421 Dl 4167 3421 4257 3495 Dl 4171 3388 4147 3392 Dl 4059 3317 4059 3318 Dl 4059 3319 4113 3362 Dl 4069 3314 4059 3317 Dl 4070 3314 4118 3354 Dl 4118 3354 4113 3362 Dl 4001 3267 4006 3282 Dl 4007 3283 4027 3286 Dl 4032 3281 4027 3286 Dl 3927 3266 3918 3271 Dl 3964 3256 3918 3271 Dl 3965 3255 3964 3256 Dl 4114 3362 4117 3369 Dl 4118 3369 4147 3392 Dl 4128 3347 4118 3354 Dl 4078 3308 4069 3313 Dl 4028 3287 4059 3317 Dl 3962 3260 3966 3265 Dl 3964 3256 3962 3260 Dl 3967 3266 4001 3267 Dl 4143 3439 4718 4342 Dl 4166 3421 4143 3438 Dl (83)4414 3900 w 4096 3386 4106 3409 Dl 4107 3408 4143 3438 Dl 4117 3370 4096 3385 Dl 4044 3331 4052 3354 Dl 4053 3355 4096 3385 Dl 4058 3319 4042 3330 Dl 3996 3289 3998 3307 Dl 3999 3307 4042 3330 Dl 4006 3282 3996 3289 Dl 3965 3266 3960 3281 Dl 3960 3282 3996 3289 Dl 3961 3261 3917 3271 Dl 4106 3410 3205 4091 Dl (89)3873 4063 w 4051 3354 3218 3968 Dl (90)3586 3733 w 3998 3307 3231 3859 Dl (91)3568 3648 w 3959 3281 3242 3790 Dl 5 R f (92)3577 3574 w 10 R f 0.1 setlinewidth 3916 3272 3253 3737 Dl 5 R f (93)3567 3531 w 20 R f 16 setlinewidth 5040 4878 3024 4878 Dl 5040 2862 5040 4878 Dl 3024 2862 5040 2862 Dl 3024 4878 3024 2862 Dl 3989 3426 4143 3521 Dl 3988 3426 4058 3448 Dl 3988 3426 4039 3479 Dl 3988 3388 3988 3426 Dl 4042 3332 3988 3388 Dl 4042 3330 4042 3331 Dl 4019 3317 4042 3329 Dl 3999 3307 4019 3317 Dl 3998 3304 3998 3306 Dl 3996 3290 3998 3304 Dl 4002 3285 3996 3289 Dl 4005 3283 4002 3285 Dl 10 B f (Fig. 12:)1 322 1 982 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5689 1617 5706 Dl 1604 5633 1621 5688 Dl 1617 5706 1571 5805 Dl 1668 5486 1670 5473 Dl 1669 5472 1669 5469 Dl 1687 5312 1723 5302 Dl 1723 5302 1 1 De 1694 5352 1725 5304 Dl 1552 6541 1529 6670 Dl 1568 6347 1552 6541 Dl 1514 6680 1529 6670 Dl 1511 6367 1568 6346 Dl 5 R f (36)1500 6504 w 10 R f 0.1 setlinewidth 1572 6204 1584 6330 Dl 1583 6330 1568 6346 Dl 1504 6228 1570 6203 Dl 1635 6100 1590 6180 Dl 1585 6072 1635 6099 Dl 1589 6181 1570 6203 Dl 1549 6086 1585 6072 Dl 1617 5941 1613 5983 Dl 1613 5984 1585 6072 Dl 1562 5963 1617 5941 Dl 1624 5819 1629 5927 Dl 1628 5927 1617 5941 Dl 1608 5819 1623 5819 Dl 1587 5827 1607 5819 Dl 1644 5720 1646 5727 Dl 1618 5706 1643 5719 Dl 1645 5728 1607 5819 Dl 1683 5623 1681 5630 Dl 1647 5592 1684 5622 Dl 1641 5592 1646 5592 Dl 1621 5688 1681 5630 Dl 1611 5604 1640 5592 Dl 1665 5500 1695 5500 Dl 1641 5592 1695 5500 Dl 1670 5472 1708 5426 Dl 1667 5426 1708 5426 Dl 1426 7254 1693 7254 Dl 1596 7047 1693 7254 Dl 1473 7089 1596 7046 Dl 5 R f (45)1529 7181 w 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7254 Dl 1803 6679 1962 6974 Dl 1656 6666 1804 6678 Dl (62)1739 7016 w 1691 6134 1696 6135 Dl 1696 6135 1759 6301 Dl 1759 6300 1677 6444 Dl 5 R f (63)1668 6302 w 10 R f 0.1 setlinewidth 1705 5786 1729 5785 Dl 1729 5786 1729 5950 Dl 1729 5950 1692 6006 Dl 1772 5584 1777 5588 Dl 1707 5587 1771 5584 Dl 1698 5717 1777 5588 Dl 1707 5368 1766 5279 Dl 1725 5304 1766 5279 Dl 1797 6277 1848 6397 Dl 1849 6398 1804 6678 Dl 1759 6300 1797 6276 Dl 5 R f (67)1727 6512 w 10 R f 0.1 setlinewidth 1789 6073 1828 6170 Dl 1827 6170 1797 6276 Dl 1697 6134 1789 6073 Dl 5 R f (68)1743 6191 w 10 R f 0.1 setlinewidth 1792 5908 1815 5928 Dl 1815 5929 1789 6073 Dl 1730 5950 1792 5907 Dl 5 R f (69)1720 6032 w 10 R f 0.1 setlinewidth 1807 5730 1792 5907 Dl 1729 5785 1808 5729 Dl 1777 5588 1810 5582 Dl 1809 5729 1811 5724 Dl 1811 5582 1811 5724 Dl 1756 5448 1771 5584 Dl 1741 5459 1756 5448 Dl 1757 5448 1769 5433 Dl 1715 5410 1769 5433 Dl 1724 5302 1798 5244 Dl 1766 5277 1798 5244 Dl 1971 6261 2017 6372 Dl 2016 6372 1962 6974 Dl 1849 6397 1970 6260 Dl (75)1870 6608 w 1925 5826 1931 5826 Dl 1932 5826 1962 6083 Dl 1876 5879 1925 5825 Dl 1875 5879 1902 6112 Dl 1903 6112 1962 6083 Dl 1811 5583 1884 5595 Dl 1884 5595 1859 5692 Dl 1812 5724 1859 5692 Dl 1805 5238 1837 5238 Dl 1798 5244 1805 5238 Dl 1779 5424 1837 5238 Dl 1769 5433 1779 5424 Dl 1962 6084 1980 6102 Dl 1980 6102 1970 6260 Dl 1828 6169 1902 6112 Dl 5 R f (79)1867 6240 w 10 R f 0.1 setlinewidth 1816 5927 1875 5879 Dl 5 R f (80)1822 6042 w 10 R f 0.1 setlinewidth 1859 5692 1925 5825 Dl 5 R f (81)1823 5822 w 10 R f 0.1 setlinewidth 1813 5409 1843 5423 Dl 1779 5424 1812 5409 Dl 1841 5424 1810 5582 Dl 2021 7254 2630 7254 Dl 2169 6234 2630 7254 Dl 2018 6371 2169 6233 Dl (83)2172 6881 w 2105 5979 2165 6027 Dl 2166 6028 2169 6233 Dl 1981 6101 2104 5980 Dl 5 R f (84)2046 6180 w 10 R f 0.1 setlinewidth 2018 5734 2092 5762 Dl 2092 5763 2104 5980 Dl 1932 5825 2018 5734 Dl 5 R f (85)1993 5915 w 10 R f 0.1 setlinewidth 1934 5540 2006 5536 Dl 2006 5536 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1935 5539 1991 5536 Dl 1903 5574 1933 5540 Dl 1886 5592 1902 5574 Dl 1885 5593 1886 5592 Dl 10 R f 0.1 setlinewidth 3952 6176 3950 6179 Dl 3949 6180 3943 6186 Dl 3942 6186 3934 6192 Dl 3934 6193 3903 6209 Dl 3952 6176 3913 6183 Dl 3913 6184 3903 6209 Dl 3024 5714 3024 6881 Dl 3024 6881 3325 6730 Dl 3902 6209 3325 6730 Dl 3913 6182 3024 5714 Dl (4)3305 6304 w 3394 5238 3024 5238 Dl 3024 5238 3024 5714 Dl 3395 5238 3972 6151 Dl 3972 6152 3970 6161 Dl 3969 6160 3964 6167 Dl 3963 6168 3956 6174 Dl 3955 6174 3953 6176 Dl (5)3384 5679 w 3507 6725 3325 6730 Dl 4025 6573 3509 6725 Dl 4024 6572 3934 6192 Dl (7)3724 6530 w 4132 6539 4066 6578 Dl 4066 6577 4026 6572 Dl 4132 6538 3943 6186 Dl 5 R f (8)4019 6438 w 10 R f 0.1 setlinewidth 4243 6500 4178 6530 Dl 4177 6530 4133 6538 Dl 4243 6499 3950 6179 Dl 5 R f (9)4091 6410 w 10 R f 0.1 setlinewidth 4345 6448 4314 6491 Dl 4314 6492 4242 6500 Dl 4346 6447 3956 6174 Dl 5 R f (10)4154 6383 w 10 R f 0.1 setlinewidth 4465 6366 4446 6408 Dl 4445 6408 4346 6447 Dl 4465 6365 3964 6167 Dl 5 R f (11)4230 6336 w 10 R f 0.1 setlinewidth 4598 6278 4548 6346 Dl 4548 6346 4465 6366 Dl 4599 6277 3970 6161 Dl 5 R f (12)4318 6279 w 10 R f 0.1 setlinewidth 4573 6141 3972 6151 Dl 4695 6263 4761 6168 Dl 4693 6264 4666 6271 Dl 4758 6159 4573 6140 Dl 4760 6167 4758 6160 Dl 4665 6271 4599 6277 Dl 5 R f (13)4424 6204 w 10 R f 0.1 setlinewidth 3775 6758 3509 6725 Dl 4085 6692 3775 6758 Dl 4086 6691 4066 6578 Dl 5 R f (14)3834 6688 w 10 R f 0.1 setlinewidth 4233 6663 4125 6707 Dl 4124 6706 4086 6691 Dl 4242 6644 4233 6662 Dl 4242 6644 4178 6530 Dl 5 R f (15)4122 6631 w 10 R f 0.1 setlinewidth 4378 6547 4242 6644 Dl 4378 6547 4314 6491 Dl 5 R f (16)4248 6565 w 10 R f 0.1 setlinewidth 4488 6550 4439 6566 Dl 4494 6429 4489 6549 Dl 4438 6565 4379 6547 Dl 4494 6428 4446 6408 Dl 5 R f (17)4394 6497 w 10 R f 0.1 setlinewidth 4634 6364 4635 6400 Dl 4634 6400 4494 6428 Dl 4633 6365 4548 6346 Dl 4716 6347 4633 6365 Dl 4666 6271 4717 6346 Dl 4770 6162 4765 6159 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6611 Dl 5026 6611 4983 6609 Dl 4965 6467 5016 6482 Dl 4906 6457 4965 6467 Dl 5 R f (40)4918 6545 w 10 R f 0.1 setlinewidth 5040 6393 5040 6418 Dl 4956 6367 5040 6392 Dl 5039 6419 4965 6467 Dl 5040 6295 5040 6337 Dl 4961 6277 5040 6294 Dl 4942 6277 4960 6277 Dl 4956 6350 5040 6337 Dl 4869 6280 4941 6276 Dl 4912 6211 5015 6209 Dl 4941 6276 5015 6209 Dl 4890 6194 4937 6159 Dl 4813 6169 4937 6159 Dl 3340 7254 3024 7254 Dl 3024 7253 3024 6881 Dl 3915 7031 3340 7254 Dl 3961 6892 3916 7030 Dl (45)3388 7000 w 4252 7161 4226 7182 Dl 4226 7181 3916 7030 Dl 4246 6934 4253 7160 Dl (46)4058 7019 w 4650 6961 4353 6923 Dl 4589 6886 4651 6961 Dl 4748 6791 4656 6965 Dl 4651 6961 4656 6965 Dl 4946 6646 4976 6837 Dl 4935 6818 4976 6837 Dl 5040 6418 5040 6484 Dl 5017 6483 5040 6484 Dl 5040 6338 5040 6392 Dl 5040 6207 5040 6253 Dl 5016 6209 5040 6207 Dl 4961 6277 5040 6253 Dl 4926 6148 4834 6132 Dl 4941 6157 4926 6148 Dl 4788 6141 4834 6132 Dl 4937 6159 4942 6158 Dl 4514 7186 4253 7160 Dl 4676 6991 4514 7187 Dl 4656 6965 4676 6990 Dl (55)4380 7067 w 5040 6875 5040 7015 Dl 5039 7015 4676 6990 Dl 4977 6838 5040 6875 Dl 5 R f (56)4835 6923 w 10 R f 0.1 setlinewidth 5040 6616 5040 6875 Dl 5028 6612 5040 6615 Dl 5 R f (57)4976 6738 w 10 R f 0.1 setlinewidth 5040 6484 5040 6615 Dl 5040 6253 5040 6294 Dl 5040 6205 5040 6164 Dl 4943 6158 5040 6164 Dl 4195 7254 3340 7254 Dl 4225 7183 4195 7254 Dl (62)3803 7196 w 4944 7254 4602 7254 Dl 5040 7016 5040 7086 Dl 5039 7087 4943 7254 Dl 4601 7253 4514 7187 Dl (63)4740 7148 w 4834 6131 4823 6076 Dl 4762 6104 4823 6076 Dl 4601 7254 4195 7254 Dl 5 R f (67)4351 7225 w 10 R f 0.1 setlinewidth 5039 7254 4943 7254 Dl 5040 7087 5040 7254 Dl 5040 6164 5040 6146 Dl 4927 6148 5040 6146 Dl 4759 6105 4841 6049 Dl 4823 6076 4841 6049 Dl 5040 6145 5040 6063 Dl 4842 6049 4883 5998 Dl 5039 6062 4883 5998 Dl 5 R f (78)4907 6096 w 10 R f 0.1 setlinewidth 5040 6063 5040 6037 Dl 4883 5998 4883 5996 Dl 5039 6037 4883 5996 Dl 5039 5238 4932 5238 Dl 5040 5327 5040 5238 Dl 5039 5327 4932 5238 Dl 4932 5238 3992 5238 Dl 5040 6036 5040 5327 Dl 4882 5996 3992 5238 Dl (93)4632 5549 w 3991 5238 3394 5238 Dl (94)4066 5742 w 20 R f 16 setlinewidth 5040 7254 3024 7254 Dl 5040 5238 5040 7254 Dl 3024 5238 5040 5238 Dl 3024 7254 3024 5238 Dl 10 B f (Fig. 14:)1 322 1 921 7452 t 10 R f (\(inside\))1268 7452 w 10 I f (v)1598 7452 w 10 R f (= \(0,\2617,0\),)1 422 1 1667 7452 t 10 I f (d)2114 7452 w 10 R f (= \(0,1,0\))1 347 1 2189 7452 t 10 B f (Fig. 15:)1 322 1 3261 7452 t 10 R f (iter 2,)1 233 1 3608 7452 t 10 I f (v)3866 7452 w 10 R f (= \(1,1,1\),)1 372 1 3935 7452 t 10 I f (d)4332 7452 w 10 R f (= \(\2611,0,0\))1 397 1 4407 7452 t (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 12 13 %%Page: 13 14 /saveobj save def mark 14 pagesetup 10 R f (- 13 -)2 216 1 2772 282 t 0.1 setlinewidth 1724 1491 1 1 De 1724 1491 1722 1491 Dl 1724 1490 1722 1490 Dl 1723 1490 1722 1491 Dl 1574 1387 1661 1519 Dl 1662 1519 1665 1519 Dl 1666 1519 1690 1512 Dl 1721 1493 1690 1512 Dl 1723 1489 1574 1386 Dl 1414 486 977 486 Dl 1701 1314 1727 1488 Dl 1699 1313 1560 853 Dl 1560 853 1414 486 Dl 977 486 1217 882 Dl 1217 881 1574 1386 Dl (5)1368 898 w 1695 1512 1690 1512 Dl 1715 1509 1695 1512 Dl 1717 1509 1724 1491 Dl 1720 1508 1717 1509 Dl 1716 1509 1715 1509 Dl 1721 1508 1724 1491 Dl 1726 1506 1723 1507 Dl 1723 1508 1721 1508 Dl 1727 1506 1725 1490 Dl 1732 1504 1730 1506 Dl 1730 1506 1727 1506 Dl 1733 1504 1725 1490 Dl 1742 1501 1740 1503 Dl 1740 1503 1734 1504 Dl 1743 1499 1726 1489 Dl 1754 1495 1748 1499 Dl 1748 1500 1743 1500 Dl 1754 1495 1726 1489 Dl 1760 1486 1727 1488 Dl 1772 1488 1762 1494 Dl 1762 1495 1760 1495 Dl 1773 1486 1761 1486 Dl 1759 1496 1755 1496 Dl 1702 1514 1695 1512 Dl 1714 1514 1702 1514 Dl 1715 1513 1717 1509 Dl 1720 1513 1715 1514 Dl 1715 1514 1 1 De 1721 1513 1 1 De 1722 1512 1723 1507 Dl 1731 1509 1722 1512 Dl 1730 1508 1730 1506 Dl 1735 1510 1733 1510 Dl 1741 1504 1736 1509 Dl 1733 1509 1731 1509 Dl 1741 1504 1740 1503 Dl 1753 1501 1751 1503 Dl 1750 1503 1742 1504 Dl 1751 1500 1748 1499 Dl 1758 1501 1753 1501 Dl 1759 1495 1758 1500 Dl 1773 1488 1772 1488 Dl 1769 1485 1761 1486 Dl 1774 1486 1 1 De 1774 1487 1776 1486 Dl 1774 1485 1769 1485 Dl 1733 1512 1724 1514 Dl 1723 1513 1721 1513 Dl 1733 1511 1733 1512 Dl 1755 1505 1748 1510 Dl 1747 1510 1737 1510 Dl 1752 1503 1755 1505 Dl 1773 1496 1 1 De 1772 1496 1771 1497 Dl 1771 1498 1761 1500 Dl 1762 1495 1772 1495 Dl 1760 1500 1758 1500 Dl 1736 1511 1733 1512 Dl 1761 1500 1761 1504 Dl 1761 1505 1755 1505 Dl 1774 1488 1776 1488 Dl 1776 1489 1779 1490 Dl 1780 1491 1772 1495 Dl 1780 1491 1 1 De 1711 1519 1704 1519 Dl 1704 1519 1702 1514 Dl 1715 1515 1712 1519 Dl 1713 1521 1712 1519 Dl 1722 1520 1713 1522 Dl 1723 1514 1722 1519 Dl 1734 1517 1727 1519 Dl 1726 1519 1722 1519 Dl 1733 1512 1734 1516 Dl 1749 1512 1744 1515 Dl 1744 1516 1735 1516 Dl 1748 1511 1750 1512 Dl 1764 1504 1764 1506 Dl 1763 1507 1753 1512 Dl 1752 1512 1750 1512 Dl 1762 1505 1763 1505 Dl 1773 1501 1 1 De 1772 1498 1774 1501 Dl 1773 1502 1763 1505 Dl 1769 1484 1775 1483 Dl 1776 1485 1776 1483 Dl 1716 1522 1713 1522 Dl 1726 1523 1717 1523 Dl 1713 1522 1 1 De 1726 1519 1726 1522 Dl 1735 1520 1727 1523 Dl 1726 1522 1 1 De 1735 1517 1735 1520 Dl 1744 1523 1737 1521 Dl 1745 1518 1744 1523 Dl 1736 1521 1735 1520 Dl 1744 1515 1746 1517 Dl 1758 1516 1754 1517 Dl 1754 1517 1746 1517 Dl 1753 1512 1758 1515 Dl 1768 1509 1761 1515 Dl 1760 1515 1758 1515 Dl 1767 1508 1769 1509 Dl 1764 1507 1766 1507 Dl 1772 1502 1776 1504 Dl 1776 1504 1766 1507 Dl 1789 1499 1 1 De 1779 1497 1789 1499 Dl 1778 1496 1779 1496 Dl 1789 1500 1774 1501 Dl 1773 1496 1778 1496 Dl 1781 1491 1789 1491 Dl 1788 1491 1778 1496 Dl 1786 1488 1780 1490 Dl 1776 1488 1786 1487 Dl 1672 1525 1665 1519 Dl 1701 1524 1673 1526 Dl 1704 1520 1700 1523 Dl 1707 1529 1706 1529 Dl 1705 1528 1700 1523 Dl 1712 1523 1707 1529 Dl 1726 1526 1717 1523 Dl 1726 1524 1726 1526 Dl 1736 1521 1726 1526 Dl 1754 1517 1746 1524 Dl 1744 1523 1 1 De 1789 1509 1787 1511 Dl 1777 1504 1789 1508 Dl 1787 1511 1769 1509 Dl 1788 1500 1788 1501 Dl 1787 1502 1776 1504 Dl 1796 1490 1795 1492 Dl 1789 1490 1796 1490 Dl 1794 1493 1779 1496 Dl 1780 1486 1786 1486 Dl 1787 1487 1 1 De 1775 1485 1779 1485 Dl 1714 1531 1707 1529 Dl 1726 1527 1714 1531 Dl 1726 1527 1 1 De 1747 1528 1740 1531 Dl 1740 1531 1726 1527 Dl 1745 1524 1747 1527 Dl 1756 1527 1747 1527 Dl 1764 1518 1756 1527 Dl 1761 1515 1765 1517 Dl 1787 1511 1787 1514 Dl 1787 1514 1765 1517 Dl 1791 1508 1789 1508 Dl 1789 1501 1791 1507 Dl 1796 1492 1797 1496 Dl 1796 1497 1789 1499 Dl 1787 1487 1802 1487 Dl 1801 1488 1796 1490 Dl 1678 1534 1673 1526 Dl 1694 1535 1679 1535 Dl 1706 1529 1694 1536 Dl 1740 1532 1 1 De 1740 1533 1717 1540 Dl 1716 1539 1714 1531 Dl 1788 1515 1793 1517 Dl 1793 1518 1766 1530 Dl 1766 1529 1756 1527 Dl 1826 1499 1830 1499 Dl 1797 1497 1825 1499 Dl 1829 1500 1791 1507 Dl 1780 1485 1782 1481 Dl 1776 1483 1782 1481 Dl 1714 1545 1699 1545 Dl 1699 1545 1694 1536 Dl 1717 1540 1715 1545 Dl 1742 1546 1722 1552 Dl 1722 1552 1715 1545 Dl 1741 1532 1743 1545 Dl 1781 1542 1777 1550 Dl 1777 1550 1743 1545 Dl 1767 1530 1782 1542 Dl 1841 1528 1782 1542 Dl 1794 1517 1840 1527 Dl 1830 1500 1857 1501 Dl 1843 1527 1840 1527 Dl 1856 1501 1843 1527 Dl 1806 1487 1825 1499 Dl 1802 1487 1806 1486 Dl 1808 1486 1810 1485 Dl 1787 1486 1810 1485 Dl 1775 1483 1785 1478 Dl 1783 1480 1785 1478 Dl 1684 1563 1674 1555 Dl 1675 1555 1679 1535 Dl 1685 1563 1699 1545 Dl 1875 1637 1880 1648 Dl 1881 1646 1704 1590 Dl 1802 1575 1876 1636 Dl 1800 1573 1716 1568 Dl 1716 1569 1704 1590 Dl 1857 1501 1972 1519 Dl 1972 1520 1901 1540 Dl 1844 1528 1901 1540 Dl 1785 1478 1792 1473 Dl 1792 1474 1812 1484 Dl 1810 1484 1812 1484 Dl 1704 1591 1694 1591 Dl 1693 1590 1684 1564 Dl 1721 1552 1716 1568 Dl 1778 1551 1801 1575 Dl 1901 1541 1876 1636 Dl 1826 1481 1848 1480 Dl 1812 1483 1825 1481 Dl 1848 1481 1857 1501 Dl 1651 1562 1661 1519 Dl 1674 1556 1651 1563 Dl 1646 1643 1633 1604 Dl 1633 1603 1651 1563 Dl 1694 1592 1648 1643 Dl 2735 2502 1869 2502 Dl 2736 2411 2736 2502 Dl 1869 2501 1648 1643 Dl 1881 1648 2736 2410 Dl (85)2058 2172 w 2736 1557 2736 2410 Dl 2142 1511 2736 1556 Dl 1974 1518 2142 1511 Dl (86)2363 1848 w 1848 1479 1913 1464 Dl 1915 1465 2142 1511 Dl 1792 1474 1825 1481 Dl 1633 1604 1217 882 Dl 5 R f (89)1479 1342 w 10 R f 0.1 setlinewidth 720 486 977 486 Dl 1869 2502 720 2502 Dl 720 2502 720 486 Dl (90)1108 1706 w 2735 486 1414 486 Dl 2736 1556 2736 486 Dl 1912 1464 1560 853 Dl (92)2140 980 w 1792 1473 1700 1314 Dl 5 R f (93)1718 1267 w 20 R f 16 setlinewidth 2736 2502 720 2502 Dl 2736 486 2736 2502 Dl 720 486 2736 486 Dl 720 2502 720 486 Dl 10 R f 0.1 setlinewidth 3936 1445 3935 1443 Dl 3938 1449 3936 1445 Dl 3940 1454 3939 1450 Dl 3942 1455 3943 1466 Dl 3934 1443 3927 1449 Dl 3942 1466 3927 1449 Dl 3024 1278 3024 1064 Dl 3950 1791 3024 1278 Dl 3990 1799 3950 1792 Dl 4047 1706 3990 1798 Dl 4048 1705 3943 1466 Dl 3927 1449 3024 1064 Dl (4)3524 1450 w 3024 874 3024 1064 Dl 3024 873 3918 1424 Dl 3919 1424 3926 1431 Dl 3927 1432 3931 1437 Dl 3932 1436 3934 1441 Dl 3935 1442 3935 1443 Dl (5)3328 1160 w 4083 1706 4048 1706 Dl 4147 1650 4083 1707 Dl 4146 1649 3941 1454 Dl 5 R f (7)4035 1617 w 10 R f 0.1 setlinewidth 4159 1651 4159 1632 Dl 4159 1651 4147 1649 Dl 4158 1632 3939 1450 Dl 4166 1626 4167 1609 Dl 4159 1632 4165 1627 Dl 4166 1608 3936 1445 Dl 4179 1600 4164 1575 Dl 4168 1608 4179 1601 Dl 4163 1574 3934 1441 Dl 4161 1542 4140 1514 Dl 4164 1574 4162 1544 Dl 4140 1515 3931 1437 Dl 4140 1491 4098 1434 Dl 4140 1514 4140 1491 Dl 4097 1433 3926 1431 Dl 3958 1318 3918 1424 Dl 4098 1407 4009 1306 Dl 4101 1417 4099 1407 Dl 4000 1299 3959 1318 Dl 4010 1305 4001 1298 Dl 4098 1433 4101 1418 Dl 4148 1720 4083 1707 Dl 4201 1698 4148 1720 Dl 4202 1698 4160 1652 Dl 4215 1704 4224 1684 Dl 4202 1699 4215 1704 Dl 4224 1683 4220 1676 Dl 4219 1676 4165 1627 Dl 4220 1675 4215 1626 Dl 4215 1626 4179 1601 Dl 4233 1632 4235 1620 Dl 4235 1620 4181 1552 Dl 4216 1627 4234 1632 Dl 4180 1551 4162 1544 Dl 4186 1517 4165 1494 Dl 4181 1551 4187 1518 Dl 4165 1493 4140 1491 Dl 4165 1493 4164 1468 Dl 4163 1469 4101 1418 Dl 4005 1298 4001 1296 Dl 4010 1305 4005 1298 Dl 4001 1296 4001 1298 Dl 3949 1278 3959 1318 Dl 3979 1272 3966 1267 Dl 4000 1295 3980 1272 Dl 3966 1267 3949 1277 Dl 4250 1645 4248 1643 Dl 4242 1683 4249 1645 Dl 4225 1684 4242 1684 Dl 4247 1642 4234 1632 Dl 4265 1594 4222 1530 Dl 4241 1622 4265 1594 Dl 4222 1529 4187 1518 Dl 4236 1620 4241 1622 Dl 4131 1389 4122 1384 Dl 4147 1405 4132 1389 Dl 4170 1464 4146 1405 Dl 4122 1384 4099 1407 Dl 4164 1468 4170 1465 Dl 4247 1642 4241 1622 Dl 4225 1504 4170 1465 Dl 4222 1529 4226 1505 Dl 4067 1313 4057 1308 Dl 4015 1296 4005 1298 Dl 4044 1301 4016 1296 Dl 4122 1384 4068 1314 Dl 4056 1307 4044 1301 Dl 4248 1751 4218 1765 Dl 4149 1722 4218 1765 Dl 4216 1705 4249 1751 Dl 4249 1751 4282 1774 Dl 4282 1773 4284 1728 Dl 4242 1685 4284 1728 Dl 4301 1721 4296 1680 Dl 4285 1728 4301 1722 Dl 4250 1646 4296 1680 Dl 4308 1648 4286 1602 Dl 4298 1679 4308 1648 Dl 4296 1680 4298 1680 Dl 4266 1595 4286 1602 Dl 4252 1519 4231 1504 Dl 4289 1593 4253 1519 Dl 4286 1602 4290 1593 Dl 4226 1504 4231 1504 Dl 4201 1441 4191 1430 Dl 4191 1430 4146 1405 Dl 4231 1504 4201 1442 Dl 4057 1307 4047 1301 Dl 4046 1301 4044 1301 Dl 3948 1277 3928 1240 Dl 3928 1239 3928 1240 Dl 3966 1267 3928 1239 Dl 4288 1780 4303 1775 Dl 4304 1775 4329 1751 Dl 4282 1774 4287 1780 Dl 4301 1723 4329 1751 Dl 4338 1757 4334 1709 Dl 4329 1751 4338 1757 Dl 4298 1681 4334 1709 Dl 4346 1714 4381 1714 Dl 4332 1663 4381 1714 Dl 4334 1709 4346 1714 Dl 4309 1649 4332 1662 Dl 4335 1628 4328 1604 Dl 4332 1662 4335 1629 Dl 4290 1594 4328 1604 Dl 4334 1599 4277 1519 Dl 4330 1604 4335 1600 Dl 4265 1517 4277 1519 Dl 4254 1519 4264 1517 Dl 4234 1451 4227 1446 Dl 4226 1446 4201 1442 Dl 4264 1515 4234 1451 Dl 4178 1365 4173 1358 Dl 4173 1358 4132 1365 Dl 4131 1368 4132 1365 Dl 4191 1429 4180 1365 Dl 4131 1388 4131 1368 Dl 4068 1314 4068 1284 Dl 4131 1368 4068 1284 Dl 4046 1301 4007 1252 Dl 4014 1295 4007 1252 Dl 4098 1850 3990 1798 Dl 4230 1802 4099 1851 Dl 4219 1765 4230 1801 Dl 5 R f (45)4083 1787 w 10 R f 0.1 setlinewidth 4318 1842 4315 1846 Dl 4231 1802 4315 1846 Dl 4288 1780 4318 1841 Dl 4304 1776 4361 1781 Dl 4339 1758 4361 1781 Dl 4361 1782 4346 1714 Dl 4361 1781 4362 1782 Dl 4391 1719 4335 1629 Dl 4382 1714 4392 1719 Dl 4309 1477 4284 1447 Dl 4233 1450 4284 1447 Dl 4277 1519 4310 1478 Dl 4196 1379 4180 1365 Dl 4226 1446 4196 1380 Dl 4091 1277 4060 1251 Dl 4067 1284 4060 1251 Dl 4132 1364 4091 1277 Dl 3993 1243 3970 1250 Dl 4005 1248 3993 1243 Dl 3980 1272 3970 1250 Dl 4007 1251 4006 1249 Dl 4319 1843 4363 1848 Dl 4363 1846 4369 1789 Dl 4362 1782 4369 1789 Dl 4433 1784 4423 1740 Dl 4370 1789 4434 1784 Dl 4393 1720 4423 1740 Dl 4423 1739 4430 1708 Dl 4430 1707 4359 1605 Dl 4335 1600 4359 1605 Dl 4342 1503 4310 1478 Dl 4359 1604 4343 1504 Dl 4284 1447 4273 1432 Dl 4273 1431 4196 1380 Dl 4149 1315 4091 1277 Dl 4173 1358 4150 1315 Dl 4025 1207 4006 1249 Dl 4060 1249 4025 1206 Dl 4211 1919 4099 1851 Dl 4305 1915 4211 1919 Dl 4315 1847 4306 1915 Dl 4434 1785 4437 1791 Dl 4425 1901 4437 1791 Dl 4363 1848 4424 1902 Dl 4343 1504 4369 1506 Dl 4457 1696 4369 1506 Dl 4431 1708 4458 1697 Dl 4174 1220 4165 1227 Dl 4150 1314 4165 1227 Dl 4273 1431 4175 1220 Dl 3969 1250 3890 1190 Dl 3928 1238 3890 1190 Dl 4444 1942 4384 1974 Dl 4306 1915 4384 1974 Dl 4425 1903 4445 1941 Dl 4502 1969 4517 1873 Dl 4445 1941 4501 1969 Dl 4438 1791 4517 1873 Dl 4541 1729 4583 1797 Dl 4517 1873 4583 1797 Dl 4459 1697 4541 1728 Dl 5 R f (69)4474 1786 w 10 R f 0.1 setlinewidth 4540 1727 4438 1409 Dl 4369 1506 4438 1409 Dl 5 R f (70)4426 1586 w 10 R f 0.1 setlinewidth 4174 1219 4172 1129 Dl 4438 1409 4437 1397 Dl 4436 1396 4172 1129 Dl 5 R f (71)4275 1354 w 10 R f 0.1 setlinewidth 4164 1226 4008 1178 Dl 4025 1206 4008 1178 Dl 4008 1178 3987 1154 Dl 3987 1154 3993 1243 Dl 3927 1240 3848 1152 Dl 3889 1190 3848 1152 Dl 4392 2108 4287 2057 Dl 4212 1920 4287 2057 Dl 4384 1975 4392 2108 Dl 5 R f (75)4291 2008 w 10 R f 0.1 setlinewidth 4941 1945 4975 1991 Dl 4561 2226 4975 1991 Dl 4686 1855 4942 1945 Dl 4536 2077 4685 1854 Dl 4537 2077 4562 2226 Dl (76)4673 2043 w 4171 1128 4163 797 Dl 4461 1250 4163 797 Dl 4438 1397 4462 1252 Dl (77)4245 1143 w 3848 1151 3767 1074 Dl 3971 1132 3767 1074 Dl 3985 1153 3970 1133 Dl 4561 2227 4525 2250 Dl 4393 2108 4525 2250 Dl 4501 1969 4536 2077 Dl 5 R f (79)4446 2095 w 10 R f 0.1 setlinewidth 4583 1797 4685 1854 Dl 5 R f (80)4552 1928 w 10 R f 0.1 setlinewidth 4941 1945 4462 1252 Dl (81)4585 1662 w 3920 1054 3887 959 Dl 3970 1131 3921 1054 Dl 4172 1128 3887 959 Dl 5 R f (82)4016 1121 w 10 R f 0.1 setlinewidth 4099 2079 3950 1792 Dl 4287 2057 4100 2079 Dl 5 R f (83)4096 1962 w 10 R f 0.1 setlinewidth 4193 2470 4008 2260 Dl 4099 2079 4008 2260 Dl 4525 2250 4194 2471 Dl (84)4196 2260 w 4153 2502 5040 2502 Dl 5040 2006 5040 2502 Dl 4193 2472 4152 2502 Dl 4976 1992 5040 2005 Dl (85)4684 2338 w 5039 486 3962 486 Dl 5040 2005 5040 486 Dl 4163 797 3962 486 Dl (86)4626 1039 w 3961 486 3538 486 Dl 3886 959 3525 535 Dl 3538 486 3525 535 Dl (87)3853 760 w 3766 1074 3762 1071 Dl 3920 1055 3762 1071 Dl 3024 1661 3024 1278 Dl 4008 2260 3024 1662 Dl (89)3494 1794 w 4152 2502 3024 2502 Dl 3024 2501 3024 1662 Dl (90)3404 2233 w 3537 486 3422 486 Dl 3524 535 3422 486 Dl 3422 486 3024 486 Dl 3024 486 3024 686 Dl 3762 1071 3024 686 Dl (93)3399 761 w 3024 686 3024 872 Dl (94)3448 1072 w 20 R f 16 setlinewidth 5040 2502 3024 2502 Dl 5040 486 5040 2502 Dl 3024 486 5040 486 Dl 3024 2502 3024 486 Dl 10 B f (Fig. 16:)1 322 1 1224 2700 t 10 R f (dual affine iter 3)3 662 1 1571 2700 t 10 B f (Fig. 17:)1 322 1 3528 2700 t 10 R f (dual affine iter 4)3 662 1 3875 2700 t 0.1 setlinewidth 1729 3870 1 1 De 1729 3870 1731 3870 Dl 1729 3870 1731 3870 Dl 1731 3870 1729 3870 Dl 2736 3978 2736 3987 Dl 2736 3986 1728 3870 Dl 1731 3870 2736 3977 Dl 1730 3870 1728 3870 Dl 2736 3882 2736 3844 Dl 1730 3869 2736 3844 Dl 1732 3871 2736 3883 Dl 5 R f (77)2374 3875 w 10 R f 0.1 setlinewidth 1730 3870 1 1 De 2736 3883 2736 3977 Dl 5 R f (81)2375 3920 w 10 R f 0.1 setlinewidth 1729 3870 1728 3870 Dl 2735 4878 1302 4878 Dl 2736 3988 2736 4878 Dl 1303 4878 1727 3870 Dl (85)2055 4448 w 2736 3843 2736 3788 Dl 2736 3789 1728 3870 Dl 5 R f (87)2374 3844 w 10 R f 0.1 setlinewidth 1284 2862 720 2862 Dl 720 4878 1302 4878 Dl 720 2862 720 4878 Dl 1285 2862 1727 3870 Dl (91)1075 3893 w 2735 2862 1284 2862 Dl 2736 3788 2736 2862 Dl 1727 3870 1 1 De (92)2054 3338 w 1727 3870 1 1 De 20 R f 16 setlinewidth 2736 4878 720 4878 Dl 2736 2862 2736 4878 Dl 720 2862 2736 2862 Dl 720 4878 720 2862 Dl 10 R f 0.1 setlinewidth 3404 3844 3403 3843 Dl 3404 3844 3402 3846 Dl 3402 3847 3394 3849 Dl 3393 3850 3345 3856 Dl 3403 3843 3304 3846 Dl 3345 3854 3304 3846 Dl 3024 3968 3024 3838 Dl 3024 3968 3345 3856 Dl 3304 3846 3024 3838 Dl 5 R f (4)3123 3895 w 10 R f 0.1 setlinewidth 3024 3815 3024 3838 Dl 3024 3816 3363 3834 Dl 3365 3834 3394 3837 Dl 3394 3837 3404 3839 Dl 3405 3840 3405 3842 Dl 3405 3843 3403 3843 Dl 3024 3977 3024 3968 Dl 3263 3984 3024 3978 Dl 4213 3975 3263 3985 Dl 4213 3974 3394 3849 Dl (7)3502 3955 w 4482 3970 4338 3979 Dl 4337 3979 4213 3975 Dl 4482 3969 3402 3846 Dl 5 R f (8)4008 3939 w 10 R f 0.1 setlinewidth 4769 3962 4605 3969 Dl 4604 3970 4482 3970 Dl 4769 3960 3404 3844 Dl 5 R f (9)4186 3934 w 10 R f 0.1 setlinewidth 4999 3960 5020 3943 Dl 4998 3961 4770 3961 Dl 5019 3942 3405 3842 Dl 5 R f (10)4381 3926 w 10 R f 0.1 setlinewidth 5040 3942 5040 3899 Dl 5039 3942 5020 3943 Dl 5039 3898 3404 3839 Dl 5 R f (11)4440 3903 w 10 R f 0.1 setlinewidth 5040 3898 5040 3850 Dl 5039 3850 3394 3837 Dl 5 R f (12)4440 3872 w 10 R f 0.1 setlinewidth 5040 3850 5040 3769 Dl 4439 3782 3363 3834 Dl 5039 3770 4440 3781 Dl (13)4389 3836 w 3760 4007 3263 3985 Dl 4491 4014 3761 4007 Dl 4491 4014 4338 3979 Dl 5 R f (14)3953 4003 w 10 R f 0.1 setlinewidth 4896 4016 4610 4021 Dl 4610 4021 4491 4014 Dl 4910 4011 4896 4016 Dl 4911 4011 4605 3969 Dl 5 R f (15)4585 4006 w 10 R f 0.1 setlinewidth 5040 3965 5040 4003 Dl 5039 4003 4911 4011 Dl 5039 3963 4998 3960 Dl 5040 3964 5040 3942 Dl 5040 3769 5040 3751 Dl 4625 3758 4440 3781 Dl 5039 3750 4952 3749 Dl 4951 3750 4625 3757 Dl 5040 4003 5040 4021 Dl 5039 4020 4896 4016 Dl 4656 4056 4188 4050 Dl 4189 4049 3761 4007 Dl 4610 4022 4656 4056 Dl 5 R f (28)4264 4040 w 10 R f 0.1 setlinewidth 5040 4022 5040 4078 Dl 4902 4082 4656 4056 Dl 5039 4078 4903 4083 Dl 5 R f (29)4830 4056 w 10 R f 0.1 setlinewidth 4626 3756 4656 3736 Dl 4665 3736 4656 3736 Dl 4951 3749 4666 3736 Dl 5040 4078 5040 4092 Dl 5039 4091 4913 4088 Dl 4903 4083 4913 4088 Dl 3024 4051 3024 3978 Dl 4063 4070 3024 4052 Dl 4188 4050 4063 4070 Dl (45)3460 4049 w 4797 4131 4715 4131 Dl 4714 4130 4063 4070 Dl 4912 4089 4797 4131 Dl 5 R f (46)4513 4095 w 10 R f 0.1 setlinewidth 5040 4093 5040 4146 Dl 5039 4146 4797 4131 Dl 3024 4085 3024 4052 Dl 3206 4109 3024 4086 Dl 4091 4151 3206 4109 Dl 4713 4132 4091 4152 Dl (62)3745 4121 w 5040 3751 5040 3733 Dl 5039 3732 4561 3710 Dl 4666 3735 4561 3710 Dl 5040 4146 5040 4248 Dl 5039 4248 4538 4228 Dl 4536 4228 4091 4152 Dl (67)4628 4203 w 4656 3736 4333 3693 Dl 4560 3710 4333 3693 Dl 3692 4281 3098 4199 Dl 3098 4199 3206 4109 Dl 4537 4228 3692 4281 Dl (75)3678 4216 w 5040 4467 5040 4536 Dl 5039 4535 4621 4487 Dl 5039 4466 4621 4487 Dl 5040 3732 5040 3656 Dl 4333 3692 3947 3661 Dl 5039 3657 3947 3661 Dl 5 R f (78)4631 3695 w 10 R f 0.1 setlinewidth 5040 4249 5040 4466 Dl 4621 4486 4043 4443 Dl 4042 4443 3692 4281 Dl (79)4427 4372 w 3024 4196 3024 4086 Dl 3098 4199 3024 4196 Dl 3024 4396 3024 4196 Dl 4043 4442 3024 4396 Dl (84)3373 4353 w 5040 4878 3024 4878 Dl 5040 4536 5040 4878 Dl 3024 4877 3024 4396 Dl (85)3930 4683 w 5040 3656 5040 3633 Dl 3946 3661 3923 3660 Dl 5039 3634 3923 3660 Dl 5040 2862 3024 2862 Dl 5040 3351 5040 2862 Dl 3024 2862 3024 3422 Dl 5040 3351 3024 3422 Dl (92)3958 3144 w 5040 3632 5040 3351 Dl 3024 3423 3024 3650 Dl 3923 3660 3024 3650 Dl (93)4015 3538 w 3024 3651 3024 3815 Dl (94)3644 3758 w 20 R f 16 setlinewidth 5040 4878 3024 4878 Dl 5040 2862 5040 4878 Dl 3024 2862 5040 2862 Dl 3024 4878 3024 2862 Dl 10 B f (Fig. 18:)1 322 1 1019 5076 t 10 R f (dual affine iter 6, 30)4 812 1 1366 5076 t 10 S f (\260)2178 5076 w 10 R f (view)2243 5076 w 10 B f (Fig. 19:)1 322 1 3261 5076 t 10 R f (dual affine iter 6, 0.005)4 937 1 3608 5076 t 10 S f (\260)4545 5076 w 10 R f (view)4610 5076 w 0.1 setlinewidth 1704 6246 1 1 De 1706 6246 1704 6246 Dl 1708 6246 1707 6246 Dl 1712 6246 1708 6246 Dl 1703 6246 1705 6246 Dl 1712 6246 1705 6246 Dl 1809 6245 1580 6245 Dl 1817 6246 1810 6246 Dl 1803 6246 1817 6246 Dl 1802 6246 1712 6246 Dl 1706 6245 1580 6245 Dl 1500 6246 1696 6246 Dl 1500 6245 1477 6245 Dl 1477 6245 1496 6245 Dl 1496 6245 1523 6245 Dl 1524 6245 1580 6245 Dl 1697 6246 1699 6246 Dl 1699 6246 1701 6246 Dl 1701 6246 1703 6246 Dl 1803 6246 1811 6246 Dl 1812 6246 1814 6246 Dl 1813 6246 1708 6246 Dl 1818 6246 1813 6246 Dl 1814 6246 1819 6246 Dl 1814 6246 1707 6246 Dl 1813 6246 1810 6246 Dl 1815 6246 1 1 De 1809 6246 1704 6246 Dl 1813 6246 1801 6246 Dl 1811 6246 1813 6246 Dl 1800 6246 1703 6246 Dl 1792 6246 1777 6246 Dl 1800 6246 1793 6246 Dl 1776 6246 1701 6246 Dl 1772 6246 1743 6246 Dl 1777 6246 1772 6246 Dl 1742 6246 1699 6246 Dl 1681 6246 1696 6246 Dl 1737 6246 1687 6246 Dl 1739 6246 1737 6246 Dl 1682 6246 1680 6246 Dl 1687 6246 1683 6246 Dl 1742 6246 1740 6246 Dl 1812 6246 1835 6246 Dl 1835 6246 1848 6246 Dl 1848 6246 1819 6246 Dl 1849 6246 1856 6246 Dl 1855 6246 1851 6246 Dl 1852 6246 1815 6246 Dl 1851 6246 1837 6246 Dl 1836 6246 1813 6246 Dl 1848 6246 1 1 De 1848 6246 1804 6246 Dl 1838 6246 1849 6246 Dl 1803 6246 1793 6246 Dl 1801 6246 1785 6246 Dl 1803 6246 1801 6246 Dl 1784 6246 1772 6246 Dl 1785 6246 1780 6246 Dl 1779 6246 1740 6246 Dl 1683 6246 1682 6246 Dl 1686 6246 1684 6246 Dl 1669 6246 1680 6246 Dl 1671 6246 1668 6246 Dl 1683 6246 1673 6246 Dl 1860 6246 1859 6246 Dl 1864 6246 1861 6246 Dl 1856 6246 1865 6246 Dl 1859 6246 1849 6246 Dl 1867 6246 1826 6246 Dl 1852 6246 1867 6246 Dl 1825 6246 1801 6246 Dl 1848 6246 1852 6246 Dl 1748 6246 1743 6246 Dl 1759 6246 1749 6246 Dl 1783 6246 1760 6246 Dl 1743 6246 1737 6246 Dl 1781 6246 1783 6246 Dl 1859 6246 1852 6246 Dl 1826 6246 1783 6246 Dl 1707 6246 1702 6246 Dl 1686 6246 1684 6246 Dl 1696 6246 1686 6246 Dl 1743 6246 1707 6246 Dl 1702 6246 1697 6246 Dl 1874 6246 1884 6246 Dl 1835 6246 1874 6246 Dl 1856 6246 1884 6246 Dl 1885 6246 1910 6246 Dl 1909 6246 1902 6246 Dl 1866 6246 1902 6246 Dl 1913 6246 1902 6246 Dl 1902 6246 1913 6246 Dl 1861 6246 1902 6246 Dl 1911 6246 1886 6246 Dl 1904 6246 1911 6246 Dl 1903 6246 1904 6246 Dl 1868 6246 1886 6246 Dl 1850 6246 1830 6246 Dl 1889 6246 1851 6246 Dl 1887 6246 1890 6246 Dl 1826 6246 1830 6246 Dl 1802 6246 1794 6246 Dl 1793 6246 1760 6246 Dl 1831 6246 1803 6246 Dl 1702 6246 1697 6246 Dl 1697 6246 1 1 De 1668 6246 1656 6246 Dl 1668 6246 1656 6246 Dl 1915 6246 1925 6246 Dl 1926 6246 1942 6246 Dl 1909 6246 1914 6246 Dl 1914 6246 1942 6246 Dl 1951 6246 1942 6246 Dl 1942 6246 1951 6246 Dl 1904 6246 1942 6246 Dl 1956 6246 1999 6246 Dl 1999 6246 1938 6246 Dl 1943 6246 1956 6246 Dl 1912 6246 1938 6246 Dl 1942 6246 1935 6246 Dl 1938 6246 1943 6246 Dl 1890 6246 1935 6246 Dl 1943 6246 1877 6246 Dl 1936 6246 1944 6246 Dl 1878 6246 1863 6246 Dl 1852 6246 1863 6246 Dl 1833 6246 1826 6246 Dl 1826 6246 1803 6246 Dl 1862 6246 1834 6246 Dl 1782 6246 1777 6246 Dl 1777 6246 1748 6246 Dl 1793 6246 1782 6246 Dl 1749 6246 1747 6246 Dl 1703 6246 1707 6246 Dl 1746 6246 1703 6246 Dl 1697 6246 1675 6246 Dl 1675 6246 1686 6246 Dl 1817 6246 1858 6246 Dl 1858 6246 1890 6246 Dl 1875 6246 1890 6246 Dl 1948 6246 1949 6246 Dl 1891 6246 1948 6246 Dl 1915 6246 1949 6246 Dl 1925 6246 1976 6246 Dl 1952 6246 1976 6246 Dl 1978 6246 1956 6246 Dl 1976 6246 1977 6246 Dl 2012 6246 1943 6246 Dl 1999 6246 2013 6246 Dl 1931 6246 1899 6246 Dl 1898 6246 1834 6246 Dl 1877 6246 1931 6246 Dl 1797 6246 1782 6246 Dl 1826 6246 1798 6246 Dl 1714 6246 1694 6246 Dl 1703 6246 1694 6246 Dl 1748 6246 1715 6246 Dl 1670 6246 1666 6246 Dl 1674 6246 1670 6246 Dl 1673 6246 1666 6246 Dl 1675 6246 1674 6246 Dl 1949 6246 1987 6246 Dl 1986 6246 1985 6246 Dl 1978 6246 1985 6246 Dl 2070 6247 2058 6247 Dl 1986 6247 2070 6247 Dl 2013 6247 2058 6247 Dl 2059 6247 2082 6247 Dl 2081 6246 1981 6246 Dl 1945 6246 1981 6246 Dl 1983 6246 1931 6246 Dl 1982 6246 1984 6246 Dl 1898 6246 1886 6246 Dl 1885 6246 1798 6246 Dl 1757 6246 1715 6246 Dl 1777 6246 1757 6246 Dl 1672 6246 1674 6246 Dl 1694 6246 1672 6246 Dl 1858 6246 1916 6246 Dl 1917 6246 1961 6246 Dl 1949 6246 1961 6246 Dl 2075 6247 2070 6247 Dl 2060 6247 2075 6247 Dl 1987 6247 2060 6247 Dl 1984 6246 2047 6246 Dl 2155 6246 2047 6246 Dl 2082 6247 2155 6247 Dl 1794 6246 1781 6246 Dl 1758 6246 1781 6246 Dl 1885 6246 1794 6246 Dl 1664 6245 1639 6245 Dl 1655 6245 1639 6245 Dl 2036 6247 2090 6247 Dl 1961 6247 2035 6247 Dl 2061 6247 2090 6247 Dl 2174 6248 2222 6248 Dl 2091 6247 2175 6247 Dl 2076 6248 2222 6248 Dl 2526 6248 2426 6248 Dl 2223 6247 2526 6248 Dl 2156 6248 2426 6248 Dl 2427 6248 2620 6248 Dl 2048 6246 2620 6248 Dl 1795 6246 1824 6246 Dl 2620 6248 2668 6248 Dl 2667 6248 1824 6246 Dl 1781 6246 1661 6246 Dl 1672 6246 1661 6246 Dl 1660 6245 1649 6245 Dl 1650 6246 1670 6246 Dl 1655 6245 1625 6245 Dl 1638 6245 1625 6245 Dl 2002 6247 2081 6247 Dl 1917 6247 2002 6247 Dl 2035 6247 2081 6247 Dl 2291 6249 2736 6250 Dl 2245 6247 2736 6249 Dl 2245 6248 2290 6248 Dl 2736 6248 1 1 De 2735 6248 1824 6246 Dl 2669 6249 2736 6249 Dl 1625 6245 1601 6245 Dl 1640 6245 1601 6245 Dl 1648 6245 1640 6245 Dl 2244 6248 2290 6248 Dl 2082 6248 2243 6248 Dl 2174 6248 2244 6248 Dl 2527 6249 2736 6249 Dl 1587 6245 1612 6245 Dl 1639 6245 1612 6245 Dl 1824 6245 1588 6245 Dl 1809 6246 1952 6246 Dl 2000 6246 1952 6246 Dl 2004 6247 2129 6247 Dl 1952 6247 2003 6247 Dl 2242 6247 2129 6247 Dl 2380 6249 2736 6250 Dl 2129 6247 2379 6248 Dl 2735 5238 1265 5238 Dl 2736 6248 2736 5238 Dl 1586 6245 1476 6245 Dl 1265 5238 1476 6245 Dl (87)2002 5749 w 1600 6245 1 1 De 1612 6245 1600 6245 Dl 2003 6247 1523 6245 Dl 2379 6248 1496 6245 Dl 2736 7254 720 7254 Dl 2736 6251 2736 7254 Dl 720 7254 720 7110 Dl 720 7109 1477 6245 Dl (91)1822 6811 w 720 5238 1265 5238 Dl 720 5238 720 7110 Dl (92)973 6043 w 1600 6245 1500 6245 Dl 20 R f 16 setlinewidth 2736 7254 720 7254 Dl 2736 5238 2736 7254 Dl 720 5238 2736 5238 Dl 720 7254 720 5238 Dl 10 R f 0.1 setlinewidth 5040 6319 5040 6526 Dl 3024 6518 3024 6310 Dl 5040 6526 3024 6519 Dl 5040 6318 3024 6310 Dl (4)4006 6439 w 5040 6318 5040 6295 Dl 3024 6287 3024 6310 Dl 5040 6294 3024 6287 Dl 5 R f (7)4025 6313 w 10 R f 0.1 setlinewidth 5040 6295 5040 6289 Dl 3024 6281 3024 6287 Dl 5040 6288 3024 6281 Dl 5040 6288 5040 6281 Dl 3024 6274 3024 6281 Dl 5040 6280 3024 6273 Dl 5040 6281 5040 6271 Dl 3024 6263 3024 6273 Dl 5040 6271 3024 6264 Dl 5 R f (10)4010 6282 w 10 R f 0.1 setlinewidth 5040 6269 5040 6249 Dl 3024 6244 3024 6264 Dl 5040 6249 3024 6243 Dl 5 R f (11)4010 6266 w 10 R f 0.1 setlinewidth 5040 6250 5040 6191 Dl 3024 6186 3024 6243 Dl 5040 6190 3024 6185 Dl 5 R f (12)4010 6227 w 10 R f 0.1 setlinewidth 5040 6190 5040 6113 Dl 3024 6106 3024 6185 Dl 5040 6113 3024 6106 Dl 5 R f (13)4002 6158 w 10 R f 0.1 setlinewidth 5040 6113 5040 6053 Dl 3024 6046 3024 6106 Dl 5040 6052 3024 6045 Dl 5 R f (27)4006 6089 w 10 R f 0.1 setlinewidth 5040 6053 5040 6019 Dl 3024 6011 3024 6045 Dl 5040 6018 3024 6011 Dl 5 R f (43)4007 6042 w 10 R f 0.1 setlinewidth 5040 6018 5040 5986 Dl 3024 5978 3024 6011 Dl 5040 5985 3024 5977 Dl 5 R f (52)4002 6008 w 10 R f 0.1 setlinewidth 5040 5986 5040 5949 Dl 3024 5942 3024 5977 Dl 5040 5949 3024 5942 Dl 5 R f (60)4015 5973 w 10 R f 0.1 setlinewidth 5040 5948 5040 5824 Dl 3024 5819 3024 5942 Dl 5040 5824 3024 5818 Dl (72)3982 5903 w 5040 5824 5040 5588 Dl 3024 5582 3024 5818 Dl 5040 5588 3024 5582 Dl (82)3982 5723 w 5040 5238 3024 5238 Dl 5040 5588 5040 5238 Dl 3024 5238 3024 5582 Dl (87)3984 5431 w 5040 6527 5040 6672 Dl 3024 6664 3024 6519 Dl 5040 6672 3024 6665 Dl (89)3982 6615 w 5040 6672 5040 6825 Dl 3024 6817 3024 6665 Dl 5040 6824 3024 6817 Dl (90)3982 6765 w 5040 7254 3024 7254 Dl 5040 6826 5040 7254 Dl 3024 7253 3024 6817 Dl (91)3979 7058 w 20 R f 16 setlinewidth 5040 7254 3024 7254 Dl 5040 5238 5040 7254 Dl 3024 5238 5040 5238 Dl 3024 7254 3024 5238 Dl 10 B f (Fig. 20:)1 322 1 1019 7452 t 10 R f (dual affine iter 8, 30)4 812 1 1366 7452 t 10 S f (\260)2178 7452 w 10 R f (view)2243 7452 w 10 B f (Fig. 21:)1 322 1 3286 7452 t 10 R f (dual affine iter 8, 0.01)4 887 1 3633 7452 t 10 S f (\260)4520 7452 w 10 R f (view)4585 7452 w (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 13 14 %%Page: 14 15 /saveobj save def mark 15 pagesetup 10 R f (- 14 -)2 216 1 2772 480 t ( \(10,0,0\) or \(20,0,0\), we can see the steps the algorithm takes.)11 2580(By backing away from the center to)6 1490 2 970 840 t ( retaining the view direction \(\2611,0,0\))5 1467(Moving to \(10,0,0\) in the affinely transformed space of iteration 2 \(and)11 2853 2 720 960 t ( 22 is analogous to figures 11\26113,)6 1370( Figure)1 314( and 23.)2 325(used in figures 15\26121\), for example, we obtain figures 22)9 2311 4 720 1080 t ( a)1 77( 23, on the other hand, shows)6 1225( Figure)1 320(in that you see the step shining through from inside the polytope.)11 2698 4 720 1200 t 10 I f (cutaway)720 1320 w 10 R f ( though the polytope faces were one-way mirrors,)7 2019( is drawn, from outside the polytope, as)7 1607(view: it)1 332 3 1082 1320 t ( cutaway views for some other iterations; to make)8 2007( 24\26127 show similar)3 823( Figures)1 353(visible only from the inside.)4 1137 4 720 1440 t ( the extreme early stretch-)4 1045( Despite)1 356(the step fit, figure 24 is from \(20,0,0\), while the others are from \(10,0,0\).)13 2919 3 720 1560 t ( that later iterations may bring some of the polytope)9 2154(ing shown in figures 18\26121, figures 26 and 27 show)9 2166 2 720 1680 t (detail back into view.)3 860 1 720 1800 t 0.1 setlinewidth 1203 3978 720 3978 Dl 720 3534 720 3978 Dl 1203 3977 720 3533 Dl (89)831 3849 w 1185 1962 720 1962 Dl 2735 3978 1203 3978 Dl 2736 3977 2736 3301 Dl 720 1962 720 3533 Dl 2735 3301 1185 1962 Dl (90)1534 3157 w 2141 1962 1185 1962 Dl 2736 2462 2736 3301 Dl 2735 2460 2142 1962 Dl (91)2116 2475 w 20 R f 16 setlinewidth 2736 3978 720 3978 Dl 2736 1962 2736 3978 Dl 720 1962 2736 1962 Dl 720 3978 720 1962 Dl 2586 2979 1728 2970 Dl 2586 2979 2514 2996 Dl 2586 2978 2514 2960 Dl 10 R f 0.1 setlinewidth 3953 2901 3951 2904 Dl 3950 2904 3944 2910 Dl 3943 2910 3935 2916 Dl 3935 2917 3904 2933 Dl 3953 2901 3914 2908 Dl 3914 2908 3904 2933 Dl 3024 2439 3024 3599 Dl 3024 3598 3350 3437 Dl 3903 2933 3350 3437 Dl 3914 2907 3024 2438 Dl (4)3307 3026 w 3394 1962 3024 1962 Dl 3024 1962 3024 2438 Dl 3394 1962 3972 2876 Dl 3972 2877 3970 2885 Dl 3970 2885 3965 2892 Dl 3964 2892 3957 2898 Dl 3956 2898 3954 2900 Dl (5)3384 2403 w 3535 3425 3350 3437 Dl 4026 3273 3535 3425 Dl 4025 3271 3935 2916 Dl (7)3734 3239 w 4124 3239 4063 3276 Dl 4063 3276 4026 3272 Dl 4124 3239 3944 2910 Dl 5 R f (8)4016 3146 w 10 R f 0.1 setlinewidth 4224 3202 4165 3230 Dl 4165 3231 4125 3239 Dl 4224 3202 3951 2904 Dl 5 R f (9)4082 3119 w 10 R f 0.1 setlinewidth 4316 3153 4288 3192 Dl 4287 3191 4224 3201 Dl 4317 3152 3957 2898 Dl 5 R f (10)4138 3093 w 10 R f 0.1 setlinewidth 4420 3077 4402 3115 Dl 4402 3115 4317 3152 Dl 4420 3077 3965 2892 Dl 5 R f (11)4204 3049 w 10 R f 0.1 setlinewidth 4529 2997 4488 3057 Dl 4488 3058 4420 3077 Dl 4530 2997 3970 2885 Dl 5 R f (12)4278 2997 w 10 R f 0.1 setlinewidth 4506 2876 3972 2876 Dl 4603 2984 4651 2903 Dl 4602 2985 4582 2991 Dl 4648 2896 4507 2877 Dl 4651 2903 4649 2897 Dl 4581 2992 4530 2997 Dl 5 R f (13)4360 2931 w 10 R f 0.1 setlinewidth 3796 3440 3535 3425 Dl 4081 3372 3797 3440 Dl 4080 3371 4063 3276 Dl 5 R f (14)3842 3379 w 10 R f 0.1 setlinewidth 4210 3341 4115 3382 Dl 4114 3381 4080 3371 Dl 4218 3325 4210 3340 Dl 4218 3324 4165 3230 Dl 4339 3237 4219 3324 Dl 4340 3237 4288 3192 Dl 4430 3234 4389 3250 Dl 4441 3132 4430 3234 Dl 4388 3249 4340 3237 Dl 4440 3131 4402 3115 Dl 4553 3073 4553 3103 Dl 4553 3104 4441 3132 Dl 4554 3072 4488 3057 Dl 4617 3056 4554 3073 Dl 4582 2992 4618 3056 Dl 4658 2898 4654 2896 Dl 4652 2903 4659 2899 Dl 4654 2897 4649 2897 Dl 4594 2866 4507 2877 Dl 4668 2881 4654 2874 Dl 4655 2896 4669 2882 Dl 4654 2874 4594 2866 Dl 4407 3270 4407 3274 Dl 4406 3274 4277 3340 Dl 4276 3340 4210 3340 Dl 4389 3251 4407 3270 Dl 4627 3132 4599 3214 Dl 4598 3214 4441 3239 Dl 4554 3104 4628 3132 Dl 4441 3239 4430 3234 Dl 5 R f (23)4498 3181 w 10 R f 0.1 setlinewidth 4717 2992 4728 2999 Dl 4727 3000 4726 3015 Dl 4726 3015 4644 3057 Dl 4603 2985 4716 2991 Dl 4643 3057 4618 3056 Dl 4442 3240 4407 3270 Dl 4644 3058 4698 3115 Dl 4698 3116 4628 3132 Dl 4756 2941 4749 2934 Dl 4688 2906 4659 2899 Dl 4736 2925 4688 2906 Dl 4717 2991 4757 2942 Dl 4748 2934 4736 2926 Dl 4124 3483 3970 3532 Dl 3970 3532 3797 3440 Dl 4115 3383 4124 3483 Dl 5 R f (28)3968 3460 w 10 R f 0.1 setlinewidth 4202 3528 4124 3483 Dl 4329 3427 4204 3528 Dl 4278 3341 4329 3427 Dl 5 R f (29)4188 3435 w 10 R f 0.1 setlinewidth 4487 3338 4410 3412 Dl 4409 3413 4329 3427 Dl 4408 3274 4487 3338 Dl 5 R f (30)4355 3363 w 10 R f 0.1 setlinewidth 4643 3231 4610 3295 Dl 4609 3295 4494 3338 Dl 4494 3338 4487 3338 Dl 4600 3215 4644 3232 Dl 5 R f (31)4501 3280 w 10 R f 0.1 setlinewidth 4714 3118 4741 3141 Dl 4742 3142 4680 3224 Dl 4679 3225 4644 3232 Dl 4699 3116 4714 3118 Dl 4782 3056 4781 3067 Dl 4726 3014 4782 3055 Dl 4780 3067 4714 3118 Dl 4748 2934 4741 2927 Dl 4736 2926 4741 2927 Dl 4594 2865 4644 2851 Dl 4646 2851 4644 2851 Dl 4654 2874 4647 2851 Dl 4295 3526 4209 3543 Dl 4452 3468 4295 3525 Dl 4204 3529 4209 3543 Dl 4410 3413 4453 3468 Dl 4562 3392 4475 3479 Dl 4475 3479 4453 3468 Dl 4496 3338 4564 3391 Dl 4718 3404 4598 3401 Dl 4662 3322 4718 3405 Dl 4598 3400 4564 3391 Dl 4611 3296 4662 3321 Dl 4775 3254 4747 3283 Dl 4746 3283 4662 3321 Dl 4679 3224 4776 3254 Dl 4810 3158 4803 3253 Dl 4802 3254 4776 3254 Dl 4781 3147 4811 3157 Dl 4742 3142 4780 3147 Dl 4838 3087 4845 3094 Dl 4781 3067 4836 3087 Dl 4845 3095 4780 3147 Dl 4895 3024 4893 3029 Dl 4789 2996 4895 3024 Dl 4777 2995 4788 2995 Dl 4783 3054 4893 3029 Dl 4728 2999 4776 2995 Dl 4758 2941 4824 2940 Dl 4777 2994 4824 2940 Dl 4742 2927 4772 2899 Dl 4689 2906 4772 2899 Dl 3024 3941 3024 3599 Dl 3088 3950 3024 3942 Dl 3934 3632 3088 3950 Dl 3970 3532 3934 3630 Dl (45)3379 3666 w 4204 3687 4183 3702 Dl 4183 3702 3934 3630 Dl 4208 3542 4205 3687 Dl 5 R f (46)4066 3602 w 10 R f 0.1 setlinewidth 4511 3524 4295 3525 Dl 4475 3480 4511 3524 Dl 4598 3401 4514 3526 Dl 4512 3524 4514 3526 Dl 4746 3283 4741 3414 Dl 4718 3405 4741 3414 Dl 4971 3128 4974 3156 Dl 4845 3094 4970 3127 Dl 4811 3156 4974 3156 Dl 4893 3030 4902 3045 Dl 4900 3046 4836 3087 Dl 4875 2934 4885 2957 Dl 4825 2940 4875 2934 Dl 4788 2995 4885 2957 Dl 4764 2890 4701 2875 Dl 4775 2897 4764 2890 Dl 4669 2882 4701 2875 Dl 4773 2899 4775 2898 Dl 4392 3675 4205 3687 Dl 4525 3540 4393 3674 Dl 4514 3526 4525 3540 Dl 5 R f (55)4315 3607 w 10 R f 0.1 setlinewidth 4800 3449 4763 3520 Dl 4762 3520 4525 3540 Dl 4741 3415 4800 3448 Dl 5 R f (56)4634 3481 w 10 R f 0.1 setlinewidth 4882 3407 4800 3448 Dl 4865 3271 4883 3407 Dl 4804 3253 4865 3270 Dl 5 R f (57)4784 3358 w 10 R f 0.1 setlinewidth 4975 3158 5005 3191 Dl 5004 3191 4865 3270 Dl 4974 3115 4970 3127 Dl 4903 3045 4975 3114 Dl 4886 2957 4929 3001 Dl 4896 3023 4929 3001 Dl 4776 2898 4894 2910 Dl 4875 2933 4894 2910 Dl 3866 3978 3216 3978 Dl 3216 3977 3088 3950 Dl 4052 3919 3867 3978 Dl 4183 3703 4052 3918 Dl (62)3681 3861 w 4764 3520 4767 3530 Dl 4766 3530 4573 3766 Dl 4573 3765 4393 3674 Dl 5 R f (63)4550 3638 w 10 R f 0.1 setlinewidth 5040 3202 5040 3278 Dl 5006 3191 5040 3202 Dl 5039 3279 4991 3404 Dl 4991 3404 4883 3407 Dl 5 R f (64)4930 3315 w 10 R f 0.1 setlinewidth 5040 3010 5040 3075 Dl 4930 3002 5040 3009 Dl 4976 3115 5040 3075 Dl 4700 2875 4687 2830 Dl 4647 2851 4687 2830 Dl 4392 3978 4302 3978 Dl 4613 3844 4393 3978 Dl 4301 3977 4052 3918 Dl 4573 3766 4613 3843 Dl (67)4281 3849 w 4944 3657 4808 3854 Dl 4808 3854 4613 3843 Dl 4767 3530 4945 3657 Dl (68)4707 3734 w 5040 3419 5040 3616 Dl 5039 3616 4945 3657 Dl 4992 3404 5040 3419 Dl 5 R f (69)4899 3527 w 10 R f 0.1 setlinewidth 5040 3278 5040 3419 Dl 5040 3075 5040 3202 Dl 5040 3008 5040 2975 Dl 4917 2902 5040 2975 Dl 4894 2910 4916 2902 Dl 4917 2900 4925 2890 Dl 4764 2890 4925 2890 Dl 4645 2851 4697 2808 Dl 4688 2829 4697 2808 Dl 4301 3978 3867 3978 Dl 5039 3978 4994 3978 Dl 5040 3939 5040 3978 Dl 5039 3939 4994 3978 Dl 4697 2807 4719 2769 Dl 4936 2882 4719 2769 Dl 4926 2890 4937 2883 Dl 4899 3978 4393 3978 Dl 4809 3855 4900 3978 Dl 5 R f (79)4645 3932 w 10 R f 0.1 setlinewidth 4994 3978 4900 3978 Dl 5040 3617 5040 3938 Dl 5 R f (80)4926 3830 w 10 R f 0.1 setlinewidth 5040 2975 5040 2870 Dl 4993 2868 5040 2870 Dl 4937 2882 4992 2867 Dl 3216 3978 3024 3978 Dl 3024 3978 3024 3942 Dl 4719 2770 4719 2768 Dl 4991 2868 4719 2768 Dl 5039 2460 4446 1962 Dl 4446 1962 4195 1962 Dl 5040 2676 5040 2460 Dl 5039 2676 4195 1962 Dl (92)4627 2289 w 4193 1962 3777 1962 Dl 5040 2868 5040 2676 Dl 4718 2768 3777 1962 Dl (93)4428 2404 w 3777 1962 3394 1962 Dl (94)3987 2491 w 20 R f 16 setlinewidth 5040 3978 3024 3978 Dl 5040 1962 5040 3978 Dl 3024 1962 5040 1962 Dl 3024 3978 3024 1962 Dl 4890 2979 4032 2970 Dl 4890 2979 4818 2996 Dl 4890 2978 4818 2960 Dl 10 B f (Fig. 22:)1 322 1 966 4176 t 10 R f (dual affine iter 2,)3 687 1 1313 4176 t 10 I f (v)2025 4176 w 10 R f (= \(10,0,0\))1 397 1 2094 4176 t 10 B f (Fig. 23:)1 322 1 3386 4176 t 10 R f (cutaway view of fig. 22)4 945 1 3733 4176 t 0.1 setlinewidth 1724 5343 1 1 De 1724 5343 1722 5343 Dl 1724 5342 1722 5342 Dl 1723 5342 1722 5343 Dl 1576 5240 1661 5371 Dl 1663 5371 1666 5371 Dl 1666 5371 1690 5364 Dl 1721 5345 1690 5364 Dl 1722 5342 1576 5240 Dl 1402 4338 994 4338 Dl 1702 5171 1727 5340 Dl 1700 5170 1573 4754 Dl 1573 4754 1404 4338 Dl 995 4338 1254 4777 Dl 1254 4778 1576 5240 Dl (5)1372 4756 w 1695 5364 1690 5364 Dl 1715 5361 1695 5364 Dl 1717 5361 1724 5343 Dl 1720 5360 1717 5361 Dl 1716 5361 1715 5361 Dl 1721 5360 1724 5343 Dl 1726 5358 1723 5359 Dl 1723 5359 1721 5359 Dl 1727 5358 1725 5342 Dl 1732 5356 1730 5358 Dl 1730 5358 1727 5358 Dl 1733 5356 1725 5342 Dl 1742 5352 1740 5354 Dl 1739 5355 1733 5356 Dl 1743 5351 1726 5341 Dl 1754 5348 1748 5351 Dl 1748 5352 1743 5352 Dl 1754 5347 1726 5341 Dl 1760 5338 1727 5340 Dl 1771 5340 1761 5346 Dl 1761 5347 1759 5347 Dl 1771 5338 1760 5338 Dl 1759 5348 1755 5348 Dl 1702 5366 1695 5364 Dl 1714 5366 1702 5366 Dl 1715 5365 1717 5361 Dl 1720 5365 1715 5366 Dl 1715 5365 1 1 De 1721 5365 1 1 De 1722 5364 1723 5359 Dl 1731 5361 1722 5364 Dl 1730 5360 1730 5358 Dl 1735 5362 1733 5362 Dl 1741 5356 1736 5361 Dl 1733 5361 1731 5361 Dl 1741 5355 1740 5354 Dl 1753 5353 1751 5355 Dl 1750 5355 1742 5356 Dl 1751 5352 1748 5351 Dl 1757 5353 1752 5353 Dl 1759 5348 1758 5352 Dl 1771 5340 1 1 De 1768 5337 1760 5338 Dl 1774 5338 1 1 De 1773 5339 1775 5338 Dl 1774 5337 1769 5337 Dl 1733 5364 1724 5366 Dl 1723 5365 1721 5365 Dl 1733 5362 1733 5363 Dl 1755 5357 1748 5362 Dl 1747 5362 1737 5362 Dl 1751 5355 1754 5357 Dl 1772 5348 1 1 De 1772 5348 1771 5349 Dl 1770 5350 1760 5352 Dl 1761 5347 1771 5347 Dl 1760 5352 1758 5352 Dl 1736 5362 1733 5363 Dl 1761 5352 1761 5356 Dl 1760 5357 1754 5357 Dl 1773 5340 1775 5340 Dl 1776 5341 1779 5342 Dl 1778 5343 1771 5347 Dl 1779 5343 1 1 De 1712 5371 1705 5371 Dl 1704 5371 1702 5366 Dl 1715 5367 1712 5371 Dl 1713 5373 1712 5371 Dl 1722 5372 1713 5374 Dl 1723 5366 1722 5370 Dl 1734 5369 1727 5371 Dl 1726 5370 1722 5370 Dl 1733 5364 1734 5368 Dl 1748 5363 1743 5366 Dl 1743 5368 1735 5368 Dl 1747 5363 1749 5364 Dl 1763 5356 1763 5358 Dl 1763 5359 1753 5364 Dl 1751 5364 1749 5364 Dl 1761 5356 1762 5356 Dl 1771 5353 1 1 De 1771 5350 1773 5353 Dl 1772 5353 1762 5356 Dl 1769 5336 1774 5335 Dl 1775 5337 1775 5335 Dl 1716 5374 1713 5374 Dl 1726 5374 1717 5374 Dl 1713 5374 1 1 De 1726 5371 1726 5374 Dl 1735 5372 1727 5374 Dl 1726 5374 1 1 De 1735 5368 1735 5371 Dl 1744 5374 1737 5372 Dl 1745 5370 1744 5375 Dl 1736 5371 1735 5371 Dl 1745 5367 1746 5369 Dl 1757 5367 1753 5368 Dl 1753 5369 1746 5369 Dl 1753 5364 1758 5366 Dl 1767 5360 1760 5366 Dl 1760 5366 1758 5366 Dl 1766 5360 1768 5360 Dl 1764 5359 1766 5359 Dl 1772 5353 1776 5355 Dl 1776 5356 1766 5359 Dl 1787 5351 1 1 De 1778 5349 1788 5351 Dl 1777 5348 1778 5348 Dl 1787 5352 1773 5353 Dl 1772 5348 1777 5348 Dl 1780 5343 1787 5343 Dl 1787 5343 1777 5348 Dl 1784 5340 1779 5342 Dl 1775 5339 1785 5339 Dl 1673 5377 1666 5371 Dl 1700 5376 1673 5378 Dl 1704 5371 1700 5374 Dl 1707 5381 1706 5381 Dl 1705 5379 1700 5374 Dl 1712 5374 1707 5380 Dl 1726 5376 1717 5374 Dl 1726 5375 1726 5377 Dl 1736 5373 1726 5378 Dl 1753 5369 1745 5376 Dl 1744 5375 1 1 De 1787 5360 1785 5362 Dl 1776 5356 1787 5360 Dl 1785 5362 1768 5360 Dl 1787 5351 1787 5352 Dl 1786 5353 1776 5355 Dl 1794 5342 1794 5344 Dl 1787 5342 1794 5342 Dl 1793 5345 1778 5348 Dl 1779 5338 1784 5338 Dl 1785 5339 1 1 De 1775 5337 1779 5337 Dl 1714 5382 1707 5380 Dl 1726 5379 1715 5383 Dl 1726 5379 1 1 De 1747 5379 1740 5382 Dl 1739 5382 1726 5379 Dl 1745 5377 1747 5379 Dl 1755 5379 1747 5379 Dl 1764 5370 1756 5379 Dl 1760 5367 1764 5369 Dl 1785 5363 1785 5366 Dl 1785 5366 1764 5369 Dl 1789 5360 1787 5360 Dl 1787 5352 1789 5358 Dl 1793 5344 1794 5348 Dl 1794 5349 1788 5351 Dl 1786 5340 1800 5340 Dl 1799 5340 1794 5342 Dl 1679 5386 1673 5378 Dl 1694 5387 1679 5387 Dl 1706 5381 1694 5387 Dl 1740 5383 1 1 De 1739 5384 1717 5391 Dl 1717 5390 1715 5383 Dl 1786 5367 1791 5369 Dl 1790 5369 1765 5381 Dl 1765 5381 1756 5379 Dl 1822 5351 1825 5351 Dl 1795 5349 1822 5351 Dl 1825 5351 1789 5358 Dl 1779 5337 1781 5333 Dl 1775 5335 1781 5333 Dl 1714 5396 1699 5396 Dl 1699 5396 1694 5387 Dl 1717 5390 1715 5395 Dl 1742 5396 1722 5402 Dl 1722 5401 1715 5395 Dl 1741 5384 1743 5396 Dl 1779 5393 1775 5400 Dl 1775 5399 1743 5396 Dl 1766 5382 1779 5392 Dl 1833 5378 1779 5392 Dl 1791 5368 1833 5377 Dl 1826 5352 1850 5353 Dl 1835 5377 1833 5377 Dl 1849 5352 1836 5377 Dl 1805 5340 1822 5351 Dl 1801 5339 1805 5338 Dl 1805 5338 1807 5337 Dl 1785 5338 1807 5337 Dl 1775 5335 1784 5330 Dl 1782 5332 1784 5330 Dl 1686 5413 1676 5406 Dl 1676 5406 1679 5387 Dl 1687 5413 1699 5396 Dl 1855 5468 1857 5476 Dl 1856 5475 1705 5436 Dl 1795 5421 1854 5467 Dl 1796 5420 1717 5418 Dl 1716 5417 1705 5436 Dl 1851 5354 1945 5369 Dl 1943 5369 1884 5388 Dl 1836 5378 1884 5388 Dl 1784 5330 1790 5326 Dl 1791 5326 1810 5336 Dl 1808 5336 1810 5336 Dl 1705 5438 1696 5438 Dl 1696 5437 1686 5414 Dl 1722 5403 1717 5418 Dl 1775 5400 1795 5420 Dl 1884 5388 1854 5467 Dl 1823 5333 1843 5333 Dl 1810 5335 1822 5333 Dl 1843 5333 1850 5353 Dl 1654 5412 1661 5371 Dl 1675 5405 1654 5412 Dl 1655 5480 1640 5448 Dl 1641 5446 1654 5412 Dl 1696 5437 1656 5479 Dl 2491 6028 1939 6143 Dl 1939 6142 1656 5479 Dl 1857 5477 2492 6027 Dl (85)1968 5847 w 2736 5418 2736 5852 Dl 2067 5361 2736 5418 Dl 2735 5853 2492 6027 Dl 1946 5368 2066 5360 Dl (86)2326 5646 w 1844 5332 1900 5318 Dl 1900 5319 2066 5360 Dl 1791 5326 1822 5333 Dl 1640 5447 1254 4777 Dl 5 R f (89)1493 5206 w 10 R f 0.1 setlinewidth 899 4338 994 4338 Dl 1939 6143 898 4338 Dl (90)1327 5107 w 2735 4532 2623 4338 Dl 2623 4338 1404 4338 Dl 2736 5417 2736 4532 Dl 1899 5319 1573 4754 Dl (92)2130 4840 w 1791 5326 1701 5171 Dl 5 R f (93)1717 5135 w 20 R f 16 setlinewidth 2736 6354 720 6354 Dl 2736 4338 2736 6354 Dl 720 4338 2736 4338 Dl 720 6354 720 4338 Dl 2435 5993 1728 5346 Dl 2435 5993 2370 5958 Dl 2435 5992 2394 5931 Dl 10 R f 0.1 setlinewidth 3936 5297 3935 5295 Dl 3938 5301 3936 5297 Dl 3940 5306 3939 5302 Dl 3942 5307 3943 5318 Dl 3934 5295 3927 5301 Dl 3942 5318 3927 5301 Dl 3024 5129 3024 4916 Dl 3950 5643 3024 5129 Dl 3990 5650 3950 5643 Dl 4047 5558 3990 5650 Dl 4048 5557 3943 5318 Dl 3927 5301 3024 4916 Dl (4)3524 5302 w 3024 4726 3024 4916 Dl 3024 4725 3918 5276 Dl 3919 5276 3926 5283 Dl 3927 5284 3931 5289 Dl 3932 5288 3934 5293 Dl 3935 5294 3935 5295 Dl (5)3328 5012 w 4083 5558 4048 5558 Dl 4147 5502 4083 5559 Dl 4146 5500 3941 5306 Dl 5 R f (7)4035 5469 w 10 R f 0.1 setlinewidth 4159 5503 4159 5484 Dl 4159 5503 4147 5501 Dl 4158 5483 3939 5302 Dl 4166 5478 4167 5461 Dl 4159 5483 4165 5478 Dl 4166 5460 3936 5297 Dl 4178 5452 4163 5427 Dl 4167 5460 4178 5453 Dl 4162 5426 3934 5293 Dl 4161 5394 4140 5366 Dl 4163 5425 4161 5395 Dl 4139 5367 3931 5289 Dl 4140 5343 4098 5286 Dl 4140 5366 4140 5343 Dl 4097 5285 3926 5283 Dl 3958 5171 3918 5276 Dl 4098 5259 4010 5159 Dl 4100 5270 4098 5260 Dl 4001 5153 3960 5171 Dl 4010 5159 4001 5152 Dl 4098 5285 4101 5270 Dl 4148 5572 4083 5559 Dl 4201 5550 4148 5572 Dl 4201 5549 4159 5503 Dl 4215 5556 4224 5536 Dl 4202 5551 4215 5556 Dl 4224 5535 4220 5528 Dl 4219 5527 4165 5478 Dl 4219 5527 4214 5478 Dl 4214 5478 4178 5453 Dl 4234 5484 4235 5472 Dl 4234 5471 4180 5403 Dl 4215 5479 4233 5484 Dl 4179 5402 4161 5395 Dl 4186 5369 4165 5346 Dl 4181 5403 4186 5370 Dl 4164 5345 4140 5343 Dl 4164 5346 4163 5321 Dl 4162 5320 4101 5270 Dl 4005 5151 4001 5149 Dl 4010 5158 4005 5151 Dl 4001 5150 4001 5152 Dl 3950 5131 3960 5171 Dl 3980 5125 3967 5120 Dl 4000 5149 3980 5126 Dl 3966 5120 3949 5130 Dl 4248 5497 4246 5495 Dl 4241 5535 4248 5497 Dl 4224 5536 4241 5536 Dl 4246 5494 4233 5484 Dl 4264 5446 4221 5382 Dl 4241 5474 4264 5446 Dl 4220 5381 4186 5370 Dl 4235 5472 4240 5474 Dl 4131 5242 4122 5237 Dl 4145 5257 4131 5242 Dl 4169 5317 4145 5258 Dl 4121 5237 4098 5260 Dl 4164 5320 4170 5317 Dl 4246 5494 4240 5474 Dl 4224 5356 4170 5317 Dl 4221 5381 4224 5357 Dl 4067 5166 4057 5161 Dl 4015 5149 4005 5151 Dl 4044 5155 4016 5149 Dl 4121 5236 4067 5167 Dl 4056 5161 4044 5155 Dl 4247 5602 4217 5616 Dl 4148 5573 4217 5616 Dl 4215 5556 4248 5602 Dl 4248 5601 4281 5624 Dl 4282 5624 4284 5580 Dl 4242 5537 4284 5580 Dl 4299 5572 4294 5531 Dl 4283 5579 4299 5572 Dl 4248 5497 4294 5531 Dl 4306 5499 4284 5454 Dl 4297 5530 4306 5499 Dl 4294 5531 4296 5531 Dl 4264 5447 4284 5454 Dl 4251 5370 4230 5356 Dl 4287 5444 4251 5371 Dl 4284 5453 4288 5444 Dl 4225 5356 4230 5356 Dl 4199 5294 4190 5283 Dl 4189 5283 4145 5258 Dl 4230 5355 4200 5294 Dl 4057 5161 4047 5155 Dl 4046 5155 4044 5155 Dl 3949 5130 3929 5094 Dl 3929 5093 3929 5094 Dl 3967 5120 3929 5092 Dl 4287 5631 4302 5626 Dl 4302 5625 4327 5601 Dl 4281 5625 4286 5631 Dl 4300 5573 4327 5601 Dl 4336 5606 4332 5559 Dl 4327 5602 4336 5608 Dl 4297 5531 4332 5559 Dl 4345 5564 4379 5564 Dl 4331 5513 4379 5564 Dl 4332 5560 4344 5564 Dl 4307 5500 4330 5513 Dl 4333 5479 4326 5455 Dl 4330 5512 4332 5479 Dl 4288 5445 4326 5455 Dl 4331 5450 4275 5371 Dl 4327 5455 4332 5451 Dl 4263 5369 4275 5371 Dl 4252 5370 4262 5368 Dl 4231 5304 4224 5299 Dl 4224 5298 4200 5294 Dl 4262 5368 4232 5304 Dl 4177 5219 4172 5212 Dl 4172 5212 4132 5218 Dl 4131 5221 4132 5218 Dl 4190 5283 4178 5219 Dl 4130 5242 4130 5222 Dl 4068 5166 4068 5137 Dl 4130 5220 4068 5137 Dl 4046 5154 4008 5106 Dl 4015 5149 4008 5106 Dl 4098 5701 3990 5650 Dl 4228 5653 4098 5702 Dl 4219 5616 4230 5652 Dl 5 R f (45)4082 5638 w 10 R f 0.1 setlinewidth 4316 5692 4313 5696 Dl 4229 5653 4313 5696 Dl 4287 5632 4317 5692 Dl 4302 5626 4358 5631 Dl 4336 5608 4358 5631 Dl 4359 5631 4344 5564 Dl 4359 5631 4360 5632 Dl 4388 5568 4332 5479 Dl 4379 5564 4389 5569 Dl 4306 5329 4281 5300 Dl 4232 5303 4281 5300 Dl 4276 5371 4307 5330 Dl 4194 5233 4178 5219 Dl 4224 5298 4194 5233 Dl 4090 5131 4060 5105 Dl 4067 5137 4060 5105 Dl 4132 5218 4091 5132 Dl 3993 5098 3970 5104 Dl 4005 5102 3993 5097 Dl 3980 5125 3970 5104 Dl 4007 5105 4006 5103 Dl 4318 5692 4361 5697 Dl 4361 5696 4367 5639 Dl 4360 5632 4367 5639 Dl 4429 5633 4419 5590 Dl 4368 5640 4430 5634 Dl 4389 5570 4419 5590 Dl 4419 5588 4425 5557 Dl 4425 5557 4356 5456 Dl 4333 5451 4356 5456 Dl 4338 5355 4307 5330 Dl 4355 5456 4338 5356 Dl 4281 5299 4270 5284 Dl 4269 5284 4194 5233 Dl 4148 5169 4091 5132 Dl 4171 5211 4148 5169 Dl 4025 5062 4006 5103 Dl 4059 5105 4025 5062 Dl 4208 5768 4098 5702 Dl 4303 5764 4210 5769 Dl 4313 5697 4304 5764 Dl 4430 5634 4433 5639 Dl 4421 5749 4433 5639 Dl 4361 5697 4420 5749 Dl 4339 5356 4364 5358 Dl 4451 5545 4364 5358 Dl 4426 5558 4451 5546 Dl 4172 5077 4163 5084 Dl 4149 5168 4163 5084 Dl 4270 5284 4172 5077 Dl 3970 5103 3891 5044 Dl 3928 5092 3891 5044 Dl 4439 5787 4380 5820 Dl 4304 5764 4380 5820 Dl 4421 5750 4440 5788 Dl 4494 5813 4509 5718 Dl 4440 5789 4494 5814 Dl 4434 5639 4509 5718 Dl 4530 5575 4570 5641 Dl 4509 5718 4570 5641 Dl 4453 5545 4530 5574 Dl 4529 5574 4427 5263 Dl 4364 5357 4427 5263 Dl 5 R f (70)4418 5436 w 10 R f 0.1 setlinewidth 4171 5077 4168 4991 Dl 4426 5264 4425 5252 Dl 4425 5252 4168 4991 Dl 5 R f (71)4269 5209 w 10 R f 0.1 setlinewidth 4162 5083 4008 5034 Dl 4024 5061 4008 5034 Dl 4007 5034 3987 5010 Dl 3987 5010 3993 5097 Dl 3928 5093 3849 5006 Dl 3890 5044 3849 5006 Dl 4386 5948 4284 5901 Dl 4211 5769 4284 5901 Dl 4381 5821 4386 5949 Dl 5 R f (75)4287 5854 w 10 R f 0.1 setlinewidth 4873 5763 4899 5803 Dl 4547 6056 4899 5803 Dl 4661 5692 4873 5762 Dl 4526 5917 4661 5693 Dl 4526 5917 4546 6057 Dl (76)4635 5872 w 4168 4990 4156 4687 Dl 4442 5114 4156 4687 Dl 4426 5251 4443 5114 Dl 5 R f (77)4260 5002 w 10 R f 0.1 setlinewidth 3849 5006 3769 4930 Dl 3971 4989 3769 4930 Dl 3986 5009 3971 4989 Dl 4546 6057 4510 6080 Dl 4386 5949 4510 6080 Dl 4494 5814 4525 5916 Dl 5 R f (79)4437 5934 w 10 R f 0.1 setlinewidth 4571 5642 4661 5693 Dl 5 R f (80)4537 5770 w 10 R f 0.1 setlinewidth 4873 5762 4443 5114 Dl (81)4554 5504 w 3923 4913 3890 4822 Dl 3970 4989 3922 4914 Dl 4168 4989 3890 4822 Dl 5 R f (82)4016 4981 w 10 R f 0.1 setlinewidth 4098 5920 3950 5643 Dl 4283 5902 4098 5921 Dl 5 R f (83)4094 5809 w 10 R f 0.1 setlinewidth 4184 6271 4009 6085 Dl 4099 5921 4009 6085 Dl 4510 6080 4185 6272 Dl (84)4190 6086 w 4185 6273 4021 6354 Dl 4155 4687 3921 4338 Dl 3921 4338 3572 4338 Dl 3888 4822 3541 4419 Dl 3571 4338 3541 4419 Dl (87)3845 4622 w 3768 4929 3764 4927 Dl 3921 4914 3764 4927 Dl 3024 5489 3024 5129 Dl 4009 6085 3024 5489 Dl (89)3494 5633 w 4021 6354 3024 6354 Dl 3024 6353 3024 5489 Dl (90)3406 6072 w 3572 4338 3375 4338 Dl 3541 4419 3375 4338 Dl 3375 4338 3024 4338 Dl 3024 4338 3024 4541 Dl 3764 4927 3024 4541 Dl (93)3396 4618 w 3024 4541 3024 4724 Dl (94)3449 4926 w 20 R f 16 setlinewidth 5040 6354 3024 6354 Dl 5040 4338 5040 6354 Dl 3024 4338 5040 4338 Dl 3024 6354 3024 4338 Dl 4314 5076 4032 5346 Dl 4313 5075 4274 5137 Dl 4313 5076 4249 5112 Dl 10 B f (Fig. 24:)1 322 1 1002 6552 t 10 R f (iter 3, cutaway,)2 615 1 1349 6552 t 10 I f (v)1989 6552 w 10 R f (= \(20,0,0\))1 397 1 2058 6552 t 10 B f (Fig. 25:)1 322 1 3306 6552 t 10 R f (iter 4, cutaway,)2 615 1 3653 6552 t 10 I f (v)4293 6552 w 10 R f (= \(10,0,0\))1 397 1 4362 6552 t (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 14 15 %%Page: 15 16 /saveobj save def mark 16 pagesetup 10 R f (- 15 -)2 216 1 2772 282 t 0.1 setlinewidth 1719 1471 1718 1472 Dl 1718 1472 1716 1474 Dl 1715 1474 1713 1476 Dl 1713 1477 1704 1482 Dl 1719 1471 1711 1473 Dl 1711 1475 1704 1482 Dl 1616 1362 1491 1608 Dl 1491 1608 1493 1615 Dl 1493 1615 1558 1592 Dl 1703 1482 1558 1592 Dl 1710 1473 1616 1361 Dl 5 R f (4)1591 1502 w 10 R f 0.1 setlinewidth 1724 1266 1727 1462 Dl 1723 1265 1705 1245 Dl 1705 1246 1684 1248 Dl 1683 1249 1658 1272 Dl 1658 1271 1640 1301 Dl 1639 1302 1616 1361 Dl 1726 1463 1725 1465 Dl 1725 1466 1723 1468 Dl 1722 1468 1720 1470 Dl 1720 1470 1 1 De 1561 1599 1558 1592 Dl 1614 1596 1562 1600 Dl 1615 1595 1713 1476 Dl 1629 1594 1614 1601 Dl 1614 1601 1614 1596 Dl 1632 1592 1716 1474 Dl 1650 1588 1636 1593 Dl 1635 1593 1630 1593 Dl 1651 1587 1718 1472 Dl 1677 1574 1659 1589 Dl 1658 1588 1650 1587 Dl 1677 1574 1720 1470 Dl 1720 1545 1702 1563 Dl 1702 1563 1678 1574 Dl 1721 1544 1723 1468 Dl 1770 1503 1738 1537 Dl 1738 1537 1720 1544 Dl 1771 1502 1725 1465 Dl 1799 1437 1727 1462 Dl 1830 1439 1792 1494 Dl 1791 1495 1784 1499 Dl 1799 1435 1831 1434 Dl 1831 1435 1830 1439 Dl 1783 1499 1771 1502 Dl 1559 1623 1562 1600 Dl 1581 1634 1558 1624 Dl 1582 1634 1614 1601 Dl 1594 1641 1578 1643 Dl 1579 1642 1582 1635 Dl 1601 1635 1595 1640 Dl 1602 1634 1636 1593 Dl 1643 1615 1602 1635 Dl 1643 1614 1659 1589 Dl 1648 1625 1639 1627 Dl 1698 1574 1648 1625 Dl 1640 1626 1643 1614 Dl 1699 1574 1702 1563 Dl 1740 1550 1725 1568 Dl 1726 1568 1699 1574 Dl 1740 1549 1738 1537 Dl 1760 1542 1741 1549 Dl 1784 1499 1761 1542 Dl 1833 1434 1833 1435 Dl 1833 1436 1830 1439 Dl 1832 1434 1831 1434 Dl 1820 1422 1799 1436 Dl 1836 1421 1839 1423 Dl 1839 1424 1833 1434 Dl 1821 1421 1836 1419 Dl 1629 1639 1627 1641 Dl 1627 1642 1594 1650 Dl 1595 1649 1595 1640 Dl 1639 1627 1630 1639 Dl 1719 1594 1666 1642 Dl 1665 1642 1646 1630 Dl 1725 1569 1719 1594 Dl 1646 1629 1648 1625 Dl 1815 1498 1815 1503 Dl 1814 1503 1806 1515 Dl 1806 1516 1765 1544 Dl 1792 1495 1816 1497 Dl 1764 1544 1761 1542 Dl 1646 1629 1630 1639 Dl 1764 1545 1739 1591 Dl 1739 1592 1719 1594 Dl 1848 1452 1848 1457 Dl 1834 1436 1839 1437 Dl 1840 1437 1847 1446 Dl 1847 1457 1816 1497 Dl 1848 1447 1848 1452 Dl 1539 1676 1527 1668 Dl 1527 1667 1558 1624 Dl 1578 1643 1540 1676 Dl 1518 1704 1540 1676 Dl 1553 1692 1517 1704 Dl 1594 1650 1553 1692 Dl 1591 1687 1555 1703 Dl 1555 1702 1553 1692 Dl 1627 1641 1592 1686 Dl 1656 1662 1613 1692 Dl 1613 1693 1592 1689 Dl 1592 1688 1592 1686 Dl 1666 1642 1656 1662 Dl 1739 1595 1726 1617 Dl 1726 1618 1662 1665 Dl 1661 1664 1656 1662 Dl 1740 1591 1740 1595 Dl 1792 1551 1785 1561 Dl 1805 1515 1793 1551 Dl 1785 1562 1740 1595 Dl 1848 1447 1848 1452 Dl 1847 1447 1848 1447 Dl 1821 1421 1835 1407 Dl 1836 1406 1 1 De 1836 1407 1836 1419 Dl 1511 1720 1511 1710 Dl 1522 1735 1510 1720 Dl 1511 1709 1517 1704 Dl 1555 1702 1522 1735 Dl 1555 1731 1514 1746 Dl 1514 1745 1522 1735 Dl 1591 1689 1554 1731 Dl 1525 1792 1545 1746 Dl 1592 1723 1524 1792 Dl 1544 1746 1554 1731 Dl 1612 1693 1591 1722 Dl 1637 1715 1614 1725 Dl 1612 1724 1591 1722 Dl 1662 1666 1637 1714 Dl 1718 1645 1636 1722 Dl 1637 1722 1637 1714 Dl 1724 1630 1719 1645 Dl 1725 1618 1725 1629 Dl 1779 1587 1775 1594 Dl 1784 1562 1779 1586 Dl 1774 1594 1725 1629 Dl 1843 1528 1838 1533 Dl 1831 1499 1843 1527 Dl 1829 1499 1831 1499 Dl 1839 1533 1793 1551 Dl 1815 1503 1828 1499 Dl 1848 1456 1869 1449 Dl 1869 1449 1828 1499 Dl 1865 1422 1848 1447 Dl 1840 1437 1866 1422 Dl 1461 1660 1493 1615 Dl 1495 1687 1460 1660 Dl 1526 1668 1496 1688 Dl 1453 1751 1450 1751 Dl 1450 1751 1496 1688 Dl 1511 1710 1453 1752 Dl 1484 1774 1510 1720 Dl 1513 1747 1484 1775 Dl 1543 1746 1482 1776 Dl 1483 1776 1484 1775 Dl 1614 1725 1512 1808 Dl 1512 1807 1524 1792 Dl 1766 1661 1735 1697 Dl 1774 1594 1766 1660 Dl 1734 1696 1719 1645 Dl 1838 1533 1828 1550 Dl 1827 1552 1779 1586 Dl 1890 1438 1882 1459 Dl 1870 1449 1891 1437 Dl 1882 1458 1831 1499 Dl 1850 1414 1865 1416 Dl 1865 1417 1867 1421 Dl 1839 1422 1849 1414 Dl 1867 1421 1866 1422 Dl 1429 1793 1453 1752 Dl 1472 1786 1429 1793 Dl 1483 1777 1473 1786 Dl 1469 1858 1426 1876 Dl 1427 1876 1473 1786 Dl 1511 1809 1470 1859 Dl 1477 1881 1470 1859 Dl 1615 1763 1478 1881 Dl 1635 1723 1614 1762 Dl 1734 1697 1693 1754 Dl 1692 1755 1614 1762 Dl 1780 1645 1766 1660 Dl 1828 1551 1780 1645 Dl 1882 1460 1871 1504 Dl 1869 1504 1843 1527 Dl 1867 1419 1908 1412 Dl 1907 1413 1891 1437 Dl 1403 1726 1460 1660 Dl 1392 1772 1403 1726 Dl 1449 1752 1391 1772 Dl 1425 1877 1416 1883 Dl 1416 1883 1339 1878 Dl 1340 1877 1429 1793 Dl 1693 1755 1656 1823 Dl 1655 1823 1429 1960 Dl 1430 1960 1478 1881 Dl 1936 1519 1944 1531 Dl 1871 1503 1935 1518 Dl 1943 1532 1780 1645 Dl 1849 1389 1849 1414 Dl 1836 1406 1848 1388 Dl 1289 1913 1303 1857 Dl 1304 1857 1391 1772 Dl 1340 1877 1289 1913 Dl 1223 2053 1193 2010 Dl 1194 2009 1289 1913 Dl 1416 1884 1224 2054 Dl 1170 2262 1005 2381 Dl 1006 2380 1224 2054 Dl 1428 1961 1171 2261 Dl 5 R f (69)1232 2108 w 10 R f 0.1 setlinewidth 1427 2420 1171 2261 Dl 1655 1823 1427 2421 Dl (70)1368 2166 w 1944 1532 2023 1550 Dl 1419 2469 1427 2421 Dl 2023 1550 1419 2470 Dl (71)1672 1914 w 1920 1400 1935 1518 Dl 1909 1411 1920 1399 Dl 1925 1387 1920 1399 Dl 1866 1416 1926 1387 Dl 1835 1407 1851 1374 Dl 1849 1388 1851 1374 Dl 1174 1920 1260 1830 Dl 1261 1830 1403 1726 Dl 1174 1920 1303 1857 Dl 720 2488 720 2327 Dl 720 2327 898 2162 Dl 720 2488 1036 2100 Dl 1036 2101 898 2162 Dl 5 R f (76)811 2295 w 10 R f 0.1 setlinewidth 2157 2502 1404 2502 Dl 2025 1550 2157 2502 Dl 1419 2471 1404 2502 Dl (77)1810 2204 w 1852 1373 1858 1348 Dl 1859 1349 1931 1378 Dl 1926 1387 1931 1378 Dl 898 2162 936 2111 Dl 938 2110 1174 1920 Dl 1192 2011 1036 2100 Dl 5 R f (79)1098 2015 w 10 R f 0.1 setlinewidth 874 2502 720 2502 Dl 720 2501 720 2489 Dl 1005 2382 874 2502 Dl (80)929 2300 w 1403 2502 874 2502 Dl (81)1125 2436 w 1955 1346 1992 1316 Dl 1932 1377 1954 1347 Dl 1992 1316 2024 1549 Dl 1254 1782 1491 1608 Dl 1260 1830 1253 1783 Dl 920 2001 1112 1852 Dl 1112 1852 1253 1783 Dl 936 2110 919 2001 Dl 5 R f (84)1052 1951 w 10 R f 0.1 setlinewidth 720 2327 720 2094 Dl 720 2093 919 2001 Dl 5 R f (85)790 2155 w 10 R f 0.1 setlinewidth 2058 1048 720 1245 Dl 2257 2501 2058 1049 Dl 2157 2502 2258 2502 Dl 1992 1316 1977 1206 Dl 1976 1206 2058 1049 Dl (87)2063 1831 w 1858 1347 1 1 De 1859 1347 1954 1347 Dl 1113 1851 1640 1301 Dl 5 R f (89)1381 1609 w 10 R f 0.1 setlinewidth 720 1956 720 2094 Dl 720 1956 1658 1272 Dl (90)1038 1784 w 720 1387 720 1955 Dl 720 1386 1684 1248 Dl (91)994 1550 w 720 1247 720 1388 Dl 1975 1207 1705 1245 Dl (92)1322 1241 w 1857 1347 1723 1266 Dl 5 R f (93)1852 1288 w (94)1751 1379 w 20 R f 16 setlinewidth 2736 2502 720 2502 Dl 2736 486 2736 2502 Dl 720 486 2736 486 Dl 720 2502 720 486 Dl 2092 1643 1728 1494 Dl 2091 1642 2018 1632 Dl 2091 1642 2032 1599 Dl 10 R f 0.1 setlinewidth 4003 1465 3997 1466 Dl 3997 1467 3985 1469 Dl 3984 1470 3971 1472 Dl 3971 1471 3930 1478 Dl 4003 1465 3963 1469 Dl 3963 1468 3930 1478 Dl 3592 1335 3048 1620 Dl 3049 1621 3054 1628 Dl 3054 1628 3305 1606 Dl 3929 1480 3305 1606 Dl 3962 1467 3592 1334 Dl (4)3495 1508 w 4073 1208 4037 1454 Dl 4074 1206 4001 1183 Dl 4001 1184 3907 1190 Dl 3906 1190 3791 1221 Dl 3791 1222 3705 1260 Dl 3704 1260 3592 1334 Dl 4037 1455 4029 1458 Dl 4029 1459 4019 1461 Dl 4018 1462 4007 1464 Dl 4007 1465 4003 1465 Dl (5)3859 1339 w 3316 1614 3305 1606 Dl 3523 1609 3317 1614 Dl 3524 1609 3971 1472 Dl 5 R f (7)3579 1574 w 10 R f 0.1 setlinewidth 3590 1606 3524 1614 Dl 3523 1614 3523 1609 Dl 3591 1605 3985 1469 Dl 3673 1600 3612 1607 Dl 3612 1606 3590 1606 Dl 3674 1599 3997 1466 Dl 3789 1583 3709 1601 Dl 3709 1600 3674 1599 Dl 3790 1582 4007 1464 Dl 3983 1546 3898 1568 Dl 3898 1568 3790 1583 Dl 3984 1545 4019 1461 Dl 4222 1492 4065 1535 Dl 4064 1536 3983 1546 Dl 4223 1491 4029 1458 Dl 4371 1408 4037 1454 Dl 4518 1404 4318 1478 Dl 4318 1478 4285 1484 Dl 4372 1407 4526 1398 Dl 4525 1399 4518 1404 Dl 4284 1484 4223 1491 Dl 5 R f (13)4252 1456 w 10 R f 0.1 setlinewidth 3298 1639 3317 1614 Dl 3385 1651 3296 1640 Dl 3386 1650 3524 1614 Dl 3432 1657 3368 1659 Dl 3369 1659 3386 1651 Dl 3460 1651 3434 1656 Dl 3461 1652 3612 1607 Dl 3633 1629 3461 1651 Dl 3633 1629 3709 1601 Dl 3652 1640 3614 1642 Dl 3879 1581 3653 1639 Dl 3615 1641 3633 1629 Dl 3879 1580 3898 1568 Dl 4074 1548 3998 1570 Dl 3997 1571 3879 1581 Dl 4073 1547 4065 1535 Dl 4163 1536 4074 1548 Dl 4283 1485 4163 1536 Dl 4535 1397 4536 1398 Dl 4535 1399 4518 1404 Dl 4534 1397 4526 1398 Dl 4478 1384 4372 1407 Dl 4556 1379 4571 1381 Dl 4571 1381 4535 1396 Dl 4480 1384 4556 1378 Dl 3573 1654 3564 1656 Dl 3564 1656 3430 1666 Dl 3430 1666 3434 1656 Dl 3614 1642 3574 1654 Dl 3960 1598 3720 1653 Dl 3720 1652 3643 1643 Dl 3997 1570 3961 1597 Dl 3643 1643 3653 1639 Dl 4431 1475 4425 1481 Dl 4425 1481 4379 1496 Dl 4379 1496 4180 1537 Dl 4320 1477 4433 1474 Dl 4179 1538 4163 1536 Dl 3643 1643 3574 1654 Dl 4179 1538 4049 1591 Dl 4049 1591 3961 1597 Dl 4601 1414 4599 1419 Dl 4536 1398 4564 1398 Dl 4565 1398 4599 1406 Dl 4599 1418 4433 1474 Dl 4599 1407 4601 1413 Dl 3211 1693 3165 1684 Dl 3165 1684 3296 1640 Dl 3369 1660 3211 1694 Dl 3121 1721 3211 1694 Dl 3258 1709 3120 1721 Dl 3429 1667 3258 1710 Dl 3409 1704 3263 1720 Dl 3263 1720 3258 1710 Dl 3564 1657 3410 1703 Dl 3671 1674 3489 1707 Dl 3489 1706 3407 1704 Dl 3408 1704 3410 1703 Dl 3719 1654 3672 1674 Dl 4050 1595 3983 1619 Dl 3982 1619 3695 1675 Dl 3694 1676 3672 1674 Dl 4050 1590 4050 1594 Dl 4306 1537 4265 1549 Dl 4379 1497 4306 1537 Dl 4264 1548 4050 1594 Dl 4604 1408 4601 1413 Dl 4600 1406 4605 1406 Dl 4480 1384 4554 1362 Dl 4554 1361 4558 1361 Dl 4558 1362 4556 1378 Dl 3091 1737 3096 1727 Dl 3130 1751 3090 1737 Dl 3095 1726 3120 1721 Dl 3263 1720 3130 1751 Dl 3251 1747 3095 1761 Dl 3095 1761 3130 1751 Dl 3406 1705 3250 1746 Dl 3118 1802 3209 1761 Dl 3395 1736 3117 1802 Dl 3209 1759 3250 1746 Dl 3489 1707 3396 1735 Dl 3576 1723 3481 1735 Dl 3480 1735 3396 1735 Dl 3694 1675 3576 1722 Dl 3943 1646 3571 1730 Dl 3571 1729 3576 1722 Dl 3973 1630 3942 1645 Dl 3982 1620 3975 1630 Dl 4230 1573 4207 1582 Dl 4264 1549 4231 1573 Dl 4208 1583 3975 1630 Dl 4551 1494 4526 1501 Dl 4505 1471 4553 1494 Dl 4492 1470 4504 1470 Dl 4527 1502 4306 1537 Dl 4426 1481 4491 1472 Dl 4599 1418 4707 1401 Dl 4707 1402 4491 1472 Dl 4699 1370 4605 1406 Dl 4565 1397 4699 1370 Dl 3024 1698 3024 1639 Dl 3024 1638 3054 1628 Dl 3044 1703 3024 1698 Dl 3164 1685 3044 1704 Dl 5 R f (45)3124 1660 w 10 R f 0.1 setlinewidth 3024 1738 3024 1710 Dl 3024 1711 3044 1704 Dl 3096 1727 3024 1739 Dl 3024 1777 3024 1767 Dl 3024 1767 3090 1737 Dl 3095 1762 3024 1777 Dl 3024 1782 3024 1777 Dl 3209 1761 3024 1783 Dl 3480 1736 3069 1817 Dl 3069 1816 3117 1802 Dl 4141 1645 3989 1686 Dl 4207 1582 4142 1643 Dl 3988 1685 3942 1645 Dl 4526 1502 4470 1522 Dl 4470 1522 4231 1573 Dl 4821 1379 4769 1406 Dl 4708 1401 4821 1378 Dl 4768 1405 4504 1470 Dl 4622 1366 4698 1364 Dl 4698 1365 4706 1369 Dl 4571 1381 4621 1368 Dl 4706 1368 4699 1370 Dl 3024 1767 3024 1739 Dl 3024 1829 3024 1783 Dl 3069 1817 3024 1829 Dl 3024 1858 3024 1829 Dl 3472 1768 3024 1859 Dl 3569 1731 3472 1767 Dl 3990 1685 3792 1744 Dl 3790 1744 3472 1767 Dl 5 R f (58)3743 1722 w 10 R f 0.1 setlinewidth 4211 1625 4142 1643 Dl 4470 1523 4211 1625 Dl 4768 1407 4692 1458 Dl 4692 1458 4553 1494 Dl 4707 1368 4916 1342 Dl 4915 1342 4821 1378 Dl 3024 1710 3024 1698 Dl 3024 1896 3024 1859 Dl 3791 1745 3611 1805 Dl 3611 1805 3024 1896 Dl 5 R f (64)3353 1826 w 10 R f 0.1 setlinewidth 5040 1435 5040 1437 Dl 5010 1430 5040 1434 Dl 4693 1456 5009 1429 Dl 5039 1437 4211 1625 Dl 5 R f (65)4616 1516 w 10 R f 0.1 setlinewidth 4624 1335 4621 1368 Dl 4559 1362 4625 1334 Dl 3024 2042 3024 1896 Dl 3611 1805 3024 2042 Dl 5 R f (70)3194 1925 w 10 R f 0.1 setlinewidth 5040 1437 5040 1508 Dl 3024 2104 3024 2042 Dl 5040 1508 3024 2105 Dl (71)3974 1773 w 4981 1321 5009 1429 Dl 4916 1342 4980 1321 Dl 5 R f (72)4859 1410 w 10 R f 0.1 setlinewidth 5016 1303 4980 1321 Dl 4698 1363 5016 1302 Dl 4554 1362 4644 1314 Dl 4625 1333 4644 1314 Dl 5040 1509 5040 1545 Dl 3024 2185 3024 2105 Dl 5039 1545 4388 1794 Dl 4388 1794 3024 2185 Dl (77)3921 1886 w 5040 1287 5040 1291 Dl 4644 1314 4685 1278 Dl 4686 1278 5040 1287 Dl 5017 1301 5040 1291 Dl 5 R f (78)4763 1325 w 10 R f 0.1 setlinewidth 5040 1292 5040 1434 Dl 3024 1639 3024 1625 Dl 3024 1624 3048 1620 Dl 5040 1286 5040 1245 Dl 4685 1277 4685 1276 Dl 4686 1275 5040 1245 Dl 3024 1457 3024 1625 Dl 3024 1455 3705 1260 Dl 5 R f (89)3238 1457 w 10 R f 0.1 setlinewidth 3024 1372 3024 1456 Dl 3024 1370 3791 1221 Dl 5 R f (90)3283 1355 w 10 R f 0.1 setlinewidth 3024 1136 3024 1372 Dl 3024 1135 3907 1190 Dl (91)3276 1253 w 5040 486 3024 486 Dl 5040 1026 5040 486 Dl 3024 486 3024 1135 Dl 5039 1027 4001 1183 Dl (92)3951 831 w 5040 1244 5040 1026 Dl 4684 1276 4074 1207 Dl (93)4607 1190 w (94)4247 1344 w 20 R f 16 setlinewidth 5040 2502 3024 2502 Dl 5040 486 5040 2502 Dl 3024 486 5040 486 Dl 3024 2502 3024 486 Dl 4182 1804 4032 1494 Dl 4181 1803 4134 1747 Dl 4182 1803 4167 1731 Dl 10 B f (Fig. 26:)1 322 1 1008 2700 t 10 R f (dual affine iter 10, cutaway)4 1094 1 1355 2700 t 10 B f (Fig. 27:)1 322 1 3312 2700 t 10 R f (dual affine iter 18, cutaway)4 1094 1 3659 2700 t ( in iteration 1; visi-)4 775(Figures 28 and 29 show two outside views of the polytope as affinely transformed)13 3295 2 970 2856 t ( the transformed polytope gets so long and thin that)9 2093( subsequent iterations,)2 901( In)1 138(ble inside it is the step taken.)6 1188 4 720 2976 t (there would be little point in showing outside views of it.)10 2286 1 720 3096 t 0.1 setlinewidth 1995 4951 1983 4945 Dl 1982 4944 1962 4942 Dl 1962 4942 1943 4949 Dl 1942 4949 1892 5015 Dl 1995 4952 1981 5122 Dl 1893 5015 1981 5122 Dl 1459 3851 1514 3737 Dl 1459 3852 1892 5015 Dl 2005 3773 2005 4616 Dl 2005 3772 2003 3767 Dl 2005 4617 2003 4717 Dl 2002 4717 2000 4813 Dl 1999 4814 1996 4916 Dl 1996 4918 1995 4952 Dl 1553 3683 1458 3851 Dl 1674 3527 1554 3682 Dl 1676 3528 1943 4949 Dl (7)1679 4214 w 1696 3506 1681 3513 Dl 1680 3514 1675 3528 Dl 1695 3505 1962 4942 Dl 5 R f (8)1803 4219 w 10 R f 0.1 setlinewidth 1715 3486 1703 3495 Dl 1702 3495 1695 3505 Dl 1716 3487 1983 4945 Dl 5 R f (9)1823 4208 w 10 R f 0.1 setlinewidth 1735 3474 1725 3473 Dl 1724 3473 1715 3486 Dl 1736 3474 1996 4916 Dl 5 R f (10)1829 4198 w 10 R f 0.1 setlinewidth 1752 3464 1761 3467 Dl 1750 3464 1735 3474 Dl 1761 3467 2000 4813 Dl 5 R f (11)1844 4157 w 10 R f 0.1 setlinewidth 1768 3459 1782 3461 Dl 1768 3458 1761 3467 Dl 1783 3461 2003 4717 Dl 5 R f (12)1858 4106 w 10 R f 0.1 setlinewidth 1810 3483 2005 4616 Dl 1785 3451 1800 3456 Dl 1785 3454 1786 3452 Dl 1802 3458 1809 3483 Dl 1801 3457 1802 3458 Dl 1783 3455 1782 3461 Dl 5 R f (13)1871 4057 w 10 R f 0.1 setlinewidth 1635 3537 1554 3682 Dl 1678 3481 1635 3537 Dl 1679 3482 1681 3513 Dl 1698 3461 1683 3471 Dl 1684 3472 1679 3481 Dl 1701 3461 1699 3461 Dl 1701 3462 1703 3495 Dl 1724 3455 1701 3462 Dl 1724 3455 1725 3473 Dl 1732 3442 1727 3445 Dl 1750 3453 1733 3442 Dl 1726 3446 1724 3454 Dl 1751 3454 1751 3463 Dl 1762 3443 1767 3446 Dl 1762 3443 1751 3454 Dl 1768 3447 1768 3458 Dl 1768 3446 1773 3441 Dl 1773 3441 1784 3453 Dl 1802 3457 1 1 De 1809 3470 1809 3483 Dl 1804 3458 1805 3460 Dl 1802 3457 1804 3457 Dl 1806 3460 1808 3469 Dl 1725 3441 1707 3450 Dl 1707 3451 1699 3461 Dl 1726 3445 1726 3441 Dl 1760 3431 1748 3427 Dl 1747 3428 1733 3440 Dl 1762 3442 1761 3432 Dl 1733 3442 1733 3440 Dl 1784 3438 1785 3439 Dl 1782 3436 1784 3437 Dl 1774 3437 1782 3435 Dl 1786 3440 1786 3452 Dl 1773 3440 1773 3438 Dl 1733 3441 1726 3441 Dl 1766 3428 1773 3438 Dl 1761 3431 1766 3428 Dl 1793 3442 1794 3443 Dl 1800 3452 1801 3456 Dl 1797 3445 1800 3452 Dl 1786 3439 1793 3441 Dl 1795 3443 1796 3445 Dl 1685 3455 1671 3471 Dl 1671 3472 1635 3537 Dl 1684 3471 1686 3455 Dl 1695 3442 1686 3455 Dl 1708 3436 1694 3441 Dl 1707 3449 1709 3436 Dl 1727 3428 1717 3430 Dl 1716 3431 1709 3436 Dl 1727 3440 1728 3428 Dl 1747 3423 1740 3422 Dl 1740 3422 1728 3427 Dl 1728 3428 1 1 De 1748 3428 1748 3424 Dl 1766 3426 1764 3424 Dl 1763 3423 1751 3422 Dl 1749 3423 1751 3422 Dl 1766 3428 1766 3427 Dl 1775 3428 1776 3428 Dl 1777 3428 1782 3435 Dl 1766 3427 1774 3427 Dl 1794 3443 1795 3444 Dl 1796 3445 1 1 De 1809 3469 1809 3464 Dl 1806 3460 1809 3463 Dl 1704 3434 1695 3440 Dl 1718 3425 1704 3433 Dl 1695 3441 1695 3440 Dl 1718 3430 1719 3425 Dl 1730 3421 1720 3423 Dl 1719 3424 1720 3423 Dl 1728 3427 1730 3421 Dl 1733 3419 1739 3414 Dl 1741 3418 1739 3414 Dl 1731 3421 1733 3419 Dl 1740 3422 1741 3419 Dl 1752 3417 1749 3417 Dl 1748 3417 1741 3419 Dl 1752 3422 1753 3417 Dl 1764 3420 1754 3416 Dl 1753 3416 1754 3416 Dl 1764 3422 1764 3420 Dl 1764 3424 1764 3422 Dl 1773 3422 1 1 De 1775 3427 1774 3423 Dl 1766 3422 1773 3422 Dl 1782 3425 1 1 De 1784 3432 1782 3425 Dl 1785 3433 1 1 De 1777 3427 1782 3425 Dl 1785 3436 1785 3434 Dl 1793 3441 1793 3437 Dl 1786 3435 1793 3437 Dl 1796 3445 1799 3445 Dl 1799 3452 1799 3445 Dl 1636 3527 1514 3737 Dl 1673 3463 1635 3526 Dl 1672 3470 1675 3463 Dl 1697 3434 1 1 De 1697 3435 1675 3463 Dl 1696 3439 1698 3433 Dl 1721 3421 1704 3433 Dl 1721 3422 1722 3420 Dl 1732 3420 1722 3420 Dl 1749 3417 1740 3414 Dl 1740 3414 1 1 De 1769 3416 1771 3417 Dl 1771 3422 1771 3417 Dl 1765 3419 1769 3415 Dl 1781 3424 1782 3425 Dl 1773 3424 1779 3424 Dl 1791 3432 1793 3434 Dl 1793 3436 1793 3434 Dl 1785 3434 1790 3432 Dl 1801 3447 1804 3454 Dl 1799 3445 1800 3447 Dl 1804 3456 1804 3454 Dl 1712 3423 1698 3433 Dl 1722 3420 1712 3423 Dl 1722 3420 1 1 De 1741 3412 1736 3412 Dl 1736 3413 1722 3420 Dl 1740 3414 1740 3412 Dl 1745 3412 1740 3412 Dl 1755 3413 1747 3411 Dl 1755 3416 1756 3414 Dl 1768 3416 1766 3414 Dl 1756 3414 1766 3414 Dl 1772 3417 1773 3417 Dl 1779 3423 1773 3417 Dl 1785 3427 1790 3432 Dl 1783 3426 1785 3426 Dl 1798 3436 1800 3445 Dl 1794 3434 1796 3435 Dl 1734 3412 1722 3417 Dl 1712 3423 1722 3417 Dl 1766 3413 1766 3412 Dl 1766 3411 1751 3409 Dl 1746 3409 1751 3409 Dl 1784 3420 1 1 De 1784 3426 1784 3421 Dl 1774 3418 1784 3420 Dl 1804 3454 1810 3461 Dl 1809 3463 1810 3461 Dl 1735 3411 1740 3410 Dl 1755 3409 1753 3409 Dl 1752 3409 1740 3410 Dl 1752 3409 1755 3409 Dl 1770 3411 1755 3409 Dl 1767 3412 1771 3411 Dl 1784 3419 1784 3418 Dl 1772 3411 1784 3418 Dl 1785 3421 1797 3435 Dl 1797 3435 1 1 De 1797 3436 1798 3436 Dl 1800 3446 1798 3436 Dl 1809 3464 1812 3463 Dl 1810 3462 1812 3463 Dl 1784 3419 1782 3417 Dl 1774 3413 1782 3417 Dl 1772 3412 1774 3412 Dl 1813 3463 1816 3464 Dl 1798 3436 1816 3464 Dl 1799 3435 1797 3432 Dl 1800 3435 1 1 De 1784 3420 1797 3432 Dl 1798 3433 1800 3435 Dl 1800 3435 1817 3464 Dl 1800 3434 2003 3767 Dl 1817 3465 2005 3773 Dl (94)1887 3964 w 20 R f 16 setlinewidth 2736 5274 720 5274 Dl 2736 3258 2736 5274 Dl 720 3258 2736 3258 Dl 720 5274 720 3258 Dl 1786 3475 1727 3576 Dl 1786 3475 1766 3546 Dl 1786 3475 1735 3528 Dl 10 R f 0.1 setlinewidth 3793 4900 3793 4896 Dl 3792 4895 3782 4897 Dl 3782 4897 3761 4911 Dl 3760 4911 3643 5011 Dl 3793 4900 3579 5122 Dl 3643 5012 3579 5122 Dl 3909 3605 3579 3833 Dl 3930 3602 3910 3605 Dl 3973 3724 3930 3600 Dl 3973 3725 3643 5011 Dl 3579 5122 3579 3833 Dl (4)3698 4229 w 3865 4750 3814 4861 Dl 3814 4862 3794 4900 Dl 4199 3593 3974 3725 Dl 4403 3501 4199 3592 Dl 4403 3501 3761 4911 Dl (7)3972 4162 w 4426 3488 4415 3490 Dl 4414 3490 4404 3500 Dl 4424 3488 3782 4897 Dl 5 R f (8)4086 4199 w 10 R f 0.1 setlinewidth 4440 3479 4433 3482 Dl 4433 3482 4426 3488 Dl 4441 3480 3793 4896 Dl 4448 3473 4448 3469 Dl 4447 3470 4440 3478 Dl 4448 3474 3814 4861 Dl 4451 3468 4449 3472 Dl 4450 3468 4448 3474 Dl 4448 3472 3865 4749 Dl 4350 3491 4199 3592 Dl 4418 3461 4350 3491 Dl 4419 3461 4415 3490 Dl 4436 3451 4424 3454 Dl 4424 3455 4419 3461 Dl 4437 3451 4436 3450 Dl 4437 3452 4433 3482 Dl 4450 3452 4438 3452 Dl 4450 3453 4448 3469 Dl 4452 3444 4452 3445 Dl 4453 3458 4453 3444 Dl 4451 3446 4450 3453 Dl 4452 3459 4451 3467 Dl 4450 3441 4440 3443 Dl 4440 3443 4436 3450 Dl 4451 3445 4451 3441 Dl 4453 3436 4453 3443 Dl 4453 3444 4453 3443 Dl 4452 3442 4451 3441 Dl 4417 3438 4394 3445 Dl 4393 3445 4350 3491 Dl 4424 3453 4419 3438 Dl 4422 3429 4419 3438 Dl 4435 3429 4422 3428 Dl 4440 3443 4436 3430 Dl 4447 3429 4440 3427 Dl 4439 3428 4436 3430 Dl 4450 3440 4447 3429 Dl 4450 3430 4448 3427 Dl 4448 3427 4447 3428 Dl 4452 3433 4451 3430 Dl 4427 3425 4422 3427 Dl 4436 3422 4427 3424 Dl 4422 3428 4422 3427 Dl 4439 3426 4436 3421 Dl 4442 3422 4435 3420 Dl 4435 3421 4435 3420 Dl 4448 3428 4443 3422 Dl 4440 3419 4440 3417 Dl 4445 3422 4440 3417 Dl 4442 3421 4442 3420 Dl 4448 3426 4446 3423 Dl 4264 3463 3930 3600 Dl 4386 3437 4264 3463 Dl 4393 3444 4386 3436 Dl 5 R f (45)4105 3584 w 10 R f 0.1 setlinewidth 4412 3419 4410 3419 Dl 4408 3419 4386 3436 Dl 4422 3426 4412 3419 Dl 4432 3417 4427 3424 Dl 4435 3419 4433 3417 Dl 4442 3420 4433 3417 Dl 4440 3417 1 1 De 4419 3415 4412 3419 Dl 4432 3415 4420 3414 Dl 4432 3416 1 1 De 4436 3414 4433 3413 Dl 4433 3414 4432 3416 Dl 4440 3416 4438 3414 Dl 4350 3427 4264 3463 Dl 4388 3417 4350 3426 Dl 4409 3419 4389 3417 Dl 4433 3412 1 1 De 4432 3412 4416 3410 Dl 4418 3414 4416 3410 Dl 4412 3410 4398 3411 Dl 4397 3412 4389 3417 Dl 4416 3409 4412 3409 Dl 4422 3410 4412 3409 Dl 4412 3409 1 1 De 4432 3412 4422 3410 Dl 4384 3412 4371 3415 Dl 4370 3415 4350 3426 Dl 4397 3411 4385 3411 Dl 4401 3409 4394 3409 Dl 4394 3409 4391 3409 Dl 4390 3410 4385 3411 Dl 4412 3409 4403 3409 Dl 4350 3423 3910 3605 Dl 4370 3416 4350 3422 Dl 20 R f 16 setlinewidth 5040 5274 3024 5274 Dl 5040 3258 5040 5274 Dl 3024 3258 5040 3258 Dl 3024 5274 3024 3258 Dl 4309 3456 4302 3538 Dl 4308 3455 4320 3528 Dl 4307 3455 4284 3525 Dl 10 B f (Fig. 28:)1 322 1 1020 5472 t 10 R f (iter 1, outside,)2 572 1 1367 5472 t 10 I f (d)1964 5472 w 10 R f (= \(0,\2611,0\))1 397 1 2039 5472 t 10 B f (Fig. 29:)1 322 1 3349 5472 t 10 R f (iter 1, outside,)2 572 1 3696 5472 t 10 I f (d)4293 5472 w 10 R f (= \(0,0,1\))1 347 1 4368 5472 t 10 B f (Pictures of the Dual Projective Algorithm)5 1771 1 720 5712 t 10 R f ( ver-)1 192( This)1 235( illustrate a dual projective version of Karmarkar's LP algorithm.)9 2664(The next several figures)3 979 4 970 5868 t ( the potential function \(6\) \(using quadratic interpola-)7 2126(sion chooses its step lengths by doing a line search on)10 2194 2 720 5988 t ( uses)1 198( It)1 112( value\).)1 300(tion until it reduces the directional derivative's absolute value to at most 0.01 times its initial)15 3710 4 720 6108 t ( fact, it starts out running the dual)7 1363( In)1 135( above.)1 290(the same stopping tests as the dual affine algorithm considered)9 2532 4 720 6228 t ( to the dual projective algorithm only after it has computed a primal feasible)13 3121(affine algorithm and switches)3 1199 2 720 6348 t (iterate)720 6468 w 10 I f (x)997 6468 w 10 R f ( the problem)2 509( For)1 191(\(and therewith a valid upper bound on the optimal dual objective function value\).)12 3272 3 1068 6468 t ( it computes a primal feasible)5 1199(at hand,)1 319 2 720 6588 t 10 I f (x)2267 6588 w 10 R f (on the first iteration and runs a total of 14 iterations before finding)12 2700 1 2340 6588 t ( objective)1 392( linear)1 254( The)1 207(an optimal solution.)2 802 4 720 6708 t 10 I f (b)2401 6708 w 7 R f (T)2462 6668 w 10 I f (y)2521 6708 w 10 R f ( is easy)2 296( \(It)1 145(increases in all but the second and third iterations.)8 2008 3 2591 6708 t (to make)1 321 1 720 6828 t 10 I f (b)1068 6828 w 7 R f (T)1129 6788 w 10 I f (y)1188 6828 w 10 R f ( the constraint that it remain constant on iterations where it would other-)12 2927(monotonic by adding)2 854 2 1259 6828 t ( for the problem at hand this does not change the number of iterations, but does require com-)17 3739(wise decrease;)1 581 2 720 6948 t (puting two extra projections.\))3 1182 1 720 7068 t ( followed by the dual projective)5 1338(In analogy with figure 11, figure 30 shows figure 6 with the path)12 2732 2 970 7224 t (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 15 16 %%Page: 16 17 /saveobj save def mark 17 pagesetup 10 R f (- 16 -)2 216 1 2772 480 t ( figures 12 and)3 605( 31 and 32 show the same outside views as)9 1748( Figures)1 354(algorithm showing through from inside.)4 1613 4 720 840 t ( 33 is similar to figure 14, but is drawn)9 1654( Figure)1 322( with the dual projective path visible from inside.)8 2056(13, but)1 288 4 720 960 t (from a bit further back and with a wider view angle to bring the whole path into view.)17 3433 1 720 1080 t 0.1 setlinewidth 2470 1677 2465 1716 Dl 2464 1717 2445 1790 Dl 1195 1869 1542 2909 Dl 1542 2910 1575 2980 Dl 1575 2981 1771 3134 Dl 1175 1467 1152 1522 Dl 1151 1522 1145 1583 Dl 1146 1583 1149 1662 Dl 1150 1663 1160 1733 Dl 1161 1733 1194 1869 Dl 2371 1467 2438 1517 Dl 2439 1517 2467 1580 Dl 2467 1580 2473 1652 Dl 2473 1652 2471 1676 Dl 1828 3108 1771 3134 Dl 2105 2885 1829 3107 Dl 2172 2760 2121 2863 Dl 2121 2864 2106 2884 Dl 2173 2759 2445 1790 Dl 2218 2570 2187 2698 Dl 2186 2699 2172 2759 Dl 2219 2569 2465 1716 Dl 2235 2312 2221 2462 Dl 2221 2463 2219 2571 Dl 2237 2312 2473 1652 Dl 5 R f (10)2294 2164 w 10 R f 0.1 setlinewidth 2193 1916 2203 2072 Dl 2204 2073 2237 2312 Dl 2192 1914 2467 1580 Dl (11)2260 1946 w 2044 1549 2126 1779 Dl 2128 1779 2192 1915 Dl 2045 1548 2438 1517 Dl (12)2194 1683 w 1834 1316 2370 1466 Dl 1972 1493 1823 1341 Dl 1974 1494 1997 1514 Dl 1815 1331 1833 1316 Dl 1823 1342 1815 1332 Dl 1997 1514 2044 1548 Dl 5 R f (13)2078 1462 w 10 R f 0.1 setlinewidth 1895 3019 1829 3107 Dl 2032 2890 1895 3018 Dl 2033 2890 2121 2863 Dl 2064 2750 2026 2863 Dl 2026 2863 2032 2890 Dl 2078 2729 2064 2749 Dl 2079 2728 2187 2698 Dl 5 R f (15)2078 2803 w 10 R f 0.1 setlinewidth 2150 2478 2078 2728 Dl 2151 2477 2221 2462 Dl 5 R f (16)2136 2609 w 10 R f 0.1 setlinewidth 2104 2350 2116 2435 Dl 2160 2078 2104 2350 Dl 2117 2435 2151 2478 Dl 2162 2077 2203 2072 Dl 5 R f (17)2150 2306 w 10 R f 0.1 setlinewidth 2072 1783 2072 1879 Dl 2072 1879 2161 2077 Dl 2072 1782 2126 1779 Dl 5 R f (18)2114 1930 w 10 R f 0.1 setlinewidth 2011 1694 2072 1782 Dl 1998 1514 2010 1694 Dl 5 R f (19)2026 1674 w 10 R f 0.1 setlinewidth 1814 1335 1812 1331 Dl 1823 1341 1814 1336 Dl 1813 1332 1815 1332 Dl 1775 1314 1833 1316 Dl 1779 1323 1770 1319 Dl 1811 1331 1779 1324 Dl 1770 1320 1775 1314 Dl 2087 2443 2082 2448 Dl 2082 2448 2047 2667 Dl 2047 2668 2064 2749 Dl 2117 2435 2088 2442 Dl 2005 1903 1997 2119 Dl 1997 2119 2092 2343 Dl 2071 1879 2005 1903 Dl 2092 2345 2104 2350 Dl 5 R f (23)2048 2102 w 10 R f 0.1 setlinewidth 1892 1504 1890 1522 Dl 1891 1522 1901 1559 Dl 1901 1560 1988 1688 Dl 1972 1494 1892 1504 Dl 1989 1689 2010 1694 Dl 2092 2344 2088 2442 Dl 1988 1688 1954 1819 Dl 1954 1819 2005 1903 Dl 5 R f (26)1991 1813 w 10 R f 0.1 setlinewidth 1812 1420 1808 1408 Dl 1807 1354 1814 1336 Dl 1805 1391 1806 1353 Dl 1892 1503 1812 1420 Dl 1808 1408 1805 1393 Dl 1923 2830 1863 2891 Dl 1863 2891 1895 3018 Dl 2025 2863 1923 2831 Dl 5 R f (28)1913 2919 w 10 R f 0.1 setlinewidth 1885 2760 1923 2831 Dl 1943 2640 1884 2759 Dl 2047 2667 1944 2639 Dl 5 R f (29)1955 2760 w 10 R f 0.1 setlinewidth 1974 2425 1934 2553 Dl 1935 2553 1944 2639 Dl 2082 2447 1974 2424 Dl 5 R f (30)1982 2554 w 10 R f 0.1 setlinewidth 1957 2114 1937 2245 Dl 1937 2246 1970 2416 Dl 1970 2416 1974 2424 Dl 1996 2118 1958 2113 Dl 5 R f (31)1985 2308 w 10 R f 0.1 setlinewidth 1942 1819 1918 1861 Dl 1917 1861 1936 2071 Dl 1938 2071 1958 2113 Dl 1953 1818 1941 1818 Dl 5 R f (32)1938 1978 w 10 R f 0.1 setlinewidth 1874 1655 1878 1680 Dl 1900 1559 1874 1653 Dl 1878 1680 1941 1818 Dl 1808 1408 1803 1396 Dl 1804 1396 1805 1393 Dl 1775 1313 1732 1315 Dl 1731 1315 1732 1315 Dl 1770 1320 1731 1316 Dl 1867 2673 1872 2750 Dl 1873 2530 1866 2673 Dl 1884 2758 1872 2750 Dl 1934 2553 1875 2530 Dl 1891 2389 1861 2514 Dl 1862 2515 1875 2530 Dl 1970 2414 1892 2388 Dl 1827 2275 1872 2365 Dl 1890 2233 1826 2275 Dl 1872 2365 1892 2388 Dl 1937 2244 1891 2232 Dl 1862 2055 1864 2116 Dl 1865 2117 1891 2232 Dl 1936 2070 1862 2055 Dl 1863 1865 1848 2037 Dl 1848 2038 1862 2055 Dl 1887 1858 1864 1866 Dl 1917 1860 1887 1856 Dl 1840 1718 1836 1731 Dl 1879 1680 1841 1717 Dl 1836 1731 1887 1856 Dl 1786 1592 1789 1602 Dl 1838 1525 1785 1592 Dl 1846 1522 1838 1524 Dl 1873 1653 1789 1602 Dl 1890 1522 1847 1522 Dl 1811 1420 1770 1438 Dl 1847 1521 1770 1438 Dl 1803 1396 1752 1373 Dl 1806 1354 1752 1373 Dl 1619 2883 1575 2980 Dl 1794 2850 1620 2882 Dl 1862 2891 1794 2850 Dl 5 R f (45)1723 2989 w 10 R f 0.1 setlinewidth 1783 2713 1776 2718 Dl 1776 2719 1794 2850 Dl 1872 2750 1784 2713 Dl 1825 2499 1866 2673 Dl 1861 2513 1825 2498 Dl 1871 2365 1823 2496 Dl 1825 2497 1823 2496 Dl 1863 2117 1814 2266 Dl 1826 2273 1814 2266 Dl 1770 1771 1771 1816 Dl 1836 1732 1770 1771 Dl 1863 1865 1771 1816 Dl 1789 1603 1788 1633 Dl 1789 1633 1841 1717 Dl 1740 1443 1750 1481 Dl 1769 1438 1739 1443 Dl 1838 1524 1750 1481 Dl 1745 1363 1753 1330 Dl 1749 1372 1744 1363 Dl 1779 1324 1753 1330 Dl 1751 1373 1749 1373 Dl 1767 2591 1784 2713 Dl 1812 2492 1766 2591 Dl 1822 2496 1812 2491 Dl 5 R f (55)1793 2643 w 10 R f 0.1 setlinewidth 1783 2256 1765 2322 Dl 1764 2322 1812 2491 Dl 1813 2265 1783 2255 Dl 1766 2171 1783 2255 Dl 1810 2029 1766 2171 Dl 1846 2037 1810 2028 Dl 1771 1816 1756 1861 Dl 1756 1861 1810 2028 Dl 1765 1751 1770 1771 Dl 1788 1633 1765 1750 Dl 1750 1481 1754 1560 Dl 1784 1591 1754 1560 Dl 1749 1373 1710 1424 Dl 1738 1443 1710 1424 Dl 1631 2739 1620 2882 Dl 1684 2685 1631 2739 Dl 1775 2718 1684 2685 Dl 5 R f (62)1679 2799 w 10 R f 0.1 setlinewidth 1763 2322 1758 2324 Dl 1758 2324 1702 2478 Dl 1702 2479 1766 2591 Dl 1756 1862 1726 1877 Dl 1725 1877 1725 2112 Dl 1726 2112 1766 2171 Dl 5 R f (64)1734 2026 w 10 R f 0.1 setlinewidth 1674 1614 1668 1625 Dl 1753 1561 1674 1613 Dl 1765 1750 1668 1625 Dl 1752 1329 1684 1322 Dl 1730 1316 1684 1322 Dl 1673 2459 1648 2536 Dl 1648 2536 1684 2685 Dl 1702 2478 1674 2458 Dl 5 R f (67)1688 2609 w 10 R f 0.1 setlinewidth 1672 2276 1647 2373 Dl 1647 2373 1674 2458 Dl 1758 2323 1672 2275 Dl 1662 2085 1643 2121 Dl 1643 2122 1672 2275 Dl 1725 2112 1662 2085 Dl 5 R f (69)1688 2213 w 10 R f 0.1 setlinewidth 1639 1854 1662 2085 Dl 1726 1877 1639 1854 Dl 5 R f (70)1663 1986 w 10 R f 0.1 setlinewidth 1667 1625 1631 1648 Dl 1637 1853 1635 1849 Dl 1631 1649 1635 1849 Dl 5 R f (71)1669 1775 w 10 R f 0.1 setlinewidth 1691 1425 1674 1613 Dl 1710 1423 1692 1424 Dl 1691 1424 1677 1421 Dl 1743 1364 1677 1421 Dl 1732 1315 1651 1326 Dl 1684 1322 1651 1326 Dl 1576 2443 1570 2504 Dl 1570 2505 1631 2739 Dl 1647 2535 1576 2443 Dl 1554 2058 1550 2062 Dl 1551 2062 1562 2316 Dl 1593 2093 1555 2058 Dl 1593 2093 1596 2332 Dl 1596 2331 1562 2316 Dl 1631 1649 1565 1746 Dl 1565 1746 1591 1847 Dl 1634 1849 1591 1847 Dl 1651 1327 1601 1335 Dl 1665 1422 1601 1335 Dl 1677 1421 1666 1422 Dl 1561 2317 1555 2334 Dl 1555 2334 1576 2443 Dl 1647 2372 1596 2332 Dl 1642 2121 1593 2093 Dl 1591 1848 1555 2058 Dl 5 R f (81)1587 2000 w 10 R f 0.1 setlinewidth 1629 1444 1599 1494 Dl 1665 1424 1629 1445 Dl 1599 1494 1631 1648 Dl 1514 2428 1542 2909 Dl 1568 2504 1512 2428 Dl 5 R f (83)1544 2728 w 10 R f 0.1 setlinewidth 1496 2269 1488 2313 Dl 1488 2313 1512 2428 Dl 1555 2333 1497 2268 Dl 1498 2023 1475 2093 Dl 1475 2093 1497 2268 Dl 1550 2062 1498 2022 Dl 5 R f (85)1497 2180 w 10 R f 0.1 setlinewidth 1526 1734 1486 1807 Dl 1487 1807 1498 2022 Dl 1565 1745 1527 1733 Dl 5 R f (86)1511 1900 w 10 R f 0.1 setlinewidth 1598 1495 1525 1559 Dl 1526 1559 1527 1733 Dl 5 R f (87)1546 1635 w 10 R f 0.1 setlinewidth 1601 1336 1599 1336 Dl 1629 1444 1599 1336 Dl 1488 2313 1160 1733 Dl (89)1345 2339 w 1475 2092 1149 1662 Dl 5 R f (90)1328 2015 w 10 R f 0.1 setlinewidth 1486 1806 1145 1583 Dl (91)1303 1845 w 1525 1559 1152 1522 Dl 5 R f (92)1347 1645 w 10 R f 0.1 setlinewidth 1599 1336 1175 1466 Dl 5 R f (93)1402 1474 w 20 R f 16 setlinewidth 2736 3258 720 3258 Dl 2736 1242 2736 3258 Dl 720 1242 2736 1242 Dl 720 3258 720 1242 Dl 1382 2011 1728 2435 Dl 1381 2010 1440 2054 Dl 1382 2011 1413 2077 Dl 1302 1826 1381 2010 Dl 1302 1825 1347 1884 Dl 1302 1826 1314 1899 Dl 1263 1717 1301 1825 Dl 1409 1783 1263 1717 Dl 1480 1790 1410 1783 Dl 1495 1794 1481 1790 Dl 1515 1757 1494 1794 Dl 1529 1738 1517 1757 Dl 1535 1738 1530 1738 Dl 1552 1743 1535 1737 Dl 1562 1745 1552 1743 Dl 1565 1746 1563 1746 Dl 1566 1746 1 1 De 10 R f 0.1 setlinewidth 4820 2346 4827 2363 Dl 4828 2363 4841 2407 Dl 4842 2408 4854 2470 Dl 4854 2471 4888 2748 Dl 3175 2708 3592 2980 Dl 3593 2981 3648 3005 Dl 3649 3004 4034 3060 Dl 4034 3060 4888 2748 Dl 3397 2229 3342 2325 Dl 3342 2325 3291 2430 Dl 3290 2430 3175 2707 Dl 4796 2312 4819 2345 Dl 4070 2241 4034 3060 Dl 4124 1609 4070 2241 Dl 4125 1609 4854 2470 Dl (7)4354 2465 w 4119 1542 4119 1580 Dl 4119 1580 4124 1608 Dl 4120 1541 4841 2407 Dl 5 R f (8)4457 1997 w 10 R f 0.1 setlinewidth 4109 1491 4114 1519 Dl 4115 1520 4120 1541 Dl 4108 1492 4827 2363 Dl 5 R f (9)4446 1941 w 10 R f 0.1 setlinewidth 4094 1457 4096 1468 Dl 4097 1469 4108 1491 Dl 4094 1457 4796 2312 Dl 4070 1434 4075 1438 Dl 4075 1439 4093 1457 Dl 4054 1429 4070 1434 Dl 4063 1768 4070 2241 Dl 4081 1573 4063 1768 Dl 4082 1573 4119 1580 Dl 5 R f (14)4063 1825 w 10 R f 0.1 setlinewidth 4074 1518 4075 1558 Dl 4075 1558 4082 1573 Dl 4075 1512 4073 1517 Dl 4077 1512 4114 1519 Dl 4076 1465 4076 1512 Dl 4076 1464 4096 1468 Dl 4059 1451 4065 1458 Dl 4063 1436 4058 1451 Dl 4065 1459 4076 1464 Dl 4065 1436 4075 1438 Dl 4042 1425 4042 1427 Dl 4042 1428 4065 1436 Dl 4040 1426 4052 1428 Dl 4028 1426 4040 1426 Dl 4057 1460 1 1 De 4058 1461 4062 1499 Dl 4062 1499 4073 1517 Dl 4064 1459 4058 1460 Dl 4028 1429 4029 1439 Dl 4029 1439 4055 1450 Dl 4041 1428 4028 1429 Dl 4056 1451 4058 1451 Dl 4004 1428 4006 1428 Dl 4006 1427 4023 1425 Dl 4023 1425 4027 1425 Dl 4056 1452 4058 1460 Dl 4023 1426 4017 1428 Dl 4018 1429 4028 1429 Dl 4038 1567 4025 1632 Dl 4025 1632 4063 1768 Dl 4075 1558 4039 1566 Dl 4022 1549 4039 1566 Dl 4032 1506 4021 1548 Dl 4061 1499 4032 1506 Dl 4031 1467 4026 1491 Dl 4026 1491 4032 1506 Dl 4057 1461 4032 1466 Dl 4021 1442 4019 1453 Dl 4019 1454 4030 1466 Dl 4031 1466 4032 1466 Dl 4028 1439 4021 1441 Dl 4014 1430 4010 1432 Dl 4011 1432 4016 1440 Dl 4016 1441 4021 1441 Dl 4016 1429 4014 1429 Dl 4001 1430 1 1 De 4006 1428 4001 1430 Dl 4002 1430 4014 1429 Dl 4013 1530 4017 1549 Dl 4011 1497 4013 1530 Dl 4021 1549 4017 1549 Dl 4026 1491 4011 1497 Dl 4011 1474 4006 1497 Dl 4007 1497 4011 1497 Dl 4029 1466 4011 1473 Dl 3994 1470 4006 1473 Dl 4008 1458 3994 1470 Dl 4006 1473 4011 1473 Dl 4018 1453 4008 1457 Dl 4001 1447 4001 1451 Dl 4001 1452 4008 1457 Dl 4015 1441 4000 1447 Dl 3999 1437 3997 1447 Dl 3997 1447 4000 1447 Dl 4003 1435 3999 1437 Dl 4009 1432 4004 1434 Dl 3993 1435 1 1 De 4001 1430 3994 1434 Dl 3994 1434 4004 1434 Dl 3984 1437 1 1 De 3993 1433 3983 1437 Dl 3995 1432 3994 1432 Dl 4001 1431 3984 1437 Dl 4004 1429 3996 1432 Dl 3874 1957 3648 3005 Dl 3995 1645 3875 1956 Dl 4025 1632 3996 1644 Dl (45)3862 2496 w 3986 1568 3984 1573 Dl 3985 1574 3996 1644 Dl 4017 1550 3987 1568 Dl 3997 1502 4013 1530 Dl 4006 1497 3996 1501 Dl 4006 1473 3996 1501 Dl 4000 1451 3990 1470 Dl 3992 1470 3990 1470 Dl 3980 1443 3980 1444 Dl 3993 1435 3980 1442 Dl 3999 1437 3980 1444 Dl 3983 1437 1 1 De 3984 1437 3994 1434 Dl 3980 1539 3987 1568 Dl 3992 1503 3980 1537 Dl 3995 1502 3993 1503 Dl 3982 1474 3978 1486 Dl 3979 1487 3993 1503 Dl 3990 1471 3983 1474 Dl 3979 1469 3983 1474 Dl 3988 1451 3978 1469 Dl 3995 1448 3988 1451 Dl 3979 1444 3976 1448 Dl 3976 1449 3988 1451 Dl 3980 1442 1 1 De 3983 1437 3978 1442 Dl 3983 1437 3977 1440 Dl 3914 1710 3875 1956 Dl 3947 1616 3914 1710 Dl 3983 1574 3947 1615 Dl 3978 1486 3977 1488 Dl 3977 1489 3959 1534 Dl 3960 1534 3980 1537 Dl 3977 1449 3970 1454 Dl 3968 1453 3968 1471 Dl 3968 1471 3978 1469 Dl 3958 1453 3957 1454 Dl 3977 1441 3959 1452 Dl 3978 1444 3957 1454 Dl 3948 1541 3936 1578 Dl 3937 1578 3947 1615 Dl 3958 1534 3949 1540 Dl 3952 1505 3942 1532 Dl 3942 1533 3949 1540 Dl 3976 1489 3952 1505 Dl 3951 1484 3945 1493 Dl 3946 1493 3952 1505 Dl 3969 1472 3952 1483 Dl 3949 1469 3952 1483 Dl 3969 1454 3948 1469 Dl 3957 1454 3948 1461 Dl 3947 1469 1 1 De 3947 1462 3947 1469 Dl 3907 1594 3898 1629 Dl 3899 1629 3914 1710 Dl 3936 1578 3908 1593 Dl 3917 1515 3916 1517 Dl 3915 1517 3909 1561 Dl 3929 1506 3917 1514 Dl 3930 1506 3924 1547 Dl 3923 1547 3909 1561 Dl 3947 1462 3928 1482 Dl 3928 1482 3934 1481 Dl 3946 1470 3934 1481 Dl 3909 1562 3905 1571 Dl 3906 1571 3908 1593 Dl 3942 1532 3924 1547 Dl 3945 1493 3930 1505 Dl 3934 1481 3917 1514 Dl 3867 1661 3592 2980 Dl 3897 1629 3867 1661 Dl (83)3711 2344 w 3877 1600 3866 1630 Dl 3866 1630 3867 1661 Dl 3904 1571 3877 1600 Dl 3895 1540 3879 1570 Dl 3878 1570 3877 1600 Dl 3915 1517 3895 1539 Dl 3915 1496 3898 1520 Dl 3897 1521 3895 1539 Dl 3928 1483 3916 1496 Dl 3866 1630 3291 2430 Dl (89)3488 2437 w 3879 1570 3342 2325 Dl 5 R f (90)3582 1982 w 10 R f 0.1 setlinewidth 3897 1521 3397 2229 Dl 20 R f 16 setlinewidth 5040 3258 3024 3258 Dl 5040 1242 5040 3258 Dl 3024 1242 5040 1242 Dl 3024 3258 3024 1242 Dl 3806 1684 3967 1761 Dl 3740 1760 3806 1684 Dl 3700 1810 3741 1761 Dl 3855 1585 3700 1810 Dl 3854 1585 3829 1654 Dl 3855 1586 3800 1634 Dl 3895 1525 3855 1585 Dl 3901 1516 3895 1524 Dl 3911 1504 3902 1516 Dl 3916 1495 3911 1502 Dl 3918 1493 3916 1495 Dl 3923 1488 3918 1493 Dl 3927 1484 3924 1487 Dl 3927 1483 1 1 De 10 B f (Fig. 30:)1 322 1 1158 3456 t 10 R f (dual projective path)2 793 1 1505 3456 t 10 B f (Fig. 31:)1 322 1 3286 3456 t 10 I f (d)3633 3456 w 10 R f (= \(0,0,1\), 30)2 497 1 3708 3456 t 10 S f (\260)4205 3456 w 10 R f (outside view)1 508 1 4270 3456 t 0.1 setlinewidth 872 5185 2414 5098 Dl 2415 5097 2481 5092 Dl 2482 5092 2584 5065 Dl 949 4493 938 4546 Dl 937 4546 927 4615 Dl 927 4616 914 4724 Dl 913 4726 901 4847 Dl 901 4846 871 5184 Dl 2290 4631 2584 5065 Dl 2068 4318 2290 4631 Dl 1956 4170 2067 4317 Dl 1907 4121 1944 4156 Dl 1944 4157 1955 4170 Dl 1654 4008 1653 4008 Dl 1646 4010 1643 4011 Dl 1653 4008 1648 4009 Dl 1839 4065 1 1 De 1839 4066 1885 4103 Dl 1886 4103 1906 4121 Dl 1756 4021 1786 4035 Dl 1786 4037 1821 4055 Dl 1695 4005 1697 4005 Dl 1698 4006 1704 4006 Dl 1705 4006 1725 4011 Dl 1822 4055 1838 4065 Dl 1725 4011 1743 4016 Dl 1744 4016 1756 4021 Dl 1674 4006 1672 4006 Dl 1658 4007 1654 4007 Dl 1667 4006 1658 4006 Dl 1694 4005 1675 4005 Dl 1671 4006 1668 4006 Dl 1940 4158 1977 4209 Dl 1977 4209 2067 4317 Dl 1943 4157 1939 4158 Dl 1918 4140 1939 4158 Dl 1882 4104 1918 4140 Dl 1885 4103 1882 4104 Dl 1836 4066 1861 4088 Dl 1863 4089 1882 4104 Dl 1839 4066 1836 4066 Dl 1785 4036 1805 4048 Dl 1805 4048 1834 4065 Dl 1835 4066 1836 4066 Dl 1785 4036 1784 4036 Dl 1743 4017 1748 4019 Dl 1748 4020 1778 4033 Dl 1778 4034 1784 4036 Dl 1716 4011 1720 4011 Dl 1705 4007 1717 4010 Dl 1721 4011 1743 4016 Dl 1670 4006 1668 4006 Dl 1668 4006 1 1 De 1643 4011 1634 4015 Dl 1893 4122 1915 4140 Dl 1857 4092 1893 4122 Dl 1916 4140 1915 4140 Dl 1862 4089 1858 4091 Dl 1829 4069 1854 4090 Dl 1856 4090 1858 4091 Dl 1834 4066 1829 4068 Dl 1809 4059 1825 4066 Dl 1802 4051 1808 4059 Dl 1825 4067 1829 4068 Dl 1804 4049 1802 4050 Dl 1774 4035 1783 4040 Dl 1784 4041 1802 4050 Dl 1778 4033 1774 4035 Dl 1747 4022 1771 4034 Dl 1772 4035 1774 4035 Dl 1746 4020 1746 4021 Dl 1747 4020 1746 4020 Dl 1724 4015 1725 4015 Dl 1721 4012 1724 4014 Dl 1726 4015 1746 4020 Dl 1702 4011 1704 4011 Dl 1695 4007 1702 4010 Dl 1716 4011 1704 4011 Dl 1697 4006 1695 4006 Dl 1675 4005 1675 4006 Dl 1695 4006 1675 4006 Dl 1668 4006 1659 4008 Dl 1659 4008 1 1 De 2083 4436 2481 5092 Dl 1970 4215 2083 4436 Dl 1976 4209 1969 4214 Dl (45)2256 4747 w 1912 4150 1914 4154 Dl 1914 4154 1969 4214 Dl 1915 4141 1911 4150 Dl 1852 4092 1893 4122 Dl 1853 4090 1851 4091 Dl 1825 4067 1851 4091 Dl 1784 4041 1807 4059 Dl 1808 4059 1807 4059 Dl 1729 4020 1735 4022 Dl 1726 4014 1728 4019 Dl 1746 4022 1735 4022 Dl 1705 4011 1709 4012 Dl 1709 4012 1724 4014 Dl 1674 4008 1681 4008 Dl 1675 4008 1674 4008 Dl 1694 4007 1681 4008 Dl 1655 4009 1647 4010 Dl 1659 4008 1656 4008 Dl 1647 4010 1 1 De 1876 4122 1911 4150 Dl 1851 4093 1876 4121 Dl 1851 4091 1 1 De 1805 4061 1816 4071 Dl 1817 4071 1851 4091 Dl 1806 4059 1804 4060 Dl 1789 4053 1804 4060 Dl 1769 4036 1789 4052 Dl 1770 4035 1768 4036 Dl 1735 4023 1740 4026 Dl 1741 4027 1768 4036 Dl 1725 4019 1728 4019 Dl 1710 4012 1725 4019 Dl 1682 4008 1695 4010 Dl 1702 4010 1695 4010 Dl 1659 4008 1666 4008 Dl 1673 4007 1666 4008 Dl 1953 4251 2083 4436 Dl 1915 4180 1953 4251 Dl 1914 4155 1914 4181 Dl 1816 4071 1816 4072 Dl 1817 4073 1850 4111 Dl 1850 4111 1876 4121 Dl 1740 4026 1740 4029 Dl 1741 4031 1777 4051 Dl 1778 4051 1789 4052 Dl 1696 4019 1697 4019 Dl 1696 4010 1696 4017 Dl 1724 4019 1697 4019 Dl 1647 4011 1630 4018 Dl 1634 4016 1630 4018 Dl 1845 4114 1867 4144 Dl 1868 4145 1914 4181 Dl 1849 4112 1845 4114 Dl 1805 4080 1825 4103 Dl 1825 4104 1845 4114 Dl 1816 4073 1805 4080 Dl 1769 4056 1774 4063 Dl 1775 4064 1805 4080 Dl 1776 4051 1769 4056 Dl 1730 4037 1769 4056 Dl 1740 4030 1730 4036 Dl 1697 4019 1697 4023 Dl 1729 4036 1 1 De 1697 4024 1729 4036 Dl 1666 4010 1696 4017 Dl 1666 4009 1664 4010 Dl 1663 4010 1661 4011 Dl 1656 4009 1661 4011 Dl 1629 4018 1623 4021 Dl 1843 4149 1862 4177 Dl 1863 4177 1953 4251 Dl 1867 4144 1843 4148 Dl 1755 4073 1755 4074 Dl 1755 4075 1809 4118 Dl 1765 4070 1755 4073 Dl 1766 4070 1814 4110 Dl 1814 4110 1809 4118 Dl 1697 4023 1702 4038 Dl 1703 4039 1723 4042 Dl 1728 4037 1723 4042 Dl 1623 4022 1614 4027 Dl 1660 4012 1614 4027 Dl 1661 4011 1660 4012 Dl 1810 4118 1813 4125 Dl 1814 4125 1843 4148 Dl 1824 4103 1814 4110 Dl 1774 4064 1765 4069 Dl 1724 4043 1755 4073 Dl 1658 4016 1662 4021 Dl 1660 4012 1658 4016 Dl 1663 4022 1697 4023 Dl 1839 4195 2414 5098 Dl 1862 4177 1839 4194 Dl (83)2110 4656 w 1792 4142 1802 4165 Dl 1803 4164 1839 4194 Dl 1813 4126 1792 4141 Dl 1740 4087 1748 4110 Dl 1749 4111 1792 4141 Dl 1754 4075 1738 4086 Dl 1692 4045 1694 4063 Dl 1695 4063 1738 4086 Dl 1702 4038 1692 4045 Dl 1661 4022 1656 4037 Dl 1656 4038 1692 4045 Dl 1657 4017 1613 4027 Dl 1802 4166 901 4847 Dl (89)1569 4819 w 1747 4110 914 4724 Dl (90)1282 4489 w 1694 4063 927 4615 Dl (91)1264 4404 w 1655 4037 938 4546 Dl 5 R f (92)1273 4330 w 10 R f 0.1 setlinewidth 1612 4028 949 4493 Dl 5 R f (93)1263 4287 w 20 R f 16 setlinewidth 2736 5634 720 5634 Dl 2736 3618 2736 5634 Dl 720 3618 2736 3618 Dl 720 5634 720 3618 Dl 1685 4182 1839 4277 Dl 1684 4182 1754 4204 Dl 1684 4182 1735 4235 Dl 1569 4222 1684 4182 Dl 1479 4250 1568 4222 Dl 1653 4102 1479 4250 Dl 1653 4102 1610 4162 Dl 1652 4101 1586 4134 Dl 1688 4065 1653 4101 Dl 1694 4060 1689 4065 Dl 1693 4051 1694 4060 Dl 1693 4045 1693 4050 Dl 1694 4044 1693 4045 Dl 1699 4042 1694 4044 Dl 1701 4039 1699 4041 Dl 1702 4039 1 1 De 10 R f 0.1 setlinewidth 3731 5634 3024 5634 Dl 3024 4295 3024 5634 Dl 3757 4947 3731 5634 Dl 3756 4945 3024 4294 Dl (7)3321 5126 w 3024 4089 3024 4294 Dl 3778 4808 3772 4903 Dl 3771 4903 3756 4946 Dl 3778 4806 3024 4089 Dl (8)3356 4540 w 3024 3897 3024 4089 Dl 3806 4687 3792 4760 Dl 3791 4761 3778 4807 Dl 3806 4686 3024 3896 Dl (9)3366 4373 w 3024 3715 3024 3896 Dl 3834 4580 3828 4637 Dl 3827 4638 3806 4687 Dl 3835 4579 3024 3715 Dl (10)3355 4221 w 3138 3618 3024 3618 Dl 3024 3618 3024 3715 Dl 3875 4454 3867 4502 Dl 3867 4503 3835 4579 Dl 3875 4454 3138 3618 Dl (11)3388 4079 w 3325 3618 3138 3618 Dl 3930 4346 3903 4418 Dl 3902 4418 3875 4454 Dl 3930 4346 3326 3618 Dl (12)3503 4015 w 3539 3618 3326 3618 Dl 3991 4205 3539 3618 Dl 3953 4331 3998 4254 Dl 3953 4332 3946 4338 Dl 4001 4246 3991 4205 Dl 3999 4254 4001 4248 Dl 3945 4339 3930 4346 Dl (13)3641 3964 w 3804 5634 3731 5634 Dl 3836 5293 3803 5634 Dl 3835 4914 3836 5292 Dl 3835 4913 3772 4903 Dl 5 R f (14)3762 5280 w 10 R f 0.1 setlinewidth 3857 4785 3850 4881 Dl 3850 4882 3836 4914 Dl 3855 4772 3858 4785 Dl 3853 4770 3792 4760 Dl 3860 4644 3854 4772 Dl 3860 4642 3828 4637 Dl 3890 4595 3880 4626 Dl 3883 4507 3890 4595 Dl 3878 4626 3860 4643 Dl 3882 4504 3867 4502 Dl 3921 4422 3920 4449 Dl 3919 4449 3883 4505 Dl 3922 4421 3903 4418 Dl 3942 4397 3922 4422 Dl 3945 4338 3942 4396 Dl 4002 4250 4002 4248 Dl 3999 4252 4001 4250 Dl 4001 4248 1 1 De 4013 4210 3991 4205 Dl 4014 4235 4016 4227 Dl 4003 4247 4013 4236 Dl 4016 4227 4014 4210 Dl 3890 4629 3891 4631 Dl 3891 4631 3879 4735 Dl 3878 4735 3858 4785 Dl 3880 4626 3890 4628 Dl 3939 4457 3937 4518 Dl 3937 4518 3895 4592 Dl 3921 4450 3941 4456 Dl 3895 4593 3890 4595 Dl 3980 4335 3980 4340 Dl 3978 4340 3976 4352 Dl 3976 4352 3949 4394 Dl 3954 4332 3979 4334 Dl 3948 4394 3942 4396 Dl 3895 4592 3890 4628 Dl 3949 4394 3958 4430 Dl 3958 4431 3941 4456 Dl 4003 4293 4004 4287 Dl 4003 4258 4001 4250 Dl 4005 4279 4004 4260 Dl 3979 4333 4003 4293 Dl 4006 4286 4006 4279 Dl 3910 4869 3926 4977 Dl 3924 4977 3836 5292 Dl 3850 4881 3909 4869 Dl 5 R f (28)3845 5037 w 10 R f 0.1 setlinewidth 3939 4813 3909 4869 Dl 3925 4725 3939 4812 Dl 3880 4734 3926 4724 Dl 3931 4622 3936 4679 Dl 3937 4679 3926 4724 Dl 3892 4630 3931 4621 Dl 3950 4515 3952 4556 Dl 3952 4556 3933 4618 Dl 3933 4618 3931 4621 Dl 3938 4517 3950 4515 Dl 3963 4429 3969 4439 Dl 3968 4439 3958 4500 Dl 3957 4502 3950 4515 Dl 3959 4430 3962 4430 Dl 3984 4378 3983 4385 Dl 3977 4352 3984 4377 Dl 3982 4386 3962 4430 Dl 4005 4287 4006 4281 Dl 4006 4280 4006 4279 Dl 4014 4210 4030 4206 Dl 4016 4226 4030 4206 Dl 3956 4754 3947 4808 Dl 3962 4670 3956 4753 Dl 3941 4812 3947 4808 Dl 3937 4678 3962 4669 Dl 3963 4607 3969 4662 Dl 3968 4662 3962 4669 Dl 3933 4618 3962 4607 Dl 3991 4561 3971 4597 Dl 3969 4549 3991 4561 Dl 3970 4597 3962 4607 Dl 3953 4555 3969 4549 Dl 3983 4492 3981 4510 Dl 3981 4510 3969 4549 Dl 3959 4501 3983 4491 Dl 3986 4436 3988 4484 Dl 3988 4485 3983 4491 Dl 3978 4435 3985 4435 Dl 3969 4438 3978 4435 Dl 3995 4391 3996 4394 Dl 3983 4385 3994 4391 Dl 3995 4394 3978 4435 Dl 4012 4348 4011 4351 Dl 3996 4335 4012 4348 Dl 3994 4334 3996 4334 Dl 3985 4376 4011 4351 Dl 3981 4339 3993 4334 Dl 4004 4293 4017 4293 Dl 3993 4334 4017 4293 Dl 4006 4280 4023 4260 Dl 4005 4260 4023 4260 Dl 3804 5634 4287 5634 Dl 4233 5443 4287 5634 Dl 3977 4959 4232 5442 Dl 3926 4977 3977 4958 Dl (45)3963 5402 w 3997 4798 4001 4805 Dl 4000 4805 3977 4958 Dl 3947 4807 3996 4797 Dl 3984 4656 3956 4753 Dl 3969 4661 3985 4655 Dl 3971 4598 3985 4655 Dl 3985 4655 1 1 De 3981 4510 3996 4558 Dl 3991 4561 3996 4558 Dl 4016 4398 4016 4411 Dl 3996 4395 4017 4398 Dl 3986 4435 4016 4411 Dl 4011 4352 4011 4360 Dl 4011 4361 3994 4391 Dl 4027 4290 4024 4305 Dl 4017 4292 4027 4289 Dl 3996 4333 4024 4305 Dl 4024 4252 4022 4234 Dl 4025 4260 4026 4253 Dl 4013 4236 4022 4234 Dl 4024 4260 1 1 De 4009 4712 3996 4797 Dl 3991 4653 4010 4711 Dl 3985 4655 3990 4653 Dl 4009 4553 4015 4577 Dl 4014 4577 3990 4653 Dl 3996 4557 4008 4552 Dl 4015 4521 4008 4552 Dl 4001 4478 4016 4520 Dl 3989 4484 4001 4478 Dl 4016 4412 4021 4422 Dl 4021 4422 4001 4478 Dl 4018 4391 4017 4398 Dl 4012 4361 4019 4391 Dl 4023 4305 4022 4332 Dl 4012 4347 4022 4332 Dl 4025 4260 4038 4275 Dl 4028 4289 4038 4275 Dl 4127 4923 4232 5442 Dl 4064 4808 4127 4922 Dl 4001 4806 4063 4808 Dl 5 R f (62)4068 5058 w 10 R f 0.1 setlinewidth 4016 4577 4018 4577 Dl 4018 4577 4045 4649 Dl 4045 4650 4010 4711 Dl 4022 4422 4032 4422 Dl 4032 4421 4032 4495 Dl 4032 4496 4016 4520 Dl 4051 4331 4053 4333 Dl 4023 4331 4051 4331 Dl 4018 4390 4053 4333 Dl 4024 4234 4049 4196 Dl 4031 4206 4049 4196 Dl 4062 4639 4083 4690 Dl 4082 4691 4063 4808 Dl 4046 4649 4062 4639 Dl 4058 4550 4075 4593 Dl 4075 4593 4062 4639 Dl 4018 4576 4058 4550 Dl 4060 4478 4070 4487 Dl 4070 4486 4058 4550 Dl 4033 4494 4060 4476 Dl 4067 4397 4060 4476 Dl 4033 4421 4068 4397 Dl 4053 4333 4068 4331 Dl 4067 4397 4068 4395 Dl 4068 4331 4068 4395 Dl 4045 4270 4051 4331 Dl 4038 4275 4044 4270 Dl 4045 4269 4050 4263 Dl 4026 4253 4050 4263 Dl 4029 4206 4062 4181 Dl 4048 4195 4062 4181 Dl 4135 4633 4153 4679 Dl 4152 4679 4127 4922 Dl 4083 4689 4134 4631 Dl 4119 4442 4121 4442 Dl 4121 4443 4132 4556 Dl 4097 4465 4118 4442 Dl 4097 4466 4107 4568 Dl 4107 4568 4132 4556 Dl 4069 4331 4101 4338 Dl 4100 4338 4089 4381 Dl 4069 4394 4089 4381 Dl 4063 4181 4086 4159 Dl 4054 4259 4086 4159 Dl 4051 4263 4055 4260 Dl 4133 4557 4140 4564 Dl 4139 4564 4134 4631 Dl 4076 4592 4107 4568 Dl 4071 4485 4096 4465 Dl 4090 4382 4118 4442 Dl 4071 4253 4083 4260 Dl 4055 4259 4070 4253 Dl 4082 4261 4068 4331 Dl 4288 5634 4620 5634 Dl 4216 4621 4620 5634 Dl 4154 4678 4215 4620 Dl (83)4277 5245 w 4193 4512 4216 4533 Dl 4215 4534 4215 4620 Dl 4141 4563 4192 4512 Dl 4158 4404 4188 4417 Dl 4189 4417 4192 4512 Dl 4121 4441 4158 4403 Dl 4123 4314 4153 4314 Dl 4154 4315 4158 4403 Dl 4101 4337 4122 4314 Dl 4083 4260 4122 4242 Dl 4122 4242 4122 4314 Dl 4087 4159 4088 4158 Dl 4070 4253 4088 4158 Dl 4957 3618 5040 3618 Dl 4621 5634 5040 5634 Dl 5040 3618 5040 5634 Dl 4216 4533 4956 3618 Dl (89)4678 4736 w 4800 3618 4956 3618 Dl 4189 4417 4800 3618 Dl (90)4504 4052 w 4659 3618 4800 3618 Dl 4154 4314 4659 3618 Dl (91)4408 4003 w 4558 3618 4659 3618 Dl 4123 4242 4557 3618 Dl 5 R f (92)4352 3954 w 10 R f 0.1 setlinewidth 4447 3618 4557 3618 Dl 4087 4158 4447 3618 Dl 5 R f (93)4276 3925 w 10 R f 0.1 setlinewidth 4447 3618 3539 3618 Dl (94)3953 3846 w 20 R f 16 setlinewidth 5040 5634 3024 5634 Dl 5040 3618 5040 5634 Dl 3024 3618 5040 3618 Dl 3024 5634 3024 3618 Dl 4348 4246 4032 4626 Dl 4347 4246 4315 4312 Dl 4347 4246 4288 4289 Dl 4520 3940 4348 4245 Dl 4521 3941 4501 4012 Dl 4520 3940 4469 3994 Dl 4647 3691 4520 3940 Dl 4647 3692 4631 3764 Dl 4648 3691 4600 3747 Dl 4239 4210 4649 3692 Dl 4238 4209 4268 4142 Dl 4238 4210 4297 4165 Dl 4159 4300 4238 4210 Dl 4147 4315 4158 4301 Dl 4131 4314 4147 4314 Dl 4122 4316 4130 4315 Dl 4118 4319 4121 4317 Dl 4108 4330 4118 4320 Dl 4103 4337 4108 4331 Dl 4101 4338 4102 4337 Dl 10 B f (Fig. 32:)1 322 1 1040 5832 t 10 I f (d)1387 5832 w 10 R f (= \(\2611,0,0\), outside view)3 955 1 1462 5832 t 10 B f (Fig. 33:)1 322 1 3396 5832 t 10 R f (50)3743 5832 w 10 S f (\260)3843 5832 w 10 R f (view,)3908 5832 w 10 I f (v)4152 5832 w 10 R f (= \(0,\26110,0\))1 447 1 4221 5832 t ( affine algorithm, the transformed polytopes of the dual projective algo-)10 2880(In stark contrast with the dual)5 1190 2 970 5988 t ( since the image of the current iterate is the center)10 2079( Indeed,)1 356(rithm stay reasonably round.)3 1173 3 720 6108 t 10 I f (e /)1 80 1 4362 6108 t 10 R f (\()4450 6108 w 10 I f (n)4491 6108 w 10 S f (+)4581 6108 w 10 R f ( of the)2 273(1 \))1 91 2 4676 6108 t (projectively transformed polytope, whose only inequality constraints are those of the unit simplex, the cen-)14 4320 1 720 6228 t (ter is at least a distance of 1)7 1162 1 720 6354 t 10 I f (/)1890 6354 w 11 S f (\326` ```````)1 452 1 1926 6354 t 10 I f (n)1995 6354 w 10 R f (\()2053 6354 w 10 I f (n)2094 6354 w 10 S f (+)2184 6354 w 10 R f ( at most a distance of)5 886( and)1 193(1 \))1 91 3 2279 6354 t 11 S f (\326` ```````)1 488 1 3482 6354 t 10 I f (n /)1 86 1 3551 6354 t 10 R f (\()3645 6354 w 10 I f (n)3686 6354 w 10 S f (+)3776 6354 w 10 R f ( the)1 154( the boundary of)3 681( from)1 243(1 \))1 91 4 3871 6354 t ( polytope in iter-)3 678( 34\26146 give an outside view of the projectively transformed)9 2406( Figures)1 352(transformed polytope.)1 884 4 720 6474 t (ations 2\26114, all from view direction)5 1437 1 720 6594 t 10 I f (d)2182 6594 w 10 S f (=)2281 6594 w 10 R f ( showing through from inside the polytopes in these)8 2077( Also)1 239(\( 0 , 0 , 1 \).)6 339 3 2385 6594 t ( are short \(somewhere near)4 1119( these steps)2 473( Usually)1 370(figures and depicted by heavy arrows are the steps taken.)9 2358 4 720 6714 t (1)720 6840 w 10 I f (/)778 6840 w 11 S f (\326` ```````)1 452 1 814 6840 t 10 I f (n)883 6840 w 10 R f (\()941 6840 w 10 I f (n)982 6840 w 10 S f (+)1072 6840 w 10 R f ( \(which is of fixed size\) is)6 1085( or are nearly parallel to the direction of view, so the arrowhead)12 2648( \))1 49(1 \))1 91 4 1167 6840 t ( from one iteration to the next, the polytope often appears to be rotated a bit)15 3053( going)1 254( In)1 134(about all that appears.)3 879 4 720 6960 t ( view in figure 46 is not very informative; figure 47 shows the same polytope)14 3217( The)1 214(and mildly massaged.)2 889 3 720 7080 t (from a different view direction,)4 1323 1 720 7200 t 10 I f (d)2085 7200 w 10 S f (=)2184 7200 w 10 R f (\( 0 ,)2 124 1 2288 7200 t 10 S f (-)2428 7200 w 10 R f ( 1 is an affine step, figures 28 and 29)9 1637( iteration)1 375( \(Since)1 322(1 , 0 \).)3 207 4 2499 7200 t (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 16 17 %%Page: 17 18 /saveobj save def mark 18 pagesetup 10 R f (- 17 -)2 216 1 2772 480 t (illustrate its transformed polytope.\))3 1410 1 720 840 t 0.1 setlinewidth 1475 2301 1539 2301 Dl 1944 2222 1539 2301 Dl 2021 2201 1944 2221 Dl 2418 2067 2368 2089 Dl 2484 2033 2443 2055 Dl 2443 2055 2418 2067 Dl 2537 1994 2519 2012 Dl 2518 2013 2484 2033 Dl 2568 1959 2538 1994 Dl 2124 2168 2022 2200 Dl 2320 2107 2125 2169 Dl 2367 2090 2321 2106 Dl 2397 2070 2329 2101 Dl 2329 2101 2321 2106 Dl 2410 2064 2397 2069 Dl 2442 2056 2411 2064 Dl 2515 2010 2411 2064 Dl 2516 2009 2519 2012 Dl 2535 1982 2521 1998 Dl 2571 1951 2535 1981 Dl 2521 1999 2515 2009 Dl 2571 1951 2568 1958 Dl 2584 1900 2584 1907 Dl 2583 1907 2572 1950 Dl 2577 1875 2584 1899 Dl 2511 1998 2508 1999 Dl 2507 1999 2415 2052 Dl 2415 2052 2397 2069 Dl 2511 1998 2521 1998 Dl 2573 1891 2543 1923 Dl 2543 1923 2534 1979 Dl 2575 1891 2584 1907 Dl 2534 1979 2535 1981 Dl 2540 1832 2574 1867 Dl 2575 1868 2577 1875 Dl 2534 1979 2512 1997 Dl 2567 1864 2574 1867 Dl 2566 1864 2574 1891 Dl 2234 2118 2120 2154 Dl 2120 2155 2125 2169 Dl 2328 2101 2234 2118 Dl 2209 2110 2234 2118 Dl 2336 2058 2208 2109 Dl 2416 2052 2337 2058 Dl 2451 1992 2361 2033 Dl 2361 2034 2337 2058 Dl 2451 1993 2508 1999 Dl 2525 1914 2475 1943 Dl 2475 1944 2450 1990 Dl 2450 1990 2450 1992 Dl 2525 1914 2543 1923 Dl 2544 1857 2561 1859 Dl 2543 1857 2520 1900 Dl 2520 1901 2525 1914 Dl 2561 1859 2566 1863 Dl 2528 1824 2530 1826 Dl 2529 1824 2540 1832 Dl 2531 1826 2561 1859 Dl 2215 2087 2193 2110 Dl 2291 2036 2215 2087 Dl 2208 2109 2193 2110 Dl 2360 2034 2291 2035 Dl 2375 1986 2276 2032 Dl 2276 2033 2291 2035 Dl 2376 1985 2450 1990 Dl 2328 1944 2358 1977 Dl 2433 1936 2327 1943 Dl 2358 1977 2376 1984 Dl 2434 1936 2475 1943 Dl 2458 1880 2440 1898 Dl 2439 1898 2432 1935 Dl 2458 1880 2520 1900 Dl 2502 1841 2446 1871 Dl 2447 1872 2458 1880 Dl 2503 1841 2523 1847 Dl 2524 1847 2544 1857 Dl 2494 1815 2499 1815 Dl 2499 1815 2530 1826 Dl 2494 1815 2523 1847 Dl 2455 1785 2458 1786 Dl 2459 1787 2528 1823 Dl 1582 2274 1539 2301 Dl 2007 2173 1583 2274 Dl 2120 2155 2007 2173 Dl 2024 2135 2002 2140 Dl 2002 2141 2007 2173 Dl 2192 2111 2024 2134 Dl 2217 2033 2215 2087 Dl 2276 2033 2217 2033 Dl 2357 1978 2214 2033 Dl 2215 2033 2217 2033 Dl 2440 1898 2309 1939 Dl 2309 1940 2327 1943 Dl 2412 1788 2405 1794 Dl 2414 1787 2494 1814 Dl 2405 1794 2502 1840 Dl 2458 1787 2454 1787 Dl 2456 1788 2499 1815 Dl 2031 2092 2024 2134 Dl 2194 2033 2031 2092 Dl 2214 2033 2195 2033 Dl 2251 1933 2169 1964 Dl 2169 1964 2195 2033 Dl 2252 1933 2309 1939 Dl 2252 1897 2250 1932 Dl 2398 1858 2253 1896 Dl 2399 1859 2446 1871 Dl 2403 1794 2365 1795 Dl 2366 1795 2399 1858 Dl 2410 1783 2412 1787 Dl 2410 1783 2454 1787 Dl 2420 1773 2455 1785 Dl 1567 2237 1583 2274 Dl 1738 2181 1566 2236 Dl 2001 2140 1738 2181 Dl 5 R f (62)1754 2213 w 10 R f 0.1 setlinewidth 2169 1964 2151 1966 Dl 2150 1967 1878 2067 Dl 1878 2067 2031 2092 Dl 5 R f (63)2039 2045 w 10 R f 0.1 setlinewidth 2297 1788 2365 1795 Dl 2297 1787 2178 1868 Dl 2178 1868 2253 1896 Dl 2260 1731 2278 1735 Dl 2278 1736 2419 1773 Dl 2259 1732 2409 1783 Dl 1771 2071 1630 2134 Dl 1630 2135 1738 2181 Dl 1877 2068 1771 2071 Dl 5 R f (67)1811 2130 w 10 R f 0.1 setlinewidth 1877 1958 1692 2032 Dl 1692 2033 1771 2071 Dl 1877 1958 2151 1966 Dl 5 R f (68)1871 2020 w 10 R f 0.1 setlinewidth 1972 1847 1854 1866 Dl 1854 1867 1877 1958 Dl 1973 1847 2178 1868 Dl 5 R f (69)2019 1919 w 10 R f 0.1 setlinewidth 2051 1743 1972 1847 Dl 2052 1742 2297 1787 Dl 5 R f (70)2099 1819 w 10 R f 0.1 setlinewidth 2155 1713 2259 1731 Dl 2045 1740 2052 1742 Dl 2155 1714 2044 1740 Dl 1294 2135 1287 2179 Dl 1288 2180 1566 2236 Dl 1630 2135 1295 2135 Dl 5 R f (75)1482 2185 w 10 R f 0.1 setlinewidth 1385 1835 1352 1840 Dl 1351 1841 1218 2050 Dl 1386 1835 1609 1855 Dl 1609 1855 1438 2035 Dl 1437 2037 1218 2050 Dl 5 R f (76)1381 1949 w 10 R f 0.1 setlinewidth 1837 1704 2154 1713 Dl 1838 1704 1856 1727 Dl 1857 1728 2044 1740 Dl 1218 2050 1170 2070 Dl 1170 2071 1295 2135 Dl 1692 2031 1438 2035 Dl 5 R f (79)1450 2093 w 10 R f 0.1 setlinewidth 1610 1855 1854 1866 Dl 5 R f (80)1650 1958 w 10 R f 0.1 setlinewidth 1855 1727 1386 1835 Dl 5 R f (81)1757 1813 w 10 R f 0.1 setlinewidth 1064 2182 1474 2300 Dl 1287 2180 1064 2182 Dl 5 R f (83)1348 2244 w 10 R f 0.1 setlinewidth 883 2077 893 2124 Dl 894 2126 1064 2182 Dl 1169 2071 883 2076 Dl 5 R f (84)1070 2135 w 10 R f 0.1 setlinewidth 1069 1853 871 1943 Dl 871 1943 883 2076 Dl 1352 1841 1069 1853 Dl (85)1044 1981 w 1681 1713 1381 1755 Dl 1381 1756 1069 1853 Dl 1837 1704 1681 1713 Dl 5 R f (86)1456 1788 w 20 R f 16 setlinewidth 2736 3018 720 3018 Dl 2736 1002 2736 3018 Dl 720 1002 2736 1002 Dl 720 3018 720 1002 Dl 976 2005 946 2028 Dl 976 2004 931 2063 Dl 976 2005 909 2035 Dl 10 R f 0.1 setlinewidth 4516 2285 4473 2288 Dl 4705 2217 4518 2285 Dl 4733 2203 4705 2216 Dl 4865 2109 4850 2125 Dl 4881 2085 4871 2101 Dl 4870 2102 4865 2109 Dl 4888 2056 4886 2071 Dl 4886 2072 4881 2085 Dl 4879 2015 4884 2029 Dl 4884 2029 4888 2056 Dl 4834 1965 4864 1993 Dl 4864 1994 4879 2014 Dl 4805 1943 4815 1950 Dl 4816 1950 4833 1965 Dl 4763 2184 4733 2202 Dl 4827 2143 4763 2184 Dl 4850 2127 4827 2143 Dl 4843 2120 4826 2141 Dl 4827 2141 4827 2143 Dl 4849 2114 4844 2119 Dl 4871 2103 4849 2115 Dl 4875 2075 4849 2115 Dl 4885 2072 4875 2074 Dl 4867 2057 4869 2069 Dl 4877 2026 4866 2057 Dl 4869 2069 4875 2074 Dl 4878 2026 4884 2029 Dl 4851 1982 4853 1992 Dl 4854 1992 4878 2025 Dl 4852 1983 4864 1993 Dl 4827 1961 4851 1982 Dl 4816 1950 4826 1961 Dl 4860 2070 4859 2071 Dl 4858 2073 4840 2110 Dl 4841 2110 4844 2119 Dl 4868 2069 4860 2071 Dl 4828 1984 4826 2017 Dl 4826 2018 4862 2056 Dl 4829 1985 4853 1992 Dl 4863 2057 4866 2057 Dl 4757 1913 4758 1913 Dl 4757 1914 4764 1919 Dl 4764 1919 4816 1955 Dl 4758 1914 4804 1942 Dl 4816 1956 4826 1961 Dl 4862 2057 4860 2071 Dl 4816 1955 4800 1961 Dl 4800 1961 4828 1984 Dl 4694 1887 4758 1913 Dl 4778 2159 4741 2182 Dl 4742 2183 4763 2184 Dl 4826 2141 4778 2159 Dl 4753 2159 4778 2159 Dl 4791 2122 4753 2158 Dl 4840 2110 4792 2122 Dl 4812 2076 4787 2107 Dl 4787 2107 4792 2122 Dl 4859 2072 4813 2075 Dl 4803 2013 4790 2040 Dl 4791 2041 4810 2074 Dl 4811 2074 4813 2075 Dl 4805 2014 4826 2017 Dl 4792 1958 4776 1960 Dl 4776 1960 4790 2003 Dl 4791 2003 4804 2013 Dl 4793 1959 4800 1961 Dl 4742 1918 4745 1922 Dl 4742 1919 4764 1919 Dl 4746 1923 4793 1958 Dl 4739 2148 4744 2160 Dl 4742 2113 4738 2146 Dl 4753 2158 4744 2160 Dl 4786 2108 4743 2114 Dl 4755 2077 4730 2113 Dl 4731 2114 4743 2114 Dl 4810 2075 4756 2077 Dl 4687 2054 4738 2074 Dl 4754 2039 4687 2054 Dl 4738 2075 4756 2077 Dl 4754 2039 4790 2040 Dl 4726 1994 4728 2010 Dl 4729 2010 4754 2039 Dl 4727 1993 4790 2003 Dl 4728 1949 4710 1986 Dl 4711 1987 4726 1993 Dl 4729 1950 4751 1953 Dl 4752 1953 4776 1960 Dl 4708 1917 4703 1917 Dl 4708 1916 4745 1922 Dl 4703 1917 4751 1953 Dl 4646 1876 4650 1878 Dl 4647 1877 4713 1896 Dl 4714 1897 4721 1899 Dl 4650 1879 4741 1918 Dl 4722 1899 4757 1913 Dl 4646 1868 4694 1887 Dl 4646 1869 4721 1899 Dl 4517 2274 4518 2285 Dl 4686 2201 4516 2273 Dl 4740 2183 4686 2200 Dl 4657 2185 4650 2189 Dl 4650 2190 4686 2200 Dl 4743 2160 4658 2184 Dl 4692 2118 4738 2146 Dl 4730 2113 4692 2118 Dl 4737 2074 4690 2118 Dl 4692 2118 4690 2118 Dl 4728 2010 4670 2053 Dl 4671 2053 4687 2054 Dl 4605 1898 4605 1908 Dl 4607 1898 4703 1917 Dl 4606 1908 4729 1949 Dl 4649 1879 4646 1882 Dl 4647 1883 4708 1916 Dl 4601 1850 4610 1855 Dl 4601 1850 4645 1867 Dl 4611 1856 4713 1896 Dl 4625 2164 4658 2184 Dl 4677 2121 4625 2164 Dl 4689 2119 4677 2120 Dl 4623 2052 4596 2079 Dl 4596 2080 4677 2120 Dl 4623 2053 4670 2053 Dl 4591 2025 4623 2053 Dl 4663 1980 4591 2024 Dl 4663 1979 4710 1986 Dl 4605 1908 4574 1914 Dl 4573 1915 4663 1979 Dl 4599 1891 4605 1897 Dl 4646 1884 4600 1891 Dl 4610 1855 4603 1858 Dl 4603 1859 4646 1876 Dl 4559 1838 4600 1850 Dl 4465 2262 4516 2273 Dl 4520 2226 4464 2261 Dl 4649 2190 4521 2226 Dl 4595 2080 4585 2082 Dl 4585 2083 4499 2160 Dl 4499 2161 4625 2164 Dl 4508 1909 4574 1914 Dl 4506 1910 4503 2003 Dl 4504 2004 4591 2024 Dl 4396 1811 4420 1815 Dl 4421 1815 4603 1858 Dl 4396 1812 4600 1891 Dl 4429 2169 4399 2211 Dl 4399 2212 4521 2226 Dl 4498 2161 4429 2169 Dl 4375 2090 4325 2150 Dl 4325 2151 4429 2169 Dl 4585 2082 4375 2089 Dl 4304 1991 4230 2014 Dl 4230 2014 4375 2089 Dl 4305 1991 4503 2003 Dl 5 R f (69)4409 2050 w 10 R f 0.1 setlinewidth 4207 1858 4304 1991 Dl 4208 1858 4507 1909 Dl 5 R f (70)4349 1946 w 10 R f 0.1 setlinewidth 4256 1786 4395 1811 Dl 4195 1854 4207 1858 Dl 4255 1785 4194 1853 Dl 5 R f (71)4361 1864 w 10 R f 0.1 setlinewidth 4420 1816 4528 1829 Dl 4528 1829 4559 1837 Dl 4504 1824 4528 1829 Dl 4145 2233 4196 2255 Dl 4196 2256 4464 2261 Dl 4399 2211 4145 2233 Dl 3656 1987 3626 1992 Dl 3626 1993 3944 2188 Dl 3658 1987 3969 2007 Dl 3969 2007 4123 2166 Dl 4122 2167 3944 2188 Dl 5 R f (76)3873 2089 w 10 R f 0.1 setlinewidth 3846 1762 4255 1785 Dl 3847 1762 3952 1827 Dl 3952 1828 4194 1853 Dl 5 R f (77)4042 1814 w 10 R f 0.1 setlinewidth 4481 1819 4504 1824 Dl 3944 2188 3933 2204 Dl 3935 2205 4145 2233 Dl 4324 2151 4123 2166 Dl 5 R f (79)4176 2202 w 10 R f 0.1 setlinewidth 3970 2007 4230 2014 Dl 5 R f (80)4155 2093 w 10 R f 0.1 setlinewidth 3951 1828 3657 1986 Dl (81)3968 1953 w 4274 1779 4392 1801 Dl 4392 1801 4481 1819 Dl 4272 1779 4255 1785 Dl 4000 2270 4473 2288 Dl 4195 2256 3999 2269 Dl 3613 2221 3718 2249 Dl 3719 2249 3999 2269 Dl 3932 2205 3613 2220 Dl 5 R f (84)3891 2246 w 10 R f 0.1 setlinewidth 3194 1989 3175 2094 Dl 3175 2094 3613 2220 Dl 3194 1988 3626 1992 Dl (85)3485 2119 w 3619 1745 3247 1791 Dl 3246 1792 3194 1988 Dl 3620 1745 3846 1762 Dl (86)3490 1889 w 3961 1757 4273 1778 Dl 3619 1745 3960 1757 Dl 20 R f 16 setlinewidth 5040 3018 3024 3018 Dl 5040 1002 5040 3018 Dl 3024 1002 5040 1002 Dl 3024 3018 3024 1002 Dl 3284 2022 3249 2058 Dl 3283 2022 3246 2086 Dl 3284 2023 3221 2061 Dl 10 B f (Fig. 34:)1 322 1 971 3216 t 10 R f (dual projective iter 2, outside)4 1168 1 1318 3216 t 10 B f (Fig. 35:)1 322 1 3275 3216 t 10 R f (dual projective iter 3, outside)4 1168 1 3622 3216 t 0.1 setlinewidth 1998 4690 1952 4691 Dl 2239 4616 1998 4689 Dl 2275 4604 2239 4616 Dl 2496 4491 2465 4513 Dl 2534 4459 2509 4481 Dl 2509 4481 2497 4491 Dl 2564 4417 2548 4441 Dl 2549 4442 2535 4458 Dl 2584 4354 2578 4378 Dl 2578 4379 2566 4417 Dl 2554 4279 2575 4325 Dl 2575 4325 2584 4354 Dl 2523 4250 2535 4260 Dl 2535 4260 2553 4279 Dl 2314 4589 2276 4604 Dl 2414 4542 2315 4588 Dl 2465 4514 2414 4542 Dl 2446 4515 2412 4541 Dl 2412 4542 2414 4542 Dl 2456 4507 2446 4514 Dl 2509 4481 2457 4508 Dl 2522 4452 2457 4508 Dl 2547 4442 2522 4452 Dl 2514 4433 2512 4448 Dl 2564 4378 2514 4432 Dl 2512 4449 2522 4452 Dl 2566 4378 2578 4378 Dl 2554 4316 2547 4334 Dl 2547 4334 2565 4378 Dl 2556 4315 2575 4325 Dl 2532 4287 2556 4315 Dl 2534 4260 2531 4287 Dl 2494 4453 2491 4455 Dl 2490 4456 2443 4505 Dl 2444 4505 2446 4514 Dl 2511 4448 2495 4453 Dl 2505 4331 2471 4386 Dl 2473 4386 2509 4432 Dl 2506 4332 2547 4334 Dl 2514 4432 2509 4432 Dl 2461 4217 2457 4218 Dl 2458 4219 2463 4229 Dl 2463 4229 2518 4280 Dl 2462 4217 2522 4249 Dl 2519 4281 2531 4287 Dl 2508 4433 2495 4453 Dl 2517 4281 2476 4302 Dl 2477 4302 2506 4331 Dl 2384 4178 2386 4178 Dl 2387 4179 2462 4217 Dl 2330 4571 2275 4596 Dl 2314 4589 2275 4596 Dl 2412 4542 2331 4570 Dl 2329 4571 2291 4575 Dl 2360 4530 2291 4575 Dl 2443 4506 2361 4530 Dl 2413 4472 2359 4514 Dl 2359 4515 2361 4530 Dl 2491 4456 2413 4471 Dl 2437 4388 2398 4429 Dl 2398 4429 2409 4470 Dl 2411 4470 2413 4471 Dl 2470 4387 2437 4387 Dl 2464 4300 2434 4308 Dl 2433 4309 2422 4375 Dl 2422 4375 2437 4387 Dl 2465 4300 2476 4302 Dl 2419 4241 2419 4248 Dl 2462 4229 2419 4240 Dl 2419 4248 2465 4299 Dl 2382 4176 2384 4177 Dl 2275 4565 2278 4578 Dl 2291 4529 2274 4565 Dl 2291 4575 2278 4578 Dl 2358 4514 2291 4528 Dl 2325 4483 2273 4529 Dl 2291 4528 2273 4529 Dl 2409 4471 2326 4483 Dl 2237 4464 2301 4481 Dl 2344 4433 2237 4464 Dl 2301 4482 2326 4483 Dl 2398 4429 2344 4433 Dl 2328 4373 2322 4396 Dl 2323 4397 2344 4433 Dl 2330 4374 2422 4375 Dl 2365 4303 2309 4367 Dl 2309 4368 2329 4373 Dl 2398 4303 2365 4303 Dl 2399 4303 2434 4308 Dl 2360 4250 2351 4252 Dl 2419 4249 2361 4249 Dl 2352 4252 2399 4303 Dl 2300 4190 2303 4194 Dl 2300 4190 2398 4200 Dl 2398 4201 2409 4203 Dl 2304 4194 2419 4240 Dl 2410 4203 2457 4218 Dl 2321 4158 2386 4178 Dl 2321 4158 2409 4203 Dl 2317 4155 2381 4176 Dl 1989 4687 1998 4689 Dl 2197 4619 1989 4687 Dl 2275 4596 2197 4619 Dl 2155 4613 2145 4617 Dl 2146 4617 2197 4619 Dl 2277 4578 2156 4612 Dl 2219 4541 2274 4565 Dl 2273 4530 2219 4540 Dl 2300 4481 2216 4540 Dl 2218 4540 2216 4540 Dl 2323 4397 2215 4465 Dl 2237 4465 2215 4465 Dl 2213 4245 2203 4265 Dl 2213 4246 2351 4252 Dl 2203 4266 2365 4303 Dl 2303 4194 2293 4203 Dl 2293 4204 2361 4249 Dl 2263 4139 2270 4150 Dl 2263 4139 2321 4157 Dl 2270 4151 2398 4200 Dl 2312 4153 2316 4154 Dl 2119 4594 2156 4612 Dl 2197 4544 2118 4594 Dl 2215 4541 2198 4544 Dl 2151 4472 2106 4507 Dl 2105 4508 2198 4544 Dl 2214 4465 2150 4471 Dl 2120 4439 2150 4471 Dl 2243 4366 2120 4440 Dl 2244 4366 2309 4367 Dl 2202 4266 2152 4284 Dl 2153 4284 2243 4365 Dl 2209 4236 2213 4246 Dl 2292 4204 2208 4236 Dl 2269 4151 2248 4167 Dl 2248 4167 2299 4190 Dl 2212 4123 2311 4153 Dl 2213 4123 2262 4139 Dl 1926 4686 1989 4687 Dl 1987 4658 1926 4686 Dl 2145 4618 1987 4658 Dl 2105 4508 2092 4511 Dl 2091 4510 1969 4599 Dl 2118 4594 1969 4599 Dl 2152 4284 2063 4289 Dl 2063 4289 2017 4422 Dl 2018 4423 2120 4440 Dl 5 R f (64)2095 4372 w 10 R f 0.1 setlinewidth 2004 4139 1972 4139 Dl 2006 4140 2248 4167 Dl 1972 4139 2208 4236 Dl 1889 4612 1854 4650 Dl 1855 4651 1987 4658 Dl 1969 4600 1890 4612 Dl 1845 4536 1783 4599 Dl 1783 4600 1890 4612 Dl 2091 4511 1845 4535 Dl 5 R f (68)1901 4573 w 10 R f 0.1 setlinewidth 1788 4430 1704 4463 Dl 1705 4463 1845 4535 Dl 2017 4423 1789 4429 Dl 5 R f (69)1909 4483 w 10 R f 0.1 setlinewidth 1715 4264 1789 4429 Dl 1714 4264 2063 4289 Dl 5 R f (70)1866 4356 w 10 R f 0.1 setlinewidth 1802 4128 1972 4139 Dl 1701 4260 1714 4263 Dl 1801 4128 1700 4260 Dl 5 R f (71)1921 4228 w 10 R f 0.1 setlinewidth 2171 4113 2005 4139 Dl 2171 4113 2212 4122 Dl 2142 4108 2172 4113 Dl 1608 4675 1657 4688 Dl 1658 4688 1926 4686 Dl 1853 4651 1607 4674 Dl 1196 4469 1173 4476 Dl 1174 4477 1434 4642 Dl 1197 4470 1456 4472 Dl 1456 4473 1588 4619 Dl 1588 4620 1434 4642 Dl 5 R f (76)1374 4555 w 10 R f 0.1 setlinewidth 1801 4128 1357 4169 Dl 1358 4169 1452 4256 Dl 1452 4258 1700 4260 Dl 5 R f (77)1561 4207 w 10 R f 0.1 setlinewidth 2113 4102 2141 4106 Dl 1433 4643 1425 4655 Dl 1425 4655 1607 4674 Dl 1782 4599 1588 4619 Dl 5 R f (79)1650 4648 w 10 R f 0.1 setlinewidth 1704 4463 1456 4472 Dl 5 R f (80)1629 4545 w 10 R f 0.1 setlinewidth 1451 4257 1196 4469 Dl (81)1478 4395 w 1848 4079 1998 4088 Dl 1998 4089 2112 4102 Dl 1847 4079 1801 4127 Dl 1491 4692 1952 4691 Dl 1657 4688 1490 4692 Dl 1189 4660 1269 4676 Dl 1269 4677 1490 4692 Dl 1424 4656 1188 4661 Dl 874 4478 882 4560 Dl 882 4562 1188 4661 Dl 1172 4476 874 4478 Dl 5 R f (85)1108 4576 w 10 R f 0.1 setlinewidth 1153 4165 871 4256 Dl 872 4256 874 4478 Dl 1154 4166 1357 4169 Dl (86)1077 4339 w 1846 4078 1494 4090 Dl 1494 4091 1154 4165 Dl 5 R f (87)1512 4134 w 20 R f 16 setlinewidth 2736 5394 720 5394 Dl 2736 3378 2736 5394 Dl 720 3378 2736 3378 Dl 720 5394 720 3378 Dl 954 4325 952 4384 Dl 955 4326 969 4398 Dl 954 4325 933 4396 Dl 10 R f 0.1 setlinewidth 4738 4537 4686 4567 Dl 4750 4528 4739 4536 Dl 4840 4457 4750 4527 Dl 4854 4433 4844 4453 Dl 4888 4359 4854 4433 Dl 4842 4454 4840 4456 Dl 4886 4276 4888 4301 Dl 4888 4301 4888 4359 Dl 4865 4237 4885 4275 Dl 4832 4462 4829 4464 Dl 4827 4465 4750 4526 Dl 4750 4526 4739 4536 Dl 4843 4454 4832 4462 Dl 4867 4298 4840 4375 Dl 4841 4376 4851 4434 Dl 4868 4299 4888 4301 Dl 4853 4434 4851 4434 Dl 4769 4148 4770 4148 Dl 4771 4149 4785 4161 Dl 4785 4162 4856 4229 Dl 4857 4229 4865 4237 Dl 4850 4434 4832 4462 Dl 4855 4229 4843 4259 Dl 4843 4259 4867 4298 Dl 4653 4103 4769 4147 Dl 4686 4568 4609 4604 Dl 4608 4604 4582 4613 Dl 4674 4561 4582 4613 Dl 4749 4527 4674 4560 Dl 4761 4488 4687 4542 Dl 4686 4543 4674 4560 Dl 4828 4464 4762 4488 Dl 4812 4378 4765 4435 Dl 4764 4436 4759 4487 Dl 4760 4487 4762 4488 Dl 4840 4376 4813 4378 Dl 4833 4256 4808 4269 Dl 4808 4270 4800 4362 Dl 4801 4363 4813 4378 Dl 4834 4257 4843 4259 Dl 4764 4178 4769 4188 Dl 4785 4162 4763 4177 Dl 4769 4188 4834 4256 Dl 4576 4604 4569 4617 Dl 4618 4564 4576 4604 Dl 4581 4613 4569 4617 Dl 4686 4543 4619 4563 Dl 4675 4509 4602 4566 Dl 4618 4564 4602 4566 Dl 4759 4488 4676 4508 Dl 4598 4489 4652 4507 Dl 4710 4443 4597 4489 Dl 4653 4508 4676 4508 Dl 4765 4437 4711 4444 Dl 4707 4365 4697 4396 Dl 4697 4397 4711 4444 Dl 4800 4362 4708 4364 Dl 4739 4266 4687 4357 Dl 4688 4357 4708 4364 Dl 4772 4264 4739 4265 Dl 4773 4264 4808 4269 Dl 4712 4190 4705 4195 Dl 4767 4188 4713 4190 Dl 4706 4196 4772 4264 Dl 4618 4113 4625 4118 Dl 4618 4113 4706 4125 Dl 4707 4125 4718 4128 Dl 4625 4120 4763 4177 Dl 4718 4129 4770 4148 Dl 4583 4078 4652 4103 Dl 4584 4077 4718 4128 Dl 4442 4659 4428 4663 Dl 4568 4617 4441 4658 Dl 4547 4581 4576 4604 Dl 4601 4566 4546 4581 Dl 4651 4507 4543 4581 Dl 4545 4581 4543 4581 Dl 4696 4396 4575 4491 Dl 4597 4489 4575 4491 Dl 4563 4193 4561 4221 Dl 4563 4193 4705 4195 Dl 4561 4221 4739 4265 Dl 4624 4119 4620 4131 Dl 4620 4131 4713 4190 Dl 4518 4056 4541 4067 Dl 4517 4056 4583 4077 Dl 4541 4068 4706 4125 Dl 4421 4643 4441 4658 Dl 4526 4587 4421 4643 Dl 4544 4582 4526 4586 Dl 4507 4503 4450 4548 Dl 4451 4548 4526 4586 Dl 4574 4492 4508 4502 Dl 4480 4462 4508 4502 Dl 4617 4359 4480 4463 Dl 4686 4358 4617 4358 Dl 5 R f (57)4568 4437 w 10 R f 0.1 setlinewidth 4561 4221 4510 4249 Dl 4510 4250 4617 4358 Dl 5 R f (58)4603 4298 w 10 R f 0.1 setlinewidth 4554 4180 4564 4193 Dl 4620 4132 4554 4179 Dl 4541 4068 4546 4086 Dl 4546 4086 4617 4113 Dl 4447 4041 4517 4056 Dl 4252 4703 4165 4721 Dl 4426 4663 4252 4703 Dl 4449 4548 4434 4553 Dl 4433 4553 4274 4653 Dl 4420 4643 4274 4653 Dl 4509 4249 4407 4261 Dl 4406 4262 4365 4444 Dl 4366 4445 4480 4463 Dl 5 R f (64)4451 4367 w 10 R f 0.1 setlinewidth 4273 4064 4240 4065 Dl 4274 4064 4546 4086 Dl 4241 4066 4554 4179 Dl 5 R f (65)4446 4123 w 10 R f 0.1 setlinewidth 4191 4668 4137 4702 Dl 4137 4702 4252 4703 Dl 4274 4655 4192 4668 Dl 4166 4587 4090 4656 Dl 4090 4657 4192 4668 Dl 4433 4552 4165 4586 Dl 5 R f (68)4220 4623 w 10 R f 0.1 setlinewidth 4111 4460 4021 4504 Dl 4021 4504 4165 4586 Dl 4365 4445 4112 4460 Dl 5 R f (69)4247 4519 w 10 R f 0.1 setlinewidth 4006 4247 4112 4460 Dl 4006 4246 4407 4261 Dl (70)4167 4365 w 4048 4063 4240 4065 Dl 3990 4242 4006 4246 Dl 4046 4063 3989 4242 Dl (71)4201 4192 w 4393 4032 4273 4064 Dl 4395 4032 4446 4040 Dl 4353 4028 4394 4031 Dl 3897 4722 3930 4728 Dl 4165 4722 3930 4728 Dl 4137 4703 3897 4721 Dl 3512 4520 3492 4527 Dl 3492 4527 3746 4694 Dl 3512 4519 3762 4519 Dl 3762 4520 3893 4675 Dl 3892 4675 3746 4694 Dl 5 R f (76)3685 4605 w 10 R f 0.1 setlinewidth 4046 4062 3590 4152 Dl 3590 4153 3717 4253 Dl 3989 4242 3717 4253 Dl 5 R f (77)3820 4180 w 10 R f 0.1 setlinewidth 4317 4026 4353 4028 Dl 3746 4694 3737 4704 Dl 3738 4706 3897 4721 Dl 4090 4657 3893 4675 Dl 5 R f (79)3953 4699 w 10 R f 0.1 setlinewidth 4021 4505 3762 4519 Dl 5 R f (80)3941 4595 w 10 R f 0.1 setlinewidth 3716 4255 3511 4519 Dl (81)3784 4415 w 4182 4018 4026 4018 Dl 4184 4019 4317 4025 Dl 4027 4019 4047 4062 Dl 3768 4721 3930 4728 Dl 3523 4696 3584 4704 Dl 3584 4705 3767 4720 Dl 3522 4694 3737 4704 Dl 3233 4526 3260 4599 Dl 3261 4599 3522 4695 Dl 3491 4526 3233 4525 Dl 5 R f (85)3448 4620 w 10 R f 0.1 setlinewidth 3390 4169 3175 4290 Dl 3175 4291 3233 4525 Dl 3590 4154 3390 4169 Dl (86)3380 4359 w 4026 4018 3662 4072 Dl 3662 4074 3390 4169 Dl 5 R f (87)3729 4102 w 20 R f 16 setlinewidth 5040 5394 3024 5394 Dl 5040 3378 5040 5394 Dl 3024 3378 5040 3378 Dl 3024 5394 3024 3378 Dl 3226 4287 3259 4359 Dl 3226 4286 3272 4344 Dl 3227 4287 3239 4359 Dl 10 B f (Fig. 36:)1 322 1 971 5592 t 10 R f (dual projective iter 4, outside)4 1168 1 1318 5592 t 10 B f (Fig. 37:)1 322 1 3275 5592 t 10 R f (dual projective iter 5, outside)4 1168 1 3622 5592 t (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 17 18 %%Page: 18 19 /saveobj save def mark 19 pagesetup 10 R f (- 18 -)2 216 1 2772 282 t 0.1 setlinewidth 988 1554 1072 1587 Dl 2580 1554 2580 1556 Dl 2508 1439 2556 1497 Dl 2558 1497 2573 1535 Dl 2314 1312 2340 1324 Dl 2573 1535 2579 1554 Dl 2478 1409 2507 1439 Dl 2584 1577 2574 1615 Dl 2580 1557 2584 1577 Dl 2557 1501 2571 1543 Dl 2571 1543 2584 1576 Dl 2556 1498 2556 1500 Dl 2475 1407 2482 1418 Dl 2482 1418 2545 1490 Dl 2546 1490 2556 1500 Dl 2476 1407 2478 1409 Dl 2365 1339 2381 1349 Dl 2340 1325 2365 1339 Dl 2382 1349 2475 1406 Dl 2548 1659 2544 1666 Dl 2563 1633 2548 1658 Dl 2574 1615 2564 1633 Dl 2571 1596 2561 1636 Dl 2563 1634 2561 1636 Dl 2583 1577 2571 1596 Dl 2548 1592 2566 1598 Dl 2560 1553 2547 1591 Dl 2571 1596 2566 1598 Dl 2570 1543 2560 1552 Dl 2521 1497 2533 1520 Dl 2534 1521 2560 1552 Dl 2545 1490 2520 1496 Dl 2458 1417 2509 1491 Dl 2509 1492 2520 1496 Dl 2467 1414 2457 1416 Dl 2467 1415 2482 1418 Dl 2368 1351 2370 1355 Dl 2381 1349 2366 1351 Dl 2369 1355 2466 1414 Dl 2220 1277 2232 1282 Dl 2219 1276 2260 1290 Dl 2260 1290 2268 1293 Dl 2232 1282 2365 1339 Dl 2269 1294 2313 1312 Dl 2513 1701 2507 1704 Dl 2544 1666 2514 1700 Dl 2549 1651 2548 1658 Dl 2560 1636 2550 1650 Dl 2565 1597 2550 1650 Dl 2550 1650 1 1 De 2533 1520 2540 1594 Dl 2545 1592 2540 1594 Dl 2308 1354 2340 1380 Dl 2309 1353 2370 1355 Dl 2341 1380 2457 1416 Dl 2232 1282 2248 1294 Dl 2248 1294 2366 1351 Dl 2032 1212 2078 1225 Dl 2079 1226 2260 1290 Dl 2514 1696 2514 1700 Dl 2545 1655 2514 1696 Dl 2549 1651 2545 1655 Dl 2523 1607 2516 1640 Dl 2516 1640 2545 1655 Dl 2540 1595 2523 1607 Dl 2491 1582 2523 1607 Dl 2484 1496 2491 1581 Dl 2509 1492 2484 1496 Dl 2341 1381 2343 1408 Dl 2344 1409 2484 1496 Dl 2284 1342 2307 1354 Dl 2249 1294 2285 1340 Dl 2079 1224 2133 1244 Dl 2133 1245 2219 1275 Dl 1943 1190 2031 1211 Dl 2507 1705 2435 1741 Dl 2515 1640 2510 1644 Dl 2510 1645 2462 1717 Dl 2513 1697 2462 1717 Dl 2342 1409 2293 1421 Dl 2294 1422 2422 1576 Dl 2422 1576 2491 1581 Dl 1898 1205 1873 1205 Dl 1899 1205 2133 1244 Dl 1874 1204 2285 1340 Dl 2428 1734 2396 1755 Dl 2434 1742 2396 1755 Dl 2461 1717 2428 1733 Dl 2392 1690 2376 1738 Dl 2428 1733 2376 1738 Dl 2510 1644 2392 1689 Dl 2283 1606 2257 1647 Dl 2258 1647 2392 1689 Dl 2422 1576 2284 1606 Dl 5 R f (69)2373 1639 w 10 R f 0.1 setlinewidth 1970 1414 2284 1606 Dl 1970 1414 2293 1421 Dl 5 R f (70)2202 1506 w 10 R f 0.1 setlinewidth 1675 1189 1873 1205 Dl 1948 1410 1969 1414 Dl 1675 1188 1948 1409 Dl (71)1968 1341 w 1885 1177 1898 1205 Dl 1885 1178 1943 1190 Dl 1836 1169 1884 1176 Dl 2396 1754 2264 1790 Dl 1839 1709 1828 1717 Dl 1829 1717 2171 1797 Dl 2068 1682 1840 1708 Dl 2070 1682 2262 1769 Dl 2261 1770 2171 1797 Dl 5 R f (76)2035 1745 w 10 R f 0.1 setlinewidth 1673 1189 1260 1292 Dl 1261 1292 1669 1427 Dl 1674 1188 1 1 De 1948 1409 1669 1427 Dl (77)1577 1338 w 1795 1165 1836 1170 Dl 2171 1797 2166 1803 Dl 2263 1791 2166 1803 Dl 2375 1738 2262 1769 Dl 2257 1647 2069 1681 Dl 5 R f (80)2227 1714 w 10 R f 0.1 setlinewidth 1669 1428 1840 1708 Dl (81)1908 1578 w 1473 1131 1644 1146 Dl 1644 1146 1794 1164 Dl 1474 1130 1674 1188 Dl 2165 1804 1960 1817 Dl 1497 1738 1606 1786 Dl 1606 1787 1960 1817 Dl 1827 1718 1496 1738 Dl 5 R f (85)1800 1779 w 10 R f 0.1 setlinewidth 937 1310 871 1484 Dl 871 1484 1496 1738 Dl 1259 1292 937 1309 Dl (86)1306 1528 w 1472 1131 1059 1180 Dl 1059 1180 937 1309 Dl (87)1229 1238 w 1073 1588 1606 1786 Dl 872 1484 987 1553 Dl 20 R f 16 setlinewidth 2736 2502 720 2502 Dl 2736 486 2736 2502 Dl 720 486 2736 486 Dl 720 2502 720 486 Dl 920 1456 925 1472 Dl 920 1456 959 1518 Dl 920 1456 925 1530 Dl 10 R f 0.1 setlinewidth 4641 1665 4181 1870 Dl 4666 1654 4641 1664 Dl 4744 1619 4667 1653 Dl 3999 1939 3973 1946 Dl 4053 1920 4000 1939 Dl 4180 1871 4053 1920 Dl 4765 1601 4744 1618 Dl 4834 1545 4765 1601 Dl 4850 1529 4844 1536 Dl 4842 1536 4834 1544 Dl 4854 1521 4849 1528 Dl 4799 1568 4765 1601 Dl 4851 1523 4800 1568 Dl 4852 1523 4844 1536 Dl 4869 1498 4857 1514 Dl 4857 1515 4852 1522 Dl 4870 1497 4855 1520 Dl 4881 1477 4871 1497 Dl 4886 1461 4881 1476 Dl 4888 1454 4876 1482 Dl 4875 1482 4870 1497 Dl 4888 1454 4886 1461 Dl 4845 1509 4815 1537 Dl 4814 1538 4800 1568 Dl 4846 1509 4857 1514 Dl 4845 1494 4846 1509 Dl 4865 1469 4844 1493 Dl 4867 1468 4876 1482 Dl 4882 1430 4870 1450 Dl 4869 1450 4867 1468 Dl 4881 1429 4888 1453 Dl 4860 1389 4866 1396 Dl 4866 1397 4880 1427 Dl 4881 1427 4881 1429 Dl 4850 1379 4860 1389 Dl 4843 1477 4842 1492 Dl 4853 1442 4843 1477 Dl 4841 1493 4844 1493 Dl 4854 1443 4870 1450 Dl 4859 1412 4848 1437 Dl 4847 1438 4852 1442 Dl 4859 1412 4880 1427 Dl 4823 1370 4851 1403 Dl 4823 1370 4849 1382 Dl 4851 1403 4859 1411 Dl 4850 1382 4866 1396 Dl 4813 1346 4823 1356 Dl 4822 1357 4849 1382 Dl 4812 1345 4848 1378 Dl 4800 1338 4812 1346 Dl 4687 1620 4667 1653 Dl 4792 1543 4687 1620 Dl 4815 1537 4792 1542 Dl 4804 1497 4799 1501 Dl 4799 1502 4792 1542 Dl 4841 1491 4804 1496 Dl 4832 1432 4843 1477 Dl 4832 1432 4848 1437 Dl 4851 1403 4831 1431 Dl 4831 1432 1 1 De 4822 1356 4814 1362 Dl 4815 1364 4823 1369 Dl 4795 1467 4804 1496 Dl 4825 1430 4795 1467 Dl 4826 1430 4831 1431 Dl 4787 1349 4778 1371 Dl 4779 1371 4825 1429 Dl 4788 1348 4814 1362 Dl 4752 1321 4788 1348 Dl 4765 1316 4751 1321 Dl 4766 1317 4799 1337 Dl 4627 1268 4765 1316 Dl 4685 1584 4687 1620 Dl 4727 1534 4684 1583 Dl 4798 1502 4728 1533 Dl 4778 1372 4772 1373 Dl 4771 1373 4728 1451 Dl 4729 1452 4795 1467 Dl 4560 1249 4626 1267 Dl 4560 1249 4667 1297 Dl 4667 1297 4751 1321 Dl 4688 1458 4670 1509 Dl 4670 1509 4728 1533 Dl 4727 1452 4687 1458 Dl 4625 1376 4618 1438 Dl 4618 1440 4687 1458 Dl 4772 1373 4626 1375 Dl 4482 1278 4443 1302 Dl 4444 1302 4626 1375 Dl 4482 1278 4667 1297 Dl 5 R f (69)4600 1339 w 10 R f 0.1 setlinewidth 4138 1183 4482 1277 Dl 4138 1184 4559 1249 Dl 4112 1182 4137 1183 Dl 4530 1545 4556 1576 Dl 4556 1576 4684 1583 Dl 4670 1509 4530 1544 Dl 3881 1364 3871 1377 Dl 3872 1377 4392 1508 Dl 4198 1333 3882 1363 Dl 4197 1334 4489 1472 Dl 4490 1472 4392 1508 Dl 5 R f (76)4174 1422 w 10 R f 0.1 setlinewidth 3739 1203 3430 1290 Dl 4111 1182 3740 1202 Dl 4391 1508 4395 1526 Dl 4397 1527 4530 1544 Dl 4617 1439 4489 1472 Dl 5 R f (79)4527 1505 w 10 R f 0.1 setlinewidth 4441 1303 4197 1333 Dl 5 R f (80)4421 1390 w 10 R f 0.1 setlinewidth 3741 1202 3882 1363 Dl (81)4025 1287 w 4446 1631 4641 1664 Dl 4556 1576 4446 1630 Dl 4223 1618 4296 1643 Dl 4446 1630 4296 1643 Dl 4395 1527 4222 1617 Dl 5 R f (84)4372 1598 w 10 R f 0.1 setlinewidth 3595 1550 3833 1641 Dl 4221 1618 3833 1641 Dl 3869 1378 3594 1550 Dl (85)3934 1545 w 3218 1444 3175 1599 Dl 3594 1551 3175 1599 Dl 3431 1291 3219 1443 Dl (86)3478 1431 w 4295 1644 4053 1920 Dl 5 R f (89)4313 1748 w 10 R f 0.1 setlinewidth 3833 1641 4000 1939 Dl (90)4003 1759 w 3175 1598 3973 1946 Dl (91)3596 1727 w 20 R f 16 setlinewidth 5040 2502 3024 2502 Dl 5040 486 5040 2502 Dl 3024 486 5040 486 Dl 3024 2502 3024 486 Dl 3270 1494 3232 1573 Dl 3270 1494 3255 1566 Dl 3270 1494 3223 1550 Dl 10 B f (Fig. 38:)1 322 1 971 2700 t 10 R f (dual projective iter 6, outside)4 1168 1 1318 2700 t 10 B f (Fig. 39:)1 322 1 3275 2700 t 10 R f (dual projective iter 7, outside)4 1168 1 3622 2700 t 0.1 setlinewidth 2431 3989 2430 3989 Dl 2429 3990 2421 3992 Dl 2420 3993 2413 3995 Dl 2206 4054 1794 4190 Dl 2235 4046 2207 4054 Dl 2349 4009 2234 4044 Dl 2421 3993 2350 4010 Dl 2412 3996 1794 4190 Dl 1646 4232 1630 4234 Dl 1687 4220 1646 4230 Dl 1794 4189 1688 4219 Dl 2377 3995 2350 4010 Dl 2491 3939 2377 3995 Dl 2492 3938 2430 3989 Dl 2522 3922 2504 3931 Dl 2504 3931 2492 3938 Dl 2521 3921 2431 3988 Dl 2548 3903 2533 3913 Dl 2533 3914 2522 3921 Dl 2549 3902 2431 3988 Dl 2566 3887 2549 3902 Dl 2418 3967 2377 3995 Dl 2497 3924 2419 3967 Dl 2498 3924 2504 3931 Dl 2529 3899 2503 3917 Dl 2502 3918 2497 3924 Dl 2534 3898 2530 3899 Dl 2533 3898 2533 3913 Dl 2574 3872 2534 3898 Dl 2573 3872 2566 3887 Dl 2584 3849 2580 3858 Dl 2579 3859 2574 3871 Dl 2578 3853 2577 3853 Dl 2576 3853 2538 3885 Dl 2538 3886 2530 3899 Dl 2578 3853 2580 3858 Dl 2576 3803 2584 3845 Dl 2584 3845 2584 3848 Dl 2584 3846 2579 3853 Dl 2470 3918 2424 3944 Dl 2424 3945 2419 3967 Dl 2502 3917 2469 3918 Dl 2459 3908 2469 3918 Dl 2505 3880 2459 3907 Dl 2507 3880 2538 3885 Dl 2550 3837 2513 3862 Dl 2513 3863 2506 3880 Dl 2551 3838 2577 3853 Dl 2562 3788 2546 3803 Dl 2547 3804 2549 3835 Dl 2550 3836 2550 3837 Dl 2563 3789 2575 3802 Dl 2530 3760 2552 3778 Dl 2553 3779 2563 3789 Dl 2455 3896 2453 3908 Dl 2477 3861 2455 3894 Dl 2459 3908 2453 3908 Dl 2477 3861 2513 3862 Dl 2504 3828 2468 3858 Dl 2468 3859 2477 3861 Dl 2505 3828 2549 3835 Dl 2451 3795 2490 3822 Dl 2515 3795 2451 3795 Dl 2490 3823 2504 3828 Dl 2516 3794 2546 3803 Dl 2494 3754 2494 3767 Dl 2495 3768 2515 3795 Dl 2493 3754 2552 3778 Dl 2482 3739 2477 3746 Dl 2478 3747 2494 3754 Dl 2483 3739 2505 3748 Dl 2505 3748 2530 3759 Dl 2245 4021 2234 4044 Dl 2382 3953 2246 4021 Dl 2423 3945 2382 3953 Dl 2383 3920 2376 3924 Dl 2376 3925 2382 3953 Dl 2452 3908 2384 3920 Dl 2437 3858 2455 3894 Dl 2437 3858 2468 3858 Dl 2490 3821 2435 3857 Dl 2436 3858 2437 3858 Dl 2495 3768 2436 3791 Dl 2436 3792 2451 3795 Dl 2316 3687 2483 3738 Dl 2368 3897 2384 3920 Dl 2424 3859 2368 3897 Dl 2434 3858 2424 3858 Dl 2389 3784 2360 3811 Dl 2360 3812 2424 3858 Dl 2390 3785 2436 3791 Dl 2351 3760 2389 3785 Dl 2424 3732 2352 3759 Dl 2425 3732 2477 3746 Dl 2281 3680 2316 3686 Dl 2280 3680 2424 3731 Dl 2227 3998 2246 4021 Dl 2273 3959 2226 3998 Dl 2375 3925 2273 3958 Dl 2359 3812 2349 3814 Dl 2349 3814 2267 3893 Dl 2268 3894 2368 3897 Dl 2181 3674 2280 3679 Dl 2181 3674 2240 3745 Dl 2242 3746 2352 3759 Dl 2209 3905 2189 3946 Dl 2189 3946 2273 3958 Dl 2266 3894 2210 3904 Dl 2138 3840 2118 3896 Dl 2119 3897 2210 3904 Dl 2349 3815 2139 3839 Dl 1990 3754 1929 3787 Dl 1930 3788 2139 3839 Dl 2239 3745 1990 3754 Dl 5 R f (69)2145 3797 w 10 R f 0.1 setlinewidth 1657 3659 1990 3754 Dl 1657 3659 2181 3674 Dl 5 R f (70)1974 3714 w 10 R f 0.1 setlinewidth 1629 3659 1657 3659 Dl 2020 3984 2060 4003 Dl 2226 3998 2060 4003 Dl 2188 3946 2019 3983 Dl 1351 3884 1344 3895 Dl 1344 3895 1857 3967 Dl 1656 3838 1352 3884 Dl 1656 3838 1965 3933 Dl 1965 3933 1857 3967 Dl 5 R f (76)1644 3913 w 10 R f 0.1 setlinewidth 1243 3716 1005 3778 Dl 1629 3659 1244 3715 Dl 1858 3968 1864 3980 Dl 1864 3981 2019 3983 Dl 2117 3896 1965 3933 Dl 5 R f (79)2024 3954 w 10 R f 0.1 setlinewidth 1928 3788 1656 3837 Dl 5 R f (80)1907 3867 w 10 R f 0.1 setlinewidth 1244 3716 1352 3884 Dl (81)1526 3784 w 1952 4046 2207 4054 Dl 2059 4003 1951 4044 Dl 1711 4048 1794 4060 Dl 1951 4045 1794 4060 Dl 1863 3981 1710 4047 Dl 5 R f (84)1865 4029 w 10 R f 0.1 setlinewidth 1155 4016 1370 4068 Dl 1709 4047 1370 4068 Dl 1343 3896 1155 4016 Dl (85)1441 4009 w 871 3903 872 4026 Dl 1154 4016 872 4026 Dl 1005 3778 871 3903 Dl (86)1052 3906 w 1793 4060 1688 4219 Dl 5 R f (89)1877 4118 w 10 R f 0.1 setlinewidth 1371 4068 1646 4230 Dl 5 R f (90)1587 4128 w 10 R f 0.1 setlinewidth 873 4027 1630 4234 Dl 5 R f (91)1246 4108 w 20 R f 16 setlinewidth 2736 4878 720 4878 Dl 2736 2862 2736 4878 Dl 720 2862 2736 2862 Dl 720 4878 720 2862 Dl 911 3900 924 3943 Dl 911 3900 949 3963 Dl 911 3900 915 3974 Dl 10 R f 0.1 setlinewidth 4876 3805 4869 3837 Dl 4888 3721 4888 3754 Dl 4887 3754 4877 3805 Dl 4888 3679 4888 3720 Dl 4859 3569 4865 3584 Dl 4823 3941 4805 3970 Dl 4829 3931 4824 3940 Dl 4863 3858 4828 3931 Dl 4869 3837 4864 3857 Dl 4867 3838 4863 3857 Dl 4886 3755 4867 3838 Dl 4887 3754 4887 3755 Dl 4886 3664 4886 3692 Dl 4887 3693 4887 3755 Dl 4887 3664 4888 3679 Dl 4877 3619 4887 3664 Dl 4866 3585 4878 3618 Dl 4856 3869 4855 3872 Dl 4855 3874 4826 3935 Dl 4826 3935 4824 3940 Dl 4863 3858 4857 3870 Dl 4872 3692 4856 3787 Dl 4856 3788 4865 3840 Dl 4884 3692 4872 3692 Dl 4867 3838 4865 3840 Dl 4829 3502 1 1 De 4830 3502 4836 3518 Dl 4836 3519 4872 3607 Dl 4830 3503 4858 3569 Dl 4873 3607 4878 3618 Dl 4865 3841 4857 3870 Dl 4872 3607 4860 3644 Dl 4859 3644 4872 3692 Dl 4804 3971 4771 4019 Dl 4770 4019 4755 4039 Dl 4789 3985 4755 4039 Dl 4826 3935 4790 3985 Dl 4820 3916 4790 3975 Dl 4790 3975 4790 3985 Dl 4855 3873 4821 3916 Dl 4839 3796 4816 3868 Dl 4817 3869 4819 3915 Dl 4820 3916 4821 3916 Dl 4855 3788 4840 3796 Dl 4853 3641 4837 3661 Dl 4837 3662 4832 3782 Dl 4833 3781 4840 3796 Dl 4855 3641 4860 3644 Dl 4816 3533 4818 3548 Dl 4836 3518 4816 3533 Dl 4818 3549 4854 3641 Dl 4748 4041 4749 4046 Dl 4756 4011 4747 4040 Dl 4754 4039 4749 4046 Dl 4790 3975 4757 4011 Dl 4775 3958 4747 4019 Dl 4756 4012 4747 4019 Dl 4818 3915 4775 3957 Dl 4761 3965 4721 3970 Dl 4785 3891 4721 3970 Dl 4775 3958 4762 3965 Dl 4816 3868 4786 3891 Dl 4773 3804 4771 3844 Dl 4771 3845 4786 3891 Dl 4831 3781 4774 3804 Dl 4791 3664 4759 3800 Dl 4760 3800 4774 3804 Dl 4814 3658 4792 3663 Dl 4815 3657 4837 3661 Dl 4778 3552 4772 3559 Dl 4817 3549 4778 3552 Dl 4772 3560 4814 3657 Dl 4713 3430 4718 3438 Dl 4713 3430 4788 3466 Dl 4790 3465 4797 3471 Dl 4719 3438 4816 3533 Dl 4796 3472 4829 3502 Dl 4718 3402 4797 3471 Dl 4693 4108 4688 4112 Dl 4748 4047 4692 4108 Dl 4746 4041 4718 4049 Dl 4746 4020 4718 4049 Dl 4761 3966 4717 4050 Dl 4718 4049 4717 4050 Dl 4771 3845 4707 3980 Dl 4721 3971 4707 3980 Dl 4648 3559 4645 3609 Dl 4772 3558 4649 3558 Dl 4646 3609 4792 3663 Dl 4717 3440 4711 3458 Dl 4712 3457 4778 3552 Dl 4665 3361 4674 3371 Dl 4666 3360 4718 3402 Dl 4674 3371 4788 3466 Dl 4692 4108 4670 4117 Dl 4706 4060 4670 4117 Dl 4717 4051 4708 4060 Dl 4663 4015 4641 4069 Dl 4707 4060 4641 4069 Dl 4706 3980 4663 4014 Dl 4630 3984 4663 4014 Dl 4709 3818 4630 3985 Dl 4759 3800 4710 3817 Dl 4645 3610 4600 3668 Dl 4600 3668 4710 3817 Dl 5 R f (58)4678 3715 w 10 R f 0.1 setlinewidth 4642 3535 4649 3558 Dl 4711 3458 4641 3535 Dl 4674 3371 4659 3383 Dl 4659 3384 4713 3430 Dl 4618 3339 4665 3360 Dl 4688 4113 4618 4170 Dl 4640 4070 4632 4078 Dl 4632 4078 4585 4176 Dl 4670 4117 4585 4176 Dl 4599 3668 4502 3708 Dl 4503 3709 4534 4000 Dl 4629 3985 4534 4000 Dl 5 R f (64)4569 3844 w 10 R f 0.1 setlinewidth 4303 3301 4355 3305 Dl 4356 3306 4659 3383 Dl 4303 3301 4641 3535 Dl 5 R f (65)4527 3420 w 10 R f 0.1 setlinewidth 4542 4209 4543 4219 Dl 4617 4170 4543 4219 Dl 4584 4176 4541 4209 Dl 4463 4193 4463 4245 Dl 4541 4210 4463 4245 Dl 4631 4078 4462 4192 Dl 4311 4110 4264 4190 Dl 4264 4191 4462 4192 Dl 4534 4000 4311 4109 Dl 5 R f (69)4449 4108 w 10 R f 0.1 setlinewidth 3958 3775 4311 4109 Dl 4502 3708 3957 3774 Dl (70)4255 3902 w 3997 3276 4302 3301 Dl 3927 3769 3957 3774 Dl 3996 3276 3926 3769 Dl (71)4195 3558 w 4578 3323 4355 3305 Dl 4579 3323 4618 3338 Dl 4542 4220 4421 4288 Dl 3753 4405 3753 4415 Dl 4275 4354 3753 4415 Dl 4032 4299 3753 4404 Dl 4033 4299 4352 4308 Dl 4352 4308 4276 4354 Dl 5 R f (76)4037 4358 w 10 R f 0.1 setlinewidth 3996 3276 3220 3621 Dl 3221 3622 3494 3889 Dl 3997 3276 1 1 De 3926 3769 3494 3889 Dl (77)3615 3635 w 4276 4353 4288 4351 Dl 4420 4288 4288 4351 Dl 4462 4245 4352 4308 Dl 4263 4190 4032 4298 Dl 5 R f (80)4260 4261 w 10 R f 0.1 setlinewidth 3494 3889 3753 4404 Dl (81)3839 4090 w 3752 4415 3649 4410 Dl 3176 3729 3327 4050 Dl 3327 4051 3649 4410 Dl 3220 3621 3175 3729 Dl (86)3397 4045 w 20 R f 16 setlinewidth 5040 4878 3024 4878 Dl 5040 2862 5040 4878 Dl 3024 2862 5040 2862 Dl 3024 4878 3024 2862 Dl 3207 3713 3230 3736 Dl 3207 3713 3270 3751 Dl 3208 3712 3245 3776 Dl 10 B f (Fig. 40:)1 322 1 971 5076 t 10 R f (dual projective iter 8, outside)4 1168 1 1318 5076 t 10 B f (Fig. 41:)1 322 1 3275 5076 t 10 R f (dual projective iter 9, outside)4 1168 1 3622 5076 t 0.1 setlinewidth 2420 6231 2416 6269 Dl 2427 6136 2425 6179 Dl 2425 6179 2420 6231 Dl 2425 6004 2428 6091 Dl 2428 6092 2428 6135 Dl 2388 5829 2418 5948 Dl 2419 5949 2421 5968 Dl 2421 5968 2424 6003 Dl 2392 6387 2385 6412 Dl 2394 6377 2392 6387 Dl 2409 6304 2394 6376 Dl 2415 6270 2410 6304 Dl 2409 6295 2408 6312 Dl 2423 6188 2409 6294 Dl 2410 6304 2408 6312 Dl 2425 6179 2423 6188 Dl 2424 6087 2422 6127 Dl 2422 6128 2423 6188 Dl 2425 6087 2428 6091 Dl 2419 6039 2424 6087 Dl 2421 5969 2420 6038 Dl 2386 5819 2388 5829 Dl 2403 6329 2403 6333 Dl 2402 6333 2391 6388 Dl 2391 6387 2391 6388 Dl 2408 6312 2404 6329 Dl 2410 6148 2399 6264 Dl 2401 6263 2408 6299 Dl 2421 6128 2411 6147 Dl 2409 6295 2408 6299 Dl 2401 5883 2400 5887 Dl 2400 5887 2401 5915 Dl 2402 5916 2417 6030 Dl 2401 5882 2418 5948 Dl 2418 6030 2420 6038 Dl 2408 6299 2404 6329 Dl 2416 6029 2404 6101 Dl 2404 6101 2411 6147 Dl 2376 5781 2376 5782 Dl 2381 5802 2385 5819 Dl 2376 5781 2381 5801 Dl 2376 5783 2401 5883 Dl 2376 5781 1 1 De 2385 6412 2368 6469 Dl 2367 6470 2358 6500 Dl 2371 6453 2358 6500 Dl 2391 6389 2372 6453 Dl 2382 6396 2370 6450 Dl 2371 6451 2372 6453 Dl 2403 6334 2383 6395 Dl 2389 6284 2378 6361 Dl 2378 6362 2382 6396 Dl 2382 6396 1 1 De 2399 6264 2389 6284 Dl 2399 6101 2389 6135 Dl 2389 6136 2385 6273 Dl 2384 6274 2389 6284 Dl 2401 6101 2404 6101 Dl 2385 5961 2385 5984 Dl 2401 5915 2385 5961 Dl 2385 5985 2400 6101 Dl 2375 5778 2375 5780 Dl 2354 6509 2352 6510 Dl 2352 6496 2352 6510 Dl 2357 6501 2355 6508 Dl 2370 6450 2353 6495 Dl 2358 6453 2348 6507 Dl 2353 6496 2348 6507 Dl 2382 6396 2359 6452 Dl 2352 6467 2329 6493 Dl 2361 6397 2329 6493 Dl 2359 6454 2352 6467 Dl 2377 6362 2361 6396 Dl 2352 6321 2352 6360 Dl 2352 6360 2361 6396 Dl 2384 6273 2352 6320 Dl 2363 6154 2345 6321 Dl 2352 6321 2345 6321 Dl 2375 6140 2363 6155 Dl 2388 6136 2376 6139 Dl 2360 6006 2356 6018 Dl 2384 5985 2360 6005 Dl 2356 6019 2376 6139 Dl 2330 5824 2332 5839 Dl 2330 5823 2378 5842 Dl 2379 5843 2383 5850 Dl 2333 5839 2385 5961 Dl 2383 5850 2400 5887 Dl 2348 5719 2376 5782 Dl 2348 5719 2383 5850 Dl 2350 5722 2374 5778 Dl 2354 6509 2329 6575 Dl 2352 6510 2334 6543 Dl 2348 6507 2334 6543 Dl 2351 6467 2333 6545 Dl 2333 6543 2333 6545 Dl 2351 6361 2321 6508 Dl 2328 6494 2321 6508 Dl 2280 6057 2278 6130 Dl 2356 6018 2282 6056 Dl 2279 6130 2363 6155 Dl 2332 5838 2327 5873 Dl 2327 5874 2360 6005 Dl 2318 5650 2319 5686 Dl 2318 5651 2347 5718 Dl 2319 5686 2378 5842 Dl 2349 5717 2350 5721 Dl 2328 6576 2315 6601 Dl 2328 6556 2315 6601 Dl 2333 6546 2329 6556 Dl 2298 6555 2291 6601 Dl 2329 6556 2291 6601 Dl 2321 6508 2298 6555 Dl 2279 6542 2298 6555 Dl 2317 6356 2279 6541 Dl 2344 6321 2317 6356 Dl 2278 6130 2252 6216 Dl 2253 6216 2317 6356 Dl 2279 6022 2282 6056 Dl 2326 5874 2278 6022 Dl 2318 5686 2301 5742 Dl 2302 5743 2330 5823 Dl 2293 5594 2348 5717 Dl 2293 5593 2317 5650 Dl 2290 6602 2287 6610 Dl 2286 6611 2273 6677 Dl 2314 6601 2273 6677 Dl 2252 6217 2197 6281 Dl 2197 6281 2228 6580 Dl 2279 6542 2228 6580 Dl 5 R f (64)2228 6402 w 10 R f 0.1 setlinewidth 2057 5614 2097 5618 Dl 2097 5618 2301 5742 Dl 2057 5614 2278 6022 Dl 5 R f (65)2196 5806 w 10 R f 0.1 setlinewidth 2273 6677 2253 6713 Dl 2206 6745 2214 6767 Dl 2253 6713 2214 6767 Dl 2287 6611 2206 6744 Dl 2111 6735 2093 6810 Dl 2206 6745 2093 6810 Dl 2227 6581 2111 6734 Dl 5 R f (69)2176 6685 w 10 R f 0.1 setlinewidth 1836 6449 2111 6734 Dl 2197 6281 1836 6449 Dl (70)2025 6517 w 1799 5526 2057 5613 Dl 1811 6446 1836 6449 Dl 1798 5527 1810 6446 Dl (71)1948 6021 w 2270 5557 2097 5618 Dl 2271 5557 2293 5593 Dl 5 R f (72)2210 5651 w 10 R f 0.1 setlinewidth 2255 5537 2270 5556 Dl 1805 7099 1807 7102 Dl 2127 6873 1807 7102 Dl 1969 6945 1805 7099 Dl 2161 6831 1969 6944 Dl 2163 6832 2129 6873 Dl 1797 5526 1030 6084 Dl 1030 6084 1462 6643 Dl 1798 5526 1 1 De 1809 6446 1462 6643 Dl (77)1464 6143 w 2240 5522 2255 5537 Dl 2213 6767 2162 6831 Dl 2091 6811 1969 6944 Dl 1463 6644 1805 7099 Dl (81)1754 6767 w 2036 5389 2167 5462 Dl 2167 5462 2239 5520 Dl 2036 5390 1797 5526 Dl 5 R f (82)2021 5525 w 10 R f 0.1 setlinewidth 1749 7033 1807 7102 Dl 1042 6109 1386 6563 Dl 1386 6563 1750 7032 Dl 1031 6084 1041 6109 Dl 20 R f 16 setlinewidth 2736 7254 720 7254 Dl 2736 5238 2736 7254 Dl 720 5238 2736 5238 Dl 720 7254 720 5238 Dl 1076 6105 1074 6109 Dl 1076 6105 1049 6174 Dl 1076 6105 1020 6153 Dl 10 R f 0.1 setlinewidth 4847 5876 4847 5896 Dl 4794 6241 4788 6259 Dl 4824 6125 4794 6240 Dl 4844 6017 4837 6060 Dl 4837 6061 4825 6125 Dl 4846 5966 4844 6017 Dl 4847 5895 4847 5966 Dl 4781 6279 4780 6283 Dl 4787 6260 4781 6279 Dl 4827 6081 4796 6207 Dl 4796 6208 4793 6246 Dl 4837 6061 4828 6081 Dl 4794 6241 4793 6246 Dl 4840 5807 4840 5811 Dl 4841 5811 4841 5839 Dl 4842 5840 4847 5957 Dl 4842 5808 4847 5875 Dl 4847 5957 4847 5966 Dl 4792 6246 4781 6279 Dl 4846 5958 4828 6032 Dl 4828 6033 4828 6081 Dl 4811 5712 4841 5808 Dl 4746 6353 4716 6412 Dl 4778 6283 4746 6352 Dl 4782 6230 4752 6315 Dl 4752 6316 4746 6353 Dl 4746 6353 1 1 De 4795 6207 4782 6230 Dl 4824 6032 4808 6068 Dl 4808 6069 4780 6218 Dl 4780 6219 4782 6230 Dl 4825 6032 4828 6032 Dl 4822 5886 4820 5909 Dl 4840 5840 4822 5885 Dl 4821 5910 4825 6032 Dl 4716 6412 4686 6463 Dl 4706 6417 4677 6476 Dl 4684 6464 4677 6476 Dl 4746 6353 4708 6416 Dl 4696 6434 4666 6464 Dl 4726 6356 4666 6464 Dl 4707 6417 4696 6432 Dl 4751 6316 4726 6354 Dl 4734 6272 4724 6315 Dl 4724 6315 4726 6354 Dl 4780 6219 4734 6271 Dl 4775 6090 4724 6272 Dl 4734 6271 4724 6272 Dl 4792 6073 4775 6089 Dl 4808 6070 4793 6073 Dl 4790 5931 4784 5944 Dl 4819 5910 4790 5930 Dl 4784 5945 4793 6073 Dl 4771 5746 4772 5761 Dl 4771 5746 4819 5767 Dl 4820 5768 4824 5775 Dl 4773 5762 4822 5885 Dl 4824 5774 4840 5811 Dl 4785 5650 4811 5711 Dl 4785 5651 4824 5775 Dl 4677 6476 4652 6516 Dl 4696 6432 4651 6518 Dl 4652 6516 4651 6518 Dl 4724 6315 4654 6480 Dl 4666 6464 4654 6480 Dl 4690 5984 4677 6062 Dl 4783 5944 4690 5983 Dl 4676 6062 4775 6089 Dl 4772 5762 4763 5796 Dl 4762 5796 4790 5930 Dl 4755 5588 4758 5618 Dl 4755 5588 4784 5650 Dl 4758 5618 4819 5767 Dl 4642 6531 4609 6578 Dl 4650 6519 4643 6531 Dl 4615 6534 4591 6585 Dl 4642 6531 4591 6585 Dl 4653 6480 4615 6534 Dl 4595 6520 4615 6534 Dl 4683 6312 4595 6520 Dl 4724 6273 4684 6311 Dl 4676 6063 4629 6156 Dl 4629 6155 4684 6311 Dl 5 R f (58)4675 6179 w 10 R f 0.1 setlinewidth 4690 5947 4690 5983 Dl 4763 5796 4690 5947 Dl 4757 5618 4741 5668 Dl 4742 5669 4771 5746 Dl 4724 5539 4754 5587 Dl 4591 6586 4584 6595 Dl 4583 6595 4538 6664 Dl 4608 6580 4538 6664 Dl 4627 6156 4543 6226 Dl 4543 6227 4520 6563 Dl 4595 6520 4520 6563 Dl 5 R f (64)4568 6361 w 10 R f 0.1 setlinewidth 4460 5554 4507 5556 Dl 4507 5556 4741 5668 Dl 4460 5554 4690 5947 Dl 5 R f (65)4617 5737 w 10 R f 0.1 setlinewidth 4538 6664 4502 6702 Dl 4440 6742 4438 6762 Dl 4501 6702 4438 6762 Dl 4583 6595 4441 6743 Dl 4326 6733 4280 6816 Dl 4441 6743 4280 6816 Dl 4519 6564 4327 6733 Dl 5 R f (69)4431 6677 w 10 R f 0.1 setlinewidth 4036 6402 4327 6733 Dl 4543 6227 4035 6402 Dl (70)4287 6485 w 4166 5489 4459 5553 Dl 4004 6397 4035 6402 Dl 4165 5488 4003 6397 Dl (71)4282 5975 w 4698 5508 4507 5556 Dl 4699 5508 4725 5538 Dl 5 R f (72)4638 5589 w 10 R f 0.1 setlinewidth 4678 5493 4698 5507 Dl 3824 7100 3825 7102 Dl 4289 6866 3825 7102 Dl 4077 6952 3823 7100 Dl 4349 6827 4078 6952 Dl 4349 6827 4289 6866 Dl 4164 5489 3216 6022 Dl 3216 6022 3526 6585 Dl 4165 5488 1 1 De 4003 6398 3526 6585 Dl (77)3682 6097 w 4658 5480 4678 5492 Dl 4438 6763 4350 6827 Dl 4280 6817 4078 6952 Dl 3526 6585 3823 7100 Dl (81)3877 6744 w 4423 5389 4571 5438 Dl 4571 5439 4658 5480 Dl 4422 5389 4165 5487 Dl 5 R f (82)4418 5490 w 20 R f 16 setlinewidth 5040 7254 3024 7254 Dl 5040 5238 5040 7254 Dl 3024 5238 5040 5238 Dl 3024 7254 3024 5238 Dl 3248 6030 3263 6041 Dl 3249 6030 3317 6058 Dl 3249 6030 3295 6087 Dl 10 B f (Fig. 42:)1 322 1 946 7452 t 10 R f (dual projective iter 10, outside)4 1218 1 1293 7452 t 10 B f (Fig. 43:)1 322 1 3250 7452 t 10 R f (dual projective iter 11, outside)4 1218 1 3597 7452 t (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 18 19 %%Page: 19 20 /saveobj save def mark 20 pagesetup 10 R f (- 19 -)2 216 1 2772 282 t 0.1 setlinewidth 2473 1291 2455 1404 Dl 2470 1056 2473 1078 Dl 2473 1078 2478 1185 Dl 2478 1186 2479 1241 Dl 2478 1241 2473 1291 Dl 2450 1422 2428 1502 Dl 2428 1502 2417 1542 Dl 2455 1404 2451 1421 Dl 2479 1239 2473 1268 Dl 2472 1269 2452 1409 Dl 2451 1409 2451 1421 Dl 2479 1239 2479 1241 Dl 2473 1106 2473 1126 Dl 2473 1078 2473 1105 Dl 2473 1127 2478 1239 Dl 2417 1543 2394 1599 Dl 2387 1613 2375 1638 Dl 2414 1537 2375 1638 Dl 2393 1599 2388 1612 Dl 2428 1502 2414 1536 Dl 2429 1452 2419 1495 Dl 2419 1495 2414 1536 Dl 2452 1408 2429 1451 Dl 2457 1281 2424 1451 Dl 2425 1451 2429 1451 Dl 2465 1268 2457 1280 Dl 2472 1268 2466 1268 Dl 2460 1137 2458 1147 Dl 2472 1126 2460 1136 Dl 2459 1148 2466 1268 Dl 2438 970 2440 982 Dl 2438 969 2457 1011 Dl 2457 1012 2459 1019 Dl 2440 982 2473 1105 Dl 2459 1020 2469 1056 Dl 2388 1613 2350 1697 Dl 2418 1495 2367 1653 Dl 2374 1638 2367 1653 Dl 2409 1163 2404 1235 Dl 2457 1147 2409 1162 Dl 2403 1235 2457 1280 Dl 2439 983 2437 1010 Dl 2437 1010 2460 1136 Dl 2395 859 2405 877 Dl 2406 878 2457 1011 Dl 2349 1698 2344 1709 Dl 2342 1705 2319 1756 Dl 2343 1710 2319 1756 Dl 2367 1653 2343 1704 Dl 2336 1689 2343 1704 Dl 2400 1486 2334 1689 Dl 2424 1452 2401 1485 Dl 2403 1235 2373 1322 Dl 2373 1323 2401 1485 Dl 2407 1129 2409 1162 Dl 2436 1010 2406 1128 Dl 2406 878 2411 899 Dl 2411 900 2437 969 Dl 2365 823 2394 859 Dl 2319 1757 2314 1766 Dl 2313 1767 2264 1841 Dl 2373 1323 2312 1391 Dl 2312 1391 2283 1733 Dl 2334 1689 2283 1733 Dl 5 R f (64)2315 1529 w 10 R f 0.1 setlinewidth 2204 739 2239 753 Dl 2240 753 2411 899 Dl 2204 738 2406 1128 Dl 5 R f (65)2323 938 w 10 R f 0.1 setlinewidth 2264 1841 2237 1879 Dl 2205 1918 2193 1940 Dl 2236 1880 2193 1940 Dl 2314 1767 2206 1918 Dl 2133 1917 2092 2004 Dl 2205 1918 2092 2004 Dl 2283 1734 2134 1916 Dl 1884 1590 2134 1916 Dl 2312 1391 1883 1589 Dl (70)2086 1661 w 1947 637 2204 738 Dl 1853 1587 1883 1589 Dl 1946 638 1853 1586 Dl (71)2056 1148 w 2240 753 2342 799 Dl 2342 799 2365 824 Dl 1697 2350 1 1 De 2067 2055 1697 2350 Dl 1919 2165 1697 2350 Dl 2119 2011 1919 2165 Dl 2119 2011 2068 2055 Dl 1946 637 974 1278 Dl 974 1279 1359 1865 Dl 1946 637 1 1 De 1852 1587 1359 1865 Dl (77)1480 1316 w 2192 1940 2119 2010 Dl 2091 2005 1919 2165 Dl 1360 1866 1697 2350 Dl (81)1712 1964 w 20 R f 16 setlinewidth 2736 2502 720 2502 Dl 2736 486 2736 2502 Dl 720 486 2736 486 Dl 720 2502 720 486 Dl 995 1281 1018 1295 Dl 996 1280 1066 1303 Dl 995 1281 1046 1334 Dl 10 R f 0.1 setlinewidth 4767 1882 4767 1883 Dl 4767 1883 4767 1885 Dl 4769 1886 4770 1893 Dl 4768 1882 4771 1892 Dl 4771 1892 4770 1893 Dl 4799 2030 4858 2089 Dl 4795 2023 4799 2030 Dl 4779 1975 4795 2023 Dl 4769 1893 4778 1974 Dl 4771 1892 4858 2089 Dl 4770 1881 4865 2070 Dl 4866 2070 4875 2094 Dl 4876 2095 4878 2106 Dl 4877 2107 4875 2110 Dl 4870 2107 4875 2110 Dl 4858 2090 4870 2106 Dl 4769 1879 4769 1880 Dl 4767 1880 4767 1881 Dl 4771 1963 4778 1974 Dl 4741 1897 4771 1963 Dl 4741 1895 4767 1885 Dl 4731 1874 4736 1890 Dl 4737 1890 4741 1896 Dl 4731 1873 4767 1883 Dl 4719 1846 4726 1864 Dl 4726 1865 4731 1874 Dl 4719 1846 4767 1882 Dl 4706 1816 4708 1828 Dl 4708 1828 4718 1846 Dl 4706 1815 4767 1881 Dl 4692 1773 4692 1782 Dl 4693 1783 4706 1815 Dl 4693 1773 4767 1879 Dl 4682 1732 4680 1745 Dl 4681 1745 4693 1773 Dl 4682 1731 4767 1879 Dl 4728 1793 4769 1880 Dl 4666 1697 4687 1718 Dl 4665 1697 4669 1706 Dl 4690 1724 4726 1793 Dl 4687 1719 4690 1724 Dl 4670 1707 4682 1731 Dl 4757 1945 4771 1963 Dl 4733 1902 4757 1945 Dl 4736 1890 4732 1900 Dl 4717 1874 4728 1897 Dl 4728 1897 4732 1900 Dl 4717 1870 4717 1874 Dl 4725 1864 4716 1869 Dl 4698 1822 4716 1869 Dl 4698 1823 4708 1828 Dl 4680 1797 4687 1812 Dl 4682 1772 4680 1797 Dl 4688 1813 4698 1823 Dl 4682 1772 4692 1782 Dl 4659 1715 4656 1720 Dl 4656 1720 4682 1771 Dl 4660 1716 4680 1745 Dl 4641 1681 4659 1715 Dl 4641 1681 4669 1706 Dl 4687 1717 4689 1721 Dl 4687 1718 1 1 De 4689 1722 4690 1724 Dl 4718 1775 4726 1793 Dl 4695 1730 4702 1744 Dl 4689 1722 4694 1729 Dl 4702 1744 4718 1775 Dl 4684 1813 4684 1814 Dl 4685 1815 4708 1863 Dl 4708 1864 4717 1874 Dl 4684 1812 4687 1812 Dl 4629 1690 4636 1734 Dl 4636 1735 4677 1795 Dl 4628 1690 4656 1720 Dl 4678 1795 4680 1797 Dl 4613 1613 4621 1624 Dl 4608 1611 4613 1612 Dl 4608 1611 4631 1665 Dl 4622 1624 4665 1697 Dl 4631 1666 4641 1681 Dl 4677 1794 4684 1812 Dl 4598 1640 4631 1665 Dl 4599 1640 4628 1689 Dl 4634 1631 4641 1643 Dl 4677 1699 4687 1717 Dl 4651 1658 4676 1699 Dl 4622 1624 4633 1631 Dl 4641 1643 4651 1658 Dl 4729 1919 4744 1944 Dl 4745 1944 4757 1945 Dl 4728 1898 4728 1918 Dl 4729 1918 4722 1920 Dl 4704 1881 4722 1920 Dl 4707 1863 4703 1880 Dl 4670 1821 4690 1864 Dl 4691 1865 4703 1880 Dl 4683 1815 4670 1820 Dl 4621 1724 4638 1771 Dl 4639 1772 4669 1818 Dl 4669 1819 4670 1820 Dl 4621 1724 4636 1734 Dl 4575 1624 4590 1630 Dl 4575 1623 4607 1705 Dl 4607 1706 4620 1724 Dl 4591 1630 4598 1640 Dl 4566 1569 4564 1571 Dl 4567 1568 4608 1611 Dl 4565 1571 4590 1630 Dl 4641 1644 4648 1654 Dl 4649 1653 4651 1658 Dl 4717 1772 4718 1775 Dl 4717 1771 1 1 De 4702 1744 4716 1771 Dl 4714 1914 4722 1923 Dl 4689 1880 4713 1913 Dl 4722 1921 4722 1923 Dl 4690 1865 4688 1880 Dl 4661 1833 4686 1882 Dl 4688 1880 4686 1882 Dl 4668 1819 4661 1833 Dl 4624 1815 4654 1833 Dl 4626 1775 4624 1814 Dl 4655 1833 4661 1833 Dl 4637 1772 4626 1774 Dl 4571 1688 4591 1725 Dl 4591 1725 4626 1774 Dl 4571 1687 4607 1705 Dl 4537 1590 4557 1674 Dl 4558 1675 4571 1687 Dl 4537 1591 4555 1603 Dl 4555 1603 4575 1623 Dl 4518 1529 4525 1533 Dl 4526 1534 4564 1571 Dl 4519 1529 4555 1603 Dl 4499 1463 4498 1464 Dl 4500 1464 4588 1576 Dl 4589 1576 4594 1584 Dl 4499 1465 4566 1568 Dl 4595 1584 4613 1612 Dl 4607 1590 4633 1631 Dl 4594 1584 4606 1589 Dl 4648 1655 4657 1667 Dl 4658 1667 4676 1699 Dl 4785 2021 4795 2023 Dl 4749 1963 4784 2021 Dl 4745 1943 4749 1963 Dl 4729 1958 4731 1962 Dl 4732 1962 4749 1963 Dl 4721 1923 4728 1957 Dl 4685 1896 4713 1913 Dl 4685 1882 4685 1896 Dl 4655 1833 4685 1897 Dl 4591 1725 4619 1816 Dl 4624 1814 4619 1816 Dl 4383 1400 4381 1424 Dl 4383 1401 4518 1530 Dl 4381 1424 4537 1590 Dl 4485 1457 4498 1464 Dl 4484 1456 4525 1533 Dl 4560 1525 4584 1555 Dl 4585 1556 4606 1589 Dl 4560 1525 4588 1576 Dl 4666 1683 4691 1725 Dl 4657 1667 4666 1682 Dl 4692 1724 4694 1729 Dl 4713 1952 4728 1957 Dl 4685 1902 4713 1951 Dl 4685 1897 4685 1902 Dl 4609 1829 4638 1879 Dl 4639 1881 4685 1902 Dl 4618 1817 4608 1830 Dl 4569 1793 4608 1830 Dl 4528 1664 4569 1792 Dl 4528 1664 4557 1674 Dl 4380 1425 4356 1443 Dl 4357 1443 4528 1663 Dl 4381 1385 4384 1399 Dl 4380 1385 4484 1456 Dl 4488 1438 4560 1524 Dl 4488 1439 4500 1463 Dl 4598 1574 4657 1667 Dl 4585 1555 4597 1573 Dl 4783 2022 4772 2028 Dl 4751 2008 4772 2028 Dl 4732 1962 4751 2007 Dl 4639 1880 4641 1887 Dl 4641 1887 4708 1983 Dl 4713 1952 4708 1983 Dl 4299 1441 4356 1443 Dl 4300 1440 4531 1792 Dl 4531 1792 4569 1792 Dl 5 R f (64)4422 1624 w 10 R f 0.1 setlinewidth 4145 1073 4229 1159 Dl 4229 1160 4487 1438 Dl 4144 1074 4380 1386 Dl 4717 1771 4722 1781 Dl 4714 2007 4742 2030 Dl 4750 2007 4742 2030 Dl 4708 1984 4714 2008 Dl 4654 1979 4705 2030 Dl 4714 2007 4705 2030 Dl 4641 1887 4653 1979 Dl 4507 1897 4561 1982 Dl 4562 1982 4653 1979 Dl 4530 1793 4506 1897 Dl 5 R f (69)4554 1904 w 10 R f 0.1 setlinewidth 3534 1204 4506 1897 Dl 3535 1204 4299 1440 Dl (70)4096 1553 w 3634 637 4143 1073 Dl 3433 1159 3535 1203 Dl 3634 637 3432 1159 Dl (71)3810 1111 w 4717 1772 4732 1802 Dl 4722 1782 4732 1802 Dl 4773 2078 4762 2089 Dl 4772 2028 4774 2077 Dl 4742 2030 4762 2089 Dl 4641 2297 4656 2302 Dl 4750 2135 4656 2302 Dl 4604 2133 4640 2297 Dl 4728 2091 4605 2132 Dl 4730 2092 4751 2135 Dl 5 R f (76)4647 2190 w 10 R f 0.1 setlinewidth 3190 1821 3194 1846 Dl 3432 1160 3191 1821 Dl 4733 1802 4749 1835 Dl 4751 2135 4759 2135 Dl 4762 2089 4759 2135 Dl 4705 2030 4728 2091 Dl 4562 1983 4605 2132 Dl 5 R f (80)4616 2060 w 10 R f 0.1 setlinewidth 3190 1822 4640 2297 Dl (81)3813 1781 w 4798 2032 4795 2106 Dl 4775 2079 4795 2106 Dl 4802 2148 4796 2174 Dl 4796 2105 4803 2147 Dl 4759 2136 4796 2174 Dl 4810 2260 4775 2344 Dl 4797 2175 4810 2259 Dl 4657 2303 4775 2344 Dl 5 R f (85)4721 2259 w 10 R f 0.1 setlinewidth 4526 2273 4780 2350 Dl 4775 2344 4780 2350 Dl 3194 1847 4525 2273 Dl 5 R f (86)3849 2064 w 10 R f 0.1 setlinewidth 4750 1835 4750 1837 Dl 4870 2106 4803 2147 Dl 4875 2110 4810 2259 Dl 4877 2106 4780 2350 Dl 4751 1837 4865 2070 Dl 20 R f 16 setlinewidth 5040 2502 3024 2502 Dl 5040 486 5040 2502 Dl 3024 486 5040 486 Dl 3024 2502 3024 486 Dl 3214 1850 3226 1830 Dl 3213 1851 3236 1781 Dl 3213 1851 3266 1800 Dl 10 B f (Fig. 44:)1 322 1 946 2700 t 10 R f (dual projective iter 12, outside)4 1218 1 1293 2700 t 10 B f (Fig. 45:)1 322 1 3250 2700 t 10 R f (dual projective iter 13, outside)4 1218 1 3597 2700 t 0.1 setlinewidth 1483 3019 2299 4531 Dl 1479 3013 1054 4303 Dl 1055 4303 2398 4726 Dl 1480 3013 1483 3019 Dl 2301 4531 2398 4726 Dl (77)1596 4034 w 20 R f 16 setlinewidth 2736 4878 720 4878 Dl 2736 2862 2736 4878 Dl 720 2862 2736 2862 Dl 720 4878 720 2862 Dl 1072 4294 1076 4292 Dl 1073 4296 1121 4240 Dl 1072 4295 1141 4269 Dl 10 R f 0.1 setlinewidth 3382 3381 1 1 De 3382 3381 3381 3381 Dl 3380 3381 3379 3381 Dl 3379 3381 3374 3381 Dl 3382 3381 3378 3381 Dl 3379 3381 3374 3381 Dl 3372 3414 3306 3386 Dl 3306 3385 3306 3386 Dl 3317 3381 3306 3384 Dl 3373 3381 3317 3381 Dl 3378 3381 3372 3414 Dl 3444 3430 3389 3381 Dl 3445 3432 3440 3437 Dl 3439 3436 3427 3436 Dl 3426 3436 3408 3431 Dl 3408 3430 3394 3425 Dl 3392 3424 3372 3414 Dl 3388 3381 3387 3381 Dl 3387 3381 3386 3381 Dl 3385 3381 3384 3381 Dl 3317 3380 3317 3381 Dl 3327 3374 3317 3379 Dl 3379 3380 3327 3373 Dl 3330 3373 3326 3373 Dl 3326 3373 1 1 De 3380 3380 3330 3372 Dl 3335 3370 3331 3371 Dl 3331 3372 3330 3372 Dl 3382 3380 3336 3370 Dl 3344 3368 3337 3368 Dl 3338 3369 3336 3370 Dl 3383 3380 3345 3368 Dl 3365 3366 3355 3366 Dl 3355 3366 3345 3368 Dl 3384 3381 3366 3366 Dl 3401 3364 3376 3364 Dl 3375 3364 3366 3366 Dl 3402 3365 3387 3381 Dl 3443 3376 3389 3381 Dl 3472 3368 3418 3362 Dl 3418 3363 3412 3363 Dl 3476 3369 3444 3376 Dl 3475 3368 3473 3368 Dl 3411 3362 3402 3364 Dl 3316 3378 3312 3376 Dl 3314 3372 3312 3376 Dl 3324 3372 3314 3372 Dl 3315 3370 3313 3371 Dl 3314 3371 3313 3371 Dl 3318 3370 3316 3370 Dl 3330 3371 3317 3370 Dl 3328 3368 3317 3370 Dl 3337 3367 3329 3366 Dl 3328 3365 3326 3366 Dl 3352 3364 3329 3364 Dl 3328 3367 3326 3366 Dl 3355 3365 3352 3364 Dl 3373 3360 3363 3360 Dl 3363 3361 3352 3364 Dl 3375 3362 3376 3364 Dl 3385 3358 3374 3360 Dl 3411 3362 3386 3358 Dl 3478 3368 3473 3368 Dl 3478 3369 3476 3369 Dl 3470 3376 3444 3376 Dl 3491 3371 3489 3373 Dl 3491 3371 3479 3369 Dl 3488 3374 3470 3376 Dl 3322 3365 1 1 De 3321 3365 3314 3368 Dl 3315 3369 3314 3368 Dl 3325 3365 3322 3365 Dl 3355 3357 3330 3359 Dl 3329 3359 3327 3364 Dl 3362 3359 3355 3357 Dl 3328 3364 3327 3364 Dl 3437 3355 3435 3354 Dl 3434 3353 3423 3353 Dl 3423 3354 3388 3357 Dl 3437 3356 3418 3362 Dl 3387 3357 3386 3358 Dl 3327 3365 3322 3365 Dl 3387 3357 3364 3354 Dl 3363 3354 3355 3357 Dl 3489 3359 3487 3358 Dl 3485 3366 3479 3368 Dl 3490 3361 3485 3366 Dl 3488 3357 3438 3355 Dl 3490 3359 3491 3361 Dl 3302 3372 3302 3374 Dl 3312 3376 3302 3374 Dl 3313 3372 3303 3372 Dl 3301 3371 3296 3371 Dl 3301 3369 3296 3371 Dl 3314 3368 3302 3368 Dl 3308 3365 3301 3367 Dl 3301 3367 3302 3368 Dl 3321 3364 3309 3364 Dl 3324 3358 3312 3360 Dl 3311 3361 3309 3364 Dl 3329 3359 3324 3358 Dl 3363 3352 3353 3352 Dl 3354 3353 3326 3357 Dl 3324 3357 3324 3358 Dl 3363 3353 1 1 De 3402 3349 3395 3349 Dl 3422 3353 3403 3349 Dl 3394 3350 3363 3353 Dl 3492 3360 3490 3359 Dl 3492 3361 3491 3361 Dl 3493 3377 3470 3376 Dl 3494 3377 3493 3377 Dl 3494 3377 3489 3373 Dl 3295 3371 3294 3370 Dl 3294 3368 3294 3370 Dl 3296 3371 3295 3371 Dl 3301 3367 3294 3367 Dl 3297 3365 3291 3367 Dl 3293 3367 3291 3367 Dl 3308 3363 3298 3363 Dl 3294 3363 3287 3361 Dl 3303 3361 3287 3361 Dl 3297 3363 3295 3363 Dl 3311 3360 3304 3360 Dl 3312 3355 3307 3357 Dl 3307 3357 3304 3360 Dl 3325 3357 3313 3355 Dl 3346 3349 3312 3353 Dl 3313 3353 3312 3353 Dl 3351 3350 3346 3349 Dl 3353 3351 3351 3350 Dl 3386 3345 3382 3345 Dl 3394 3348 3386 3346 Dl 3381 3345 3351 3350 Dl 3455 3340 3448 3340 Dl 3456 3340 3452 3350 Dl 3451 3351 3449 3351 Dl 3447 3341 3403 3349 Dl 3449 3352 3435 3354 Dl 3523 3354 3487 3358 Dl 3523 3353 3449 3351 Dl 3530 3363 3492 3360 Dl 3531 3364 3485 3366 Dl 3304 3384 3296 3382 Dl 3296 3376 3296 3382 Dl 3301 3376 3296 3376 Dl 3296 3375 3285 3373 Dl 3296 3372 3286 3373 Dl 3294 3369 3286 3367 Dl 3291 3367 3286 3367 Dl 3294 3364 3285 3367 Dl 3307 3356 3284 3360 Dl 3286 3360 3284 3360 Dl 3363 3337 3343 3339 Dl 3382 3345 3364 3337 Dl 3344 3339 3346 3349 Dl 3447 3340 3432 3340 Dl 3432 3340 3386 3346 Dl 3573 3349 3543 3345 Dl 3571 3350 3523 3353 Dl 3542 3345 3452 3350 Dl 3532 3366 3509 3371 Dl 3534 3364 3533 3366 Dl 3509 3371 3492 3371 Dl 3533 3364 3531 3364 Dl 3284 3372 3279 3371 Dl 3282 3368 3279 3371 Dl 3284 3367 3283 3367 Dl 3276 3361 3272 3363 Dl 3283 3366 3272 3363 Dl 3284 3360 3276 3360 Dl 3275 3358 3276 3360 Dl 3303 3353 3275 3358 Dl 3311 3354 3303 3353 Dl 3343 3339 3322 3340 Dl 3321 3342 3303 3353 Dl 3374 3336 3364 3337 Dl 3432 3339 3374 3336 Dl 3542 3345 3501 3337 Dl 3501 3337 3456 3340 Dl 3632 3353 3534 3364 Dl 3631 3352 3572 3350 Dl 3296 3382 3285 3380 Dl 3284 3379 3279 3376 Dl 3284 3373 3279 3376 Dl 3271 3364 3270 3364 Dl 3270 3364 3268 3371 Dl 3280 3371 3268 3371 Dl 3321 3340 3305 3340 Dl 3304 3341 3265 3357 Dl 3274 3357 3265 3357 Dl 3671 3288 3648 3299 Dl 3648 3299 3501 3337 Dl 3670 3288 3374 3336 Dl 3521 3381 3509 3371 Dl 3520 3381 3494 3377 Dl 3268 3376 3263 3373 Dl 3279 3376 3268 3376 Dl 3267 3372 3263 3373 Dl 3252 3368 3254 3373 Dl 3262 3373 3254 3373 Dl 3270 3365 3252 3368 Dl 3239 3360 3233 3364 Dl 3251 3367 3233 3364 Dl 3265 3358 3240 3360 Dl 3242 3334 3240 3360 Dl 3304 3340 3242 3333 Dl 4550 3082 3671 3287 Dl 3242 3333 3240 3332 Dl 4549 3082 3240 3332 Dl 5 R f (71)3734 3257 w 10 R f 0.1 setlinewidth 3649 3299 3682 3354 Dl 3680 3353 3632 3353 Dl 3717 3358 3682 3354 Dl 3716 3358 3533 3366 Dl 3533 3386 3493 3377 Dl 3533 3386 3521 3381 Dl 3269 3381 3260 3380 Dl 3284 3380 3269 3381 Dl 3267 3376 3260 3380 Dl 3194 3380 3194 3379 Dl 3244 3381 3196 3381 Dl 3215 3372 3194 3379 Dl 3246 3376 3216 3371 Dl 3246 3378 3243 3381 Dl 4562 3080 4888 3355 Dl 4561 3079 4550 3081 Dl 3240 3332 3175 3346 Dl 3558 3395 3533 3386 Dl 3750 3361 3559 3396 Dl 3749 3360 3716 3358 Dl 3245 3381 3243 3381 Dl 3259 3381 3246 3381 Dl 3254 3373 3247 3377 Dl 3233 3364 3216 3371 Dl 3194 3379 3175 3346 Dl 4590 3399 3931 3374 Dl 3931 3373 3751 3361 Dl 4562 3079 4590 3400 Dl (82)4169 3293 w 3306 3386 3273 3386 Dl 3273 3386 3269 3381 Dl 3264 3389 3253 3389 Dl 3273 3387 3265 3389 Dl 3253 3388 3246 3381 Dl 3241 3399 3212 3399 Dl 3253 3390 3242 3399 Dl 3212 3399 3196 3381 Dl 4816 4692 3281 3464 Dl 3281 3464 3212 3399 Dl 4888 3355 4817 4692 Dl 4591 3401 4616 3601 Dl 4617 3601 4817 4692 Dl (87)4696 3735 w 3930 3374 3559 3396 Dl 3393 3424 3265 3389 Dl 3408 3431 3242 3399 Dl 3426 3436 3281 3464 Dl 4616 3601 3440 3437 Dl (92)4169 3923 w 3559 3397 3444 3431 Dl (93)4100 3482 w 20 R f 16 setlinewidth 5040 4878 3024 4878 Dl 5040 2862 5040 4878 Dl 3024 2862 5040 2862 Dl 3024 4878 3024 2862 Dl 4867 3353 4865 3373 Dl 4867 3354 4878 3427 Dl 4866 3354 4842 3423 Dl 10 B f (Fig. 46:)1 322 1 946 5076 t 10 R f (dual projective iter 14, outside)4 1218 1 1293 5076 t 10 B f (Fig. 47:)1 322 1 3299 5076 t 10 R f (iter 14, outside,)2 622 1 3646 5076 t 10 I f (d)4293 5076 w 10 R f (= \(0,\2611,0\))1 397 1 4368 5076 t (Figures 48\26173 show views in direction)5 1562 1 970 5232 t 10 I f (d)2559 5232 w 10 S f (=)2658 5232 w 10 R f (\()2762 5232 w 10 S f (-)2811 5232 w 10 R f ( The)1 208( projectively transformed polytope.)3 1418( of the)2 259(1 , 0 , 0 \))5 273 4 2882 5232 t ( center of the transformed polytope, and the odd)8 2009(even numbered figures in this range are views from the)9 2311 2 720 5352 t ( from the center plus \(0.2,0,0\), i.e., from outside of the polytope, show-)12 2858(numbered figures are cutaway views)4 1462 2 720 5472 t ( from this perspective the)4 1043( Again)1 301( in the current iteration \(analogously to figures 23\26127\).)8 2250(ing the step taken)3 726 4 720 5592 t (picture changes less wildly than for the dual affine algorithm.)9 2457 1 720 5712 t (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 19 20 %%Page: 20 21 /saveobj save def mark 21 pagesetup 10 R f (- 20 -)2 216 1 2772 282 t 0.1 setlinewidth 1717 1440 1714 1442 Dl 1713 1442 1706 1447 Dl 1705 1447 1697 1452 Dl 1696 1453 1668 1465 Dl 1717 1440 1689 1445 Dl 1688 1446 1668 1465 Dl 915 486 720 486 Dl 720 486 720 2001 Dl 1018 1872 720 2001 Dl 1668 1466 1018 1872 Dl 1689 1445 915 486 Dl (4)1028 1287 w 1935 486 915 486 Dl 1935 486 1743 1421 Dl 1742 1421 1736 1428 Dl 1735 1429 1728 1434 Dl 1727 1433 1720 1438 Dl 1719 1439 1717 1440 Dl (5)1500 840 w 1140 1865 1018 1872 Dl 1547 1741 1139 1864 Dl 1697 1453 1548 1741 Dl (7)1381 1717 w 1630 1716 1569 1746 Dl 1569 1745 1548 1741 Dl 1706 1448 1632 1715 Dl 1718 1685 1663 1708 Dl 1663 1709 1632 1715 Dl 1719 1683 1714 1442 Dl 1808 1645 1766 1678 Dl 1766 1678 1719 1685 Dl 1808 1644 1720 1438 Dl 1923 1584 1889 1615 Dl 1888 1615 1809 1645 Dl 1922 1583 1728 1434 Dl 5 R f (11)1793 1563 w 10 R f 0.1 setlinewidth 2049 1517 1983 1568 Dl 1982 1569 1923 1584 Dl 2049 1516 1736 1428 Dl 5 R f (12)1876 1520 w 10 R f 0.1 setlinewidth 2108 1415 1743 1421 Dl 2201 1436 2111 1506 Dl 2110 1507 2091 1512 Dl 2203 1430 2108 1415 Dl 2203 1431 2201 1436 Dl 2091 1512 2049 1517 Dl 5 R f (13)1978 1464 w 10 R f 0.1 setlinewidth 1291 1884 1139 1864 Dl 1520 1830 1292 1885 Dl 1569 1746 1521 1830 Dl 5 R f (14)1361 1833 w 10 R f 0.1 setlinewidth 1626 1807 1537 1841 Dl 1536 1841 1521 1830 Dl 1641 1794 1626 1807 Dl 1662 1708 1641 1792 Dl 1774 1719 1641 1792 Dl 1774 1719 1766 1678 Dl 1839 1720 1801 1732 Dl 1906 1630 1839 1719 Dl 1800 1731 1775 1719 Dl 1907 1630 1889 1615 Dl 2022 1583 2004 1609 Dl 2004 1609 1907 1630 Dl 2022 1582 1983 1568 Dl 2080 1568 2022 1582 Dl 2090 1512 2080 1568 Dl 2209 1431 2208 1429 Dl 2209 1433 2201 1436 Dl 2208 1430 2203 1430 Dl 2182 1404 2108 1415 Dl 2230 1415 2225 1409 Dl 2230 1417 2208 1429 Dl 2225 1410 2183 1404 Dl 1802 1751 1800 1754 Dl 1799 1755 1670 1810 Dl 1670 1810 1626 1807 Dl 1801 1750 1801 1732 Dl 2043 1636 1974 1709 Dl 1973 1709 1844 1724 Dl 2044 1635 2004 1609 Dl 1844 1724 1839 1719 Dl 2201 1520 2197 1513 Dl 2201 1520 2191 1533 Dl 2191 1534 2100 1570 Dl 2197 1511 2111 1506 Dl 2099 1570 2080 1568 Dl 1844 1726 1802 1751 Dl 2109 1622 2100 1570 Dl 2108 1623 2044 1635 Dl 2263 1469 2261 1463 Dl 2230 1437 2210 1432 Dl 2256 1454 2230 1438 Dl 2263 1470 2197 1513 Dl 2261 1462 2257 1455 Dl 1475 1939 1337 1982 Dl 1336 1982 1292 1885 Dl 1536 1842 1475 1939 Dl 5 R f (28)1386 1913 w 10 R f 0.1 setlinewidth 1495 1990 1475 1939 Dl 1650 1897 1496 1991 Dl 1669 1811 1650 1897 Dl 5 R f (29)1547 1900 w 10 R f 0.1 setlinewidth 1817 1820 1716 1888 Dl 1715 1889 1650 1897 Dl 1818 1818 1800 1754 Dl 1998 1728 1936 1787 Dl 1935 1787 1823 1820 Dl 1823 1820 1818 1820 Dl 1998 1727 1974 1709 Dl 2128 1647 2120 1625 Dl 2128 1648 2031 1722 Dl 2031 1723 1999 1728 Dl 2119 1624 2108 1622 Dl 2213 1571 2206 1581 Dl 2214 1570 2191 1533 Dl 2205 1581 2120 1625 Dl 2260 1462 2260 1456 Dl 2260 1456 2257 1455 Dl 2233 1391 2183 1404 Dl 2235 1389 2233 1389 Dl 2226 1409 2236 1389 Dl 1561 1997 1490 2007 Dl 1711 1950 1560 1996 Dl 1496 1992 1490 2007 Dl 1716 1888 1712 1949 Dl 1841 1880 1720 1964 Dl 1720 1963 1712 1949 Dl 1841 1879 1823 1820 Dl 1956 1908 1863 1892 Dl 1961 1817 1956 1909 Dl 1862 1891 1842 1879 Dl 1961 1817 1936 1787 Dl 2094 1758 2053 1785 Dl 2052 1785 1961 1816 Dl 2093 1757 2031 1722 Dl 2178 1667 2117 1759 Dl 2116 1758 2093 1758 Dl 2177 1666 2157 1655 Dl 2157 1654 2129 1648 Dl 2244 1609 2242 1602 Dl 2242 1601 2206 1581 Dl 2244 1609 2157 1655 Dl 2332 1544 2327 1549 Dl 2332 1544 2255 1517 Dl 2255 1517 2245 1517 Dl 2327 1550 2214 1571 Dl 2245 1516 2202 1519 Dl 2322 1467 2263 1469 Dl 2322 1468 2245 1517 Dl 2306 1431 2260 1456 Dl 2306 1431 2230 1438 Dl 720 2281 720 2001 Dl 1236 2086 720 2281 Dl 1337 1983 1236 2086 Dl (45)945 2061 w 1375 2172 1348 2188 Dl 1348 2188 1236 2086 Dl 1489 2007 1376 2172 Dl 5 R f (46)1346 2067 w 10 R f 0.1 setlinewidth 1716 2016 1560 1996 Dl 1719 1964 1717 2017 Dl 1862 1893 1718 2020 Dl 1717 2019 1717 2017 Dl 2052 1786 1970 1922 Dl 1969 1921 1956 1909 Dl 2342 1646 2329 1674 Dl 2341 1645 2245 1609 Dl 2327 1673 2178 1666 Dl 2327 1549 2327 1564 Dl 2326 1565 2242 1602 Dl 2373 1461 2368 1482 Dl 2373 1461 2323 1467 Dl 2367 1482 2255 1517 Dl 2305 1421 2262 1409 Dl 2310 1429 2306 1422 Dl 2262 1410 2231 1416 Dl 2309 1430 2306 1430 Dl 1519 2183 1376 2172 Dl 1717 2038 1519 2183 Dl 1717 2021 1717 2038 Dl 5 R f (55)1516 2095 w 10 R f 0.1 setlinewidth 2000 1968 1923 2047 Dl 1922 2047 1717 2038 Dl 1999 1967 1970 1922 Dl 5 R f (56)1844 1989 w 10 R f 0.1 setlinewidth 2099 1932 1999 1967 Dl 2161 1782 2099 1932 Dl 2162 1781 2117 1759 Dl 5 R f (57)2042 1872 w 10 R f 0.1 setlinewidth 2330 1675 2340 1711 Dl 2339 1712 2162 1782 Dl 2354 1633 2342 1645 Dl 2354 1633 2327 1564 Dl 2380 1523 2368 1482 Dl 2379 1524 2333 1544 Dl 2407 1439 2309 1429 Dl 2408 1439 2374 1460 Dl 964 2502 720 2502 Dl 720 2501 720 2281 Dl 1047 2474 964 2502 Dl 1348 2189 1048 2473 Dl (62)951 2331 w 1922 2049 1919 2062 Dl 1918 2061 1584 2348 Dl 1583 2347 1519 2183 Dl 5 R f (63)1667 2172 w 10 R f 0.1 setlinewidth 2391 1738 2340 1711 Dl 2390 1738 2206 1946 Dl 2206 1945 2099 1932 Dl 5 R f (64)2208 1838 w 10 R f 0.1 setlinewidth 2577 1544 2554 1537 Dl 2554 1537 2380 1524 Dl 2577 1545 2354 1633 Dl 2263 1409 2286 1368 Dl 2285 1369 2236 1389 Dl 1522 2502 1067 2502 Dl 1550 2486 1522 2502 Dl 1066 2501 1048 2473 Dl 1583 2349 1550 2485 Dl (67)1312 2386 w 1795 2502 1579 2502 Dl 2005 2287 1795 2502 Dl 1578 2501 1550 2485 Dl 2006 2286 1919 2062 Dl (68)1738 2343 w 2377 2060 2378 2191 Dl 2376 2192 2005 2286 Dl 2375 2060 2206 1946 Dl (69)2094 2123 w 2687 1783 2376 2061 Dl 2687 1782 2391 1738 Dl (70)2375 1900 w 2705 1552 2578 1545 Dl 2702 1779 2687 1782 Dl 2705 1552 2703 1779 Dl (71)2498 1684 w 2555 1537 2437 1430 Dl 2437 1431 2409 1439 Dl 2454 1420 2437 1430 Dl 2455 1420 2306 1422 Dl 2310 1348 2233 1389 Dl 2311 1348 2286 1368 Dl 1066 2502 964 2502 Dl 2735 2502 2543 2502 Dl 2736 2459 2736 2502 Dl 2735 2457 2666 2416 Dl 2665 2417 2543 2502 Dl 2736 1558 2736 1784 Dl 2735 1557 2706 1551 Dl 2735 1783 2703 1779 Dl 2362 1311 2311 1348 Dl 2471 1412 2362 1311 Dl 2471 1412 2454 1419 Dl 1579 2502 1522 2502 Dl 2543 2502 1795 2502 Dl 2666 2415 2378 2191 Dl (80)2201 2401 w 2736 1785 2736 2458 Dl (81)2547 2134 w 2650 1395 2544 1395 Dl 2543 1395 2471 1412 Dl 2706 1551 2650 1396 Dl 5 R f (82)2559 1478 w 10 R f 0.1 setlinewidth 2736 1557 2736 1370 Dl 2651 1395 2736 1370 Dl 2362 1310 2363 1308 Dl 2543 1393 2363 1308 Dl 2735 486 2229 486 Dl 2736 1370 2736 486 Dl 2362 1308 2229 486 Dl (93)2468 925 w 2228 486 1935 486 Dl (94)2014 1019 w 20 R f 16 setlinewidth 2736 2502 720 2502 Dl 2736 486 2736 2502 Dl 720 486 2736 486 Dl 720 2502 720 486 Dl 10 R f 0.1 setlinewidth 4024 1457 4022 1459 Dl 4022 1460 4017 1463 Dl 4016 1462 4011 1465 Dl 4011 1467 3992 1475 Dl 4025 1457 4006 1461 Dl 4005 1463 3992 1475 Dl 3600 959 3222 1856 Dl 3222 1856 3260 1861 Dl 3611 1717 3260 1861 Dl 3991 1475 3611 1717 Dl 4005 1461 3600 959 Dl (4)3582 1469 w 4153 903 4042 1445 Dl 4153 902 4126 709 Dl 4125 709 4042 583 Dl 4042 582 3888 555 Dl 3887 556 3753 656 Dl 3753 657 3600 959 Dl 4041 1445 4037 1449 Dl 4037 1449 4032 1452 Dl 4031 1453 4026 1456 Dl 4027 1457 4025 1457 Dl (5)3891 974 w 3672 1719 3611 1717 Dl 3910 1660 3673 1720 Dl 4011 1466 3911 1659 Dl 5 R f (7)3825 1629 w 10 R f 0.1 setlinewidth 3966 1645 3925 1663 Dl 3924 1662 3911 1659 Dl 4016 1463 3966 1644 Dl 4026 1626 3988 1640 Dl 3986 1641 3966 1644 Dl 4025 1625 4022 1459 Dl 4087 1600 4058 1622 Dl 4059 1622 4026 1625 Dl 4087 1599 4026 1456 Dl 4169 1556 4145 1578 Dl 4144 1579 4088 1599 Dl 4168 1555 4032 1452 Dl 4257 1510 4211 1546 Dl 4211 1547 4169 1557 Dl 4256 1509 4037 1449 Dl 4291 1441 4042 1445 Dl 4356 1455 4300 1503 Dl 4299 1503 4286 1506 Dl 4358 1450 4291 1440 Dl 4358 1450 4357 1454 Dl 4286 1507 4257 1510 Dl 3757 1740 3673 1720 Dl 3893 1717 3757 1740 Dl 3924 1663 3894 1717 Dl 3962 1706 3904 1725 Dl 3904 1724 3894 1717 Dl 3972 1697 3962 1705 Dl 3987 1641 3973 1697 Dl 4064 1651 3973 1697 Dl 4063 1650 4058 1622 Dl 4109 1651 4083 1659 Dl 4157 1589 4109 1650 Dl 4083 1659 4065 1650 Dl 4157 1588 4145 1578 Dl 4238 1556 4226 1574 Dl 4226 1574 4157 1589 Dl 4239 1556 4211 1546 Dl 4280 1546 4239 1556 Dl 4286 1507 4280 1546 Dl 4362 1451 4361 1450 Dl 4362 1452 4357 1454 Dl 4361 1450 4358 1450 Dl 4340 1433 4291 1440 Dl 4374 1441 4369 1437 Dl 4373 1442 4361 1450 Dl 4369 1436 4340 1432 Dl 4082 1672 4081 1674 Dl 4081 1675 3993 1709 Dl 3991 1708 3962 1705 Dl 4083 1671 4083 1659 Dl 4253 1593 4204 1643 Dl 4203 1644 4113 1654 Dl 4253 1592 4226 1574 Dl 4112 1653 4109 1650 Dl 4362 1512 4359 1507 Dl 4363 1513 4356 1522 Dl 4355 1523 4293 1548 Dl 4359 1507 4300 1503 Dl 4293 1547 4280 1546 Dl 4113 1654 4083 1671 Dl 4298 1584 4293 1548 Dl 4298 1584 4253 1593 Dl 4400 1476 4399 1472 Dl 4376 1454 4363 1451 Dl 4395 1466 4376 1455 Dl 4400 1477 4359 1507 Dl 4398 1472 4395 1467 Dl 3867 1783 3786 1800 Dl 3785 1800 3757 1740 Dl 3903 1726 3867 1783 Dl 3882 1813 3867 1783 Dl 3979 1763 3882 1814 Dl 3992 1709 3980 1762 Dl 4093 1717 4024 1758 Dl 4023 1758 3980 1762 Dl 4093 1716 4081 1674 Dl 4220 1657 4175 1695 Dl 4174 1695 4097 1717 Dl 4096 1717 4093 1717 Dl 4220 1655 4204 1643 Dl 4312 1601 4307 1586 Dl 4311 1602 4242 1653 Dl 4242 1653 4220 1656 Dl 4306 1586 4299 1584 Dl 4370 1548 4365 1555 Dl 4371 1547 4356 1522 Dl 4365 1555 4307 1586 Dl 4399 1472 4398 1468 Dl 4397 1467 4395 1467 Dl 4371 1424 4340 1432 Dl 4373 1424 4372 1424 Dl 4371 1435 4374 1423 Dl 3923 1819 3879 1823 Dl 4021 1794 3924 1818 Dl 3882 1815 3879 1823 Dl 4023 1758 4021 1794 Dl 4108 1754 4027 1802 Dl 4026 1802 4021 1794 Dl 4108 1753 4097 1717 Dl 4183 1769 4122 1761 Dl 4190 1713 4183 1769 Dl 4122 1760 4109 1753 Dl 4190 1713 4175 1695 Dl 4281 1674 4253 1692 Dl 4253 1693 4191 1713 Dl 4282 1675 4242 1653 Dl 4344 1614 4298 1675 Dl 4297 1675 4282 1675 Dl 4342 1613 4330 1606 Dl 4330 1606 4312 1602 Dl 4389 1573 4388 1568 Dl 4388 1568 4365 1555 Dl 4389 1574 4330 1606 Dl 4447 1529 4444 1532 Dl 4446 1527 4397 1509 Dl 4398 1509 4392 1509 Dl 4444 1533 4371 1548 Dl 4391 1510 4363 1512 Dl 4439 1475 4401 1476 Dl 4440 1476 4392 1509 Dl 4425 1451 4398 1468 Dl 4424 1450 4376 1455 Dl 3366 1940 3260 1861 Dl 3734 1852 3367 1942 Dl 3785 1801 3734 1852 Dl 5 R f (45)3517 1837 w 10 R f 0.1 setlinewidth 3818 1907 3803 1913 Dl 3802 1913 3734 1852 Dl 3879 1823 3818 1906 Dl 4025 1831 3924 1818 Dl 4027 1803 4025 1832 Dl 4122 1761 4026 1833 Dl 4025 1833 4025 1832 Dl 4253 1693 4192 1777 Dl 4191 1776 4183 1769 Dl 4449 1597 4439 1616 Dl 4449 1596 4390 1573 Dl 4439 1615 4344 1613 Dl 4443 1532 4443 1542 Dl 4442 1543 4388 1568 Dl 4470 1472 4468 1486 Dl 4471 1472 4440 1476 Dl 4467 1486 4397 1509 Dl 4423 1445 4394 1437 Dl 4427 1449 4424 1445 Dl 4394 1437 4374 1441 Dl 4427 1450 4425 1450 Dl 3905 1913 3818 1906 Dl 4025 1843 3905 1914 Dl 4025 1834 4025 1843 Dl 4209 1803 4156 1846 Dl 4156 1846 4025 1843 Dl 4208 1802 4192 1777 Dl 4274 1779 4209 1802 Dl 4325 1688 4274 1779 Dl 4326 1687 4298 1675 Dl 4440 1617 4443 1640 Dl 4442 1640 4325 1688 Dl 4457 1588 4450 1596 Dl 4457 1588 4443 1542 Dl 4475 1514 4468 1486 Dl 4476 1514 4448 1528 Dl 4491 1457 4428 1450 Dl 4490 1457 4471 1471 Dl 3469 2043 3367 1942 Dl 3667 2019 3469 2044 Dl 3802 1913 3667 2018 Dl 5 R f (62)3567 1961 w 10 R f 0.1 setlinewidth 4155 1847 4153 1854 Dl 4152 1854 3949 1985 Dl 3949 1984 3905 1914 Dl 4470 1655 4443 1640 Dl 4470 1656 4338 1783 Dl 4337 1781 4274 1779 Dl 4589 1526 4577 1522 Dl 4576 1522 4476 1514 Dl 4590 1528 4458 1589 Dl 4396 1435 4403 1410 Dl 4403 1411 4374 1423 Dl 3934 2035 3762 2094 Dl 3762 2092 3667 2018 Dl 3949 1985 3935 2035 Dl 5 R f (67)3794 2008 w 10 R f 0.1 setlinewidth 4190 1948 4026 2061 Dl 4026 2061 3935 2035 Dl 4191 1949 4153 1854 Dl 5 R f (68)4043 1977 w 10 R f 0.1 setlinewidth 4419 1833 4401 1890 Dl 4400 1891 4191 1949 Dl 4419 1832 4338 1783 Dl 5 R f (69)4255 1868 w 10 R f 0.1 setlinewidth 4622 1672 4419 1832 Dl 4622 1670 4470 1655 Dl 5 R f (70)4443 1743 w 10 R f 0.1 setlinewidth 4655 1530 4590 1527 Dl 4630 1669 4623 1671 Dl 4655 1530 4631 1668 Dl 5 R f (71)4534 1613 w 10 R f 0.1 setlinewidth 4576 1522 4507 1451 Dl 4506 1452 4491 1457 Dl 4516 1444 4507 1451 Dl 4516 1445 4424 1445 Dl 4415 1399 4372 1424 Dl 4415 1398 4403 1410 Dl 3679 2278 3525 2242 Dl 3524 2242 3469 2044 Dl 3761 2094 3679 2278 Dl 5 R f (75)3590 2148 w 10 R f 0.1 setlinewidth 4648 2005 4649 2023 Dl 4648 2023 3960 2327 Dl 4646 2003 4495 1949 Dl 4495 1950 4014 2179 Dl 4013 2179 3960 2327 Dl (76)4243 2137 w 4800 1572 4656 1530 Dl 4800 1574 4730 1676 Dl 4730 1675 4631 1668 Dl 4440 1376 4415 1398 Dl 4524 1439 4440 1375 Dl 4525 1440 4516 1444 Dl 3959 2328 3878 2371 Dl 3878 2371 3679 2278 Dl 4026 2061 4014 2179 Dl (79)3818 2219 w 4494 1949 4401 1890 Dl 5 R f (80)4204 2026 w 10 R f 0.1 setlinewidth 4729 1677 4647 2004 Dl 5 R f (81)4556 1843 w 10 R f 0.1 setlinewidth 4617 1431 4563 1429 Dl 4562 1430 4525 1440 Dl 4656 1530 4618 1431 Dl 3378 2294 3222 1856 Dl 3524 2242 3378 2294 Dl 5 R f (83)3356 2099 w 10 R f 0.1 setlinewidth 3782 2502 3751 2502 Dl 3750 2501 3522 2438 Dl 3522 2438 3378 2294 Dl 3877 2372 3782 2502 Dl (84)3586 2388 w 3794 2502 3782 2502 Dl 4805 2025 4520 2218 Dl 4520 2219 3795 2502 Dl 4648 2023 4806 2023 Dl (85)4241 2263 w 4865 1530 4943 1559 Dl 4942 1559 4806 2023 Dl 4801 1573 4865 1530 Dl (86)4742 1809 w 4618 1431 4702 1397 Dl 4864 1529 4702 1397 Dl 5 R f (87)4705 1500 w 10 R f 0.1 setlinewidth 4440 1375 1 1 De 4562 1429 4440 1375 Dl 4943 1559 4042 583 Dl 4702 1396 4126 709 Dl 5 R f (92)4513 1166 w 10 R f 0.1 setlinewidth 4440 1374 4153 902 Dl (93)4347 1164 w (94)4167 1275 w 20 R f 16 setlinewidth 5040 2502 3024 2502 Dl 5040 486 5040 2502 Dl 3024 486 5040 486 Dl 3024 2502 3024 486 Dl 4162 1045 4032 1494 Dl 4161 1044 4159 1118 Dl 4161 1044 4124 1108 Dl 10 B f (Fig. 48:)1 322 1 1048 2700 t 10 R f (dual proj. it. 2,)3 589 1 1395 2700 t 10 I f (v)2009 2700 w 10 R f (=)2078 2700 w 10 I f (center)2159 2700 w 10 B f (Fig. 49:)1 322 1 3179 2700 t 10 R f (dual proj. it. 2,)3 589 1 3526 2700 t 10 I f (v)4140 2700 w 10 R f (=)4209 2700 w 10 I f (center)4290 2700 w 10 S f (+)4539 2700 w 10 R f (\(.2,0,0\))4594 2700 w 0.1 setlinewidth 1722 3857 1720 3857 Dl 1719 3857 1713 3858 Dl 1713 3858 1706 3859 Dl 1705 3860 1684 3864 Dl 1722 3856 1701 3857 Dl 1700 3858 1684 3864 Dl 779 3424 1028 4010 Dl 1062 4010 1028 4010 Dl 1322 3963 1063 4010 Dl 1684 3863 1322 3962 Dl 1701 3857 779 3423 Dl (4)1150 3789 w 2394 2862 720 2862 Dl 720 2862 720 3319 Dl 2255 3180 1743 3850 Dl 2256 3180 2394 2862 Dl 720 3320 779 3423 Dl 1742 3850 1737 3852 Dl 1736 3853 1731 3854 Dl 1731 3854 1725 3855 Dl 1724 3855 1722 3855 Dl (5)1476 3262 w 1364 3969 1322 3962 Dl 1560 3965 1365 3970 Dl 1706 3860 1560 3965 Dl 1610 3964 1571 3969 Dl 1570 3969 1560 3965 Dl 1712 3859 1610 3965 Dl 1668 3963 1630 3965 Dl 1629 3966 1610 3965 Dl 1718 3856 1667 3963 Dl 1733 3960 1698 3967 Dl 1697 3966 1667 3963 Dl 1733 3958 1725 3855 Dl 1829 3949 1796 3958 Dl 1795 3959 1733 3959 Dl 1829 3949 1731 3854 Dl 1948 3941 1879 3953 Dl 1879 3952 1830 3949 Dl 1949 3940 1737 3852 Dl 2028 3904 1743 3850 Dl 2117 3934 2008 3949 Dl 2007 3948 1988 3947 Dl 2120 3931 2028 3904 Dl 2121 3932 2117 3934 Dl 1987 3947 1949 3941 Dl 1419 3991 1365 3970 Dl 1529 3997 1419 3992 Dl 1570 3969 1529 3997 Dl 1586 4003 1535 4004 Dl 1534 4003 1529 3997 Dl 1597 4000 1586 4003 Dl 1629 3966 1598 3999 Dl 1693 3988 1598 3999 Dl 1697 3968 1692 3988 Dl 1731 3999 1704 3998 Dl 1803 3970 1732 4000 Dl 1704 3998 1692 3988 Dl 1803 3968 1796 3958 Dl 1905 3968 1882 3978 Dl 1883 3978 1804 3969 Dl 1905 3968 1879 3953 Dl 1959 3973 1906 3968 Dl 1987 3948 1959 3975 Dl 2127 3933 2127 3932 Dl 2127 3934 2117 3934 Dl 2126 3931 2121 3931 Dl 2105 3914 2028 3904 Dl 2154 3931 2149 3927 Dl 2154 3932 2127 3932 Dl 2149 3927 2106 3915 Dl 1699 4008 1697 4009 Dl 1697 4009 1609 4011 Dl 1608 4012 1586 4003 Dl 1705 3999 1700 4008 Dl 1904 4002 1826 4024 Dl 1826 4023 1734 4003 Dl 1903 4001 1882 3978 Dl 1734 4003 1732 4000 Dl 2090 3979 2088 3974 Dl 2088 3979 2073 3984 Dl 2072 3983 1975 3980 Dl 2087 3974 2008 3949 Dl 1974 3980 1959 3975 Dl 1733 4004 1700 4008 Dl 1975 3981 1963 4012 Dl 1963 4011 1905 4002 Dl 2172 3968 2172 3964 Dl 2147 3941 2128 3934 Dl 2170 3958 2147 3942 Dl 2172 3969 2088 3974 Dl 2172 3964 2170 3959 Dl 1485 4035 1419 4033 Dl 1419 4033 1419 3992 Dl 1534 4004 1485 4035 Dl 1483 4059 1485 4035 Dl 1576 4048 1483 4060 Dl 1608 4012 1576 4047 Dl 1689 4045 1612 4056 Dl 1612 4056 1576 4047 Dl 1697 4008 1689 4044 Dl 1836 4041 1772 4056 Dl 1772 4056 1692 4047 Dl 1691 4045 1689 4044 Dl 1836 4039 1826 4024 Dl 1971 4017 1969 4032 Dl 1969 4033 1862 4047 Dl 1862 4046 1837 4041 Dl 1971 4017 1963 4012 Dl 2079 4013 2067 4016 Dl 2078 4012 2073 3984 Dl 2066 4016 1971 4016 Dl 2173 3961 2172 3964 Dl 2173 3960 2170 3959 Dl 2162 3920 2106 3915 Dl 2164 3920 2162 3920 Dl 2164 3921 2149 3927 Dl 1508 4074 1476 4065 Dl 1592 4083 1509 4074 Dl 1482 4060 1476 4065 Dl 1611 4057 1592 4084 Dl 1682 4081 1592 4093 Dl 1592 4092 1592 4084 Dl 1691 4047 1683 4080 Dl 1741 4125 1691 4092 Dl 1776 4080 1740 4126 Dl 1690 4091 1683 4080 Dl 1777 4078 1772 4056 Dl 1893 4086 1852 4088 Dl 1851 4088 1777 4079 Dl 1894 4085 1862 4047 Dl 2004 4059 1912 4093 Dl 1911 4092 1894 4085 Dl 2003 4057 1991 4045 Dl 1990 4044 1969 4032 Dl 2092 4041 2092 4046 Dl 2092 4040 2067 4016 Dl 2091 4045 1991 4045 Dl 2214 4036 2206 4037 Dl 2215 4036 2144 3993 Dl 2144 3993 2134 3990 Dl 2206 4038 2079 4013 Dl 2133 3989 2089 3979 Dl 2239 3985 2172 3968 Dl 2239 3986 2134 3990 Dl 2233 3960 2173 3960 Dl 2234 3959 2147 3942 Dl 1099 4065 1063 4010 Dl 1363 4059 1100 4065 Dl 1418 4034 1362 4059 Dl 5 R f (45)1229 4029 w 10 R f 0.1 setlinewidth 1396 4111 1384 4112 Dl 1382 4113 1362 4059 Dl 1476 4065 1397 4111 Dl 1575 4116 1509 4074 Dl 1592 4093 1576 4116 Dl 1690 4093 1575 4118 Dl 1575 4117 1575 4118 Dl 1853 4089 1745 4137 Dl 1743 4136 1740 4126 Dl 2171 4105 2142 4117 Dl 2171 4105 2092 4046 Dl 2141 4117 2003 4058 Dl 2206 4038 2198 4047 Dl 2198 4046 2093 4040 Dl 2304 3999 2286 4010 Dl 2303 3997 2239 3985 Dl 2285 4009 2144 3993 Dl 2235 3954 2190 3936 Dl 2238 3960 2236 3955 Dl 2190 3936 2154 3931 Dl 2238 3960 2234 3960 Dl 1446 4144 1397 4111 Dl 1569 4126 1447 4144 Dl 1575 4119 1570 4126 Dl 1746 4170 1672 4186 Dl 1672 4185 1570 4126 Dl 1746 4169 1745 4137 Dl 1824 4183 1746 4168 Dl 1937 4121 1825 4183 Dl 1937 4121 1912 4093 Dl 2141 4117 2132 4145 Dl 2132 4145 1937 4121 Dl 2190 4103 2171 4105 Dl 2197 4047 2190 4101 Dl 2284 4011 2278 4041 Dl 2279 4042 2215 4037 Dl 2356 3998 2238 3960 Dl 2357 3999 2304 3999 Dl 1112 4144 1100 4065 Dl 1243 4163 1113 4145 Dl 1383 4113 1243 4163 Dl 5 R f (62)1209 4115 w 10 R f 0.1 setlinewidth 1672 4186 1665 4191 Dl 1665 4192 1431 4227 Dl 1432 4226 1447 4144 Dl 2168 4186 2132 4145 Dl 2168 4186 1894 4232 Dl 1894 4231 1825 4183 Dl 5 R f (64)1962 4185 w 10 R f 0.1 setlinewidth 2529 4147 2499 4130 Dl 2499 4130 2278 4041 Dl 2528 4147 2190 4101 Dl 2226 3924 2190 3936 Dl 2226 3923 2165 3921 Dl 1386 4271 1242 4261 Dl 1243 4260 1243 4163 Dl 1430 4227 1387 4271 Dl 5 R f (67)1319 4206 w 10 R f 0.1 setlinewidth 1629 4330 1420 4356 Dl 1420 4355 1387 4271 Dl 1665 4192 1630 4330 Dl 5 R f (68)1502 4286 w 10 R f 0.1 setlinewidth 1967 4377 1898 4449 Dl 1897 4449 1630 4330 Dl 1966 4376 1894 4232 Dl 5 R f (69)1772 4311 w 10 R f 0.1 setlinewidth 2498 4391 1967 4377 Dl 2498 4391 2168 4186 Dl (70)2102 4323 w 2733 4230 2530 4147 Dl 2524 4401 2499 4392 Dl 2732 4231 2524 4400 Dl (71)2386 4250 w 2499 4129 2398 4003 Dl 2398 4003 2357 3998 Dl 2426 4003 2398 4003 Dl 2426 4003 2236 3955 Dl 2261 3920 2162 3920 Dl 2261 3922 2227 3924 Dl 1023 4444 972 4351 Dl 972 4351 1113 4145 Dl 1242 4261 1022 4445 Dl 5 R f (75)1087 4288 w 10 R f 0.1 setlinewidth 2049 4878 1247 4878 Dl 1246 4877 1071 4747 Dl 2048 4877 1992 4751 Dl 1992 4751 1288 4528 Dl 1288 4528 1071 4747 Dl (76)1472 4766 w 2736 4233 2736 4541 Dl 2735 4233 2733 4232 Dl 2733 4232 1 1 De 2735 4540 2524 4400 Dl 5 R f (77)2640 4400 w 10 R f 0.1 setlinewidth 2335 3917 2262 3921 Dl 2453 4006 2335 3916 Dl 2454 4006 2427 4004 Dl 1070 4747 974 4748 Dl 974 4748 1022 4445 Dl 1419 4357 1288 4528 Dl (79)1128 4504 w 1993 4750 1898 4449 Dl (80)1612 4537 w 2735 4878 2049 4878 Dl 2736 4542 2736 4878 Dl (81)2281 4653 w 2736 4081 2736 4207 Dl 2735 4081 2568 4028 Dl 2569 4028 2454 4007 Dl 2735 4208 2733 4232 Dl 5 R f (82)2572 4115 w 10 R f 0.1 setlinewidth 720 4454 720 4447 Dl 720 4446 1028 4010 Dl 972 4352 720 4454 Dl 5 R f (83)927 4241 w 10 R f 0.1 setlinewidth 833 4878 720 4878 Dl 720 4877 720 4454 Dl 973 4749 833 4878 Dl (84)806 4635 w 1246 4878 833 4878 Dl 5 R f (85)1008 4836 w 10 R f 0.1 setlinewidth 2736 4207 2736 4232 Dl 2337 3916 2335 3916 Dl 2568 4028 2337 3916 Dl 720 3321 720 4447 Dl (89)773 3937 w 2735 2862 2394 2862 Dl 2736 4081 2736 2862 Dl 2337 3916 2255 3180 Dl (93)2475 3453 w (94)2060 3678 w 20 R f 16 setlinewidth 2736 4878 720 4878 Dl 2736 2862 2736 4878 Dl 720 2862 2736 2862 Dl 720 4878 720 2862 Dl 10 R f 0.1 setlinewidth 4027 3859 4025 3859 Dl 4025 3860 4021 3861 Dl 4021 3861 4016 3862 Dl 4015 3863 3999 3865 Dl 4026 3859 4011 3860 Dl 4011 3860 3999 3865 Dl 3622 3677 3545 3967 Dl 3564 3967 3545 3967 Dl 3734 3938 3564 3968 Dl 3999 3865 3735 3937 Dl 4011 3859 3623 3677 Dl (4)3703 3860 w 4265 3562 4042 3855 Dl 4267 3561 4304 3345 Dl 4303 3345 4178 3171 Dl 4178 3172 3862 3219 Dl 3862 3219 3684 3419 Dl 3683 3419 3623 3677 Dl 4043 3856 4039 3857 Dl 4038 3856 4034 3857 Dl 4034 3859 4029 3859 Dl 4029 3859 4028 3859 Dl (5)3952 3521 w 3764 3942 3735 3937 Dl 3906 3942 3765 3944 Dl 4015 3862 3906 3941 Dl 3943 3941 3914 3944 Dl 3913 3943 3906 3941 Dl 4021 3862 3944 3941 Dl 3986 3941 3958 3942 Dl 3958 3941 3944 3941 Dl 4024 3860 3986 3940 Dl 4035 3937 4009 3943 Dl 4009 3942 3986 3940 Dl 4035 3937 4029 3859 Dl 4108 3929 4083 3936 Dl 4082 3937 4036 3937 Dl 4108 3929 4034 3857 Dl 4196 3923 4145 3932 Dl 4146 3931 4109 3929 Dl 4197 3923 4039 3857 Dl 4252 3895 4042 3855 Dl 4317 3918 4240 3929 Dl 4240 3928 4226 3927 Dl 4319 3914 4253 3895 Dl 4319 3915 4317 3917 Dl 4225 3928 4197 3923 Dl 3803 3960 3765 3944 Dl 3882 3965 3803 3960 Dl 3914 3945 3884 3965 Dl 3926 3970 3888 3970 Dl 3887 3970 3884 3965 Dl 3934 3967 3926 3969 Dl 3957 3943 3934 3967 Dl 4004 3960 3934 3967 Dl 4009 3943 4005 3958 Dl 4034 3966 4014 3966 Dl 4089 3944 4035 3967 Dl 4014 3965 4005 3958 Dl 4088 3943 4083 3936 Dl 4164 3944 4147 3951 Dl 4148 3950 4089 3944 Dl 4164 3943 4145 3932 Dl 4203 3948 4165 3944 Dl 4225 3928 4204 3948 Dl 4323 3917 4323 3916 Dl 4324 3917 4317 3917 Dl 4323 3915 4320 3915 Dl 4307 3902 4253 3895 Dl 4341 3914 4338 3911 Dl 4341 3916 4323 3916 Dl 4337 3911 4307 3903 Dl 4010 3974 4008 3974 Dl 4008 3974 3942 3976 Dl 3942 3975 3926 3969 Dl 4014 3967 4011 3973 Dl 4164 3969 4105 3985 Dl 4105 3985 4037 3970 Dl 4162 3968 4147 3951 Dl 4036 3969 4035 3967 Dl 4298 3950 4297 3947 Dl 4297 3951 4286 3954 Dl 4286 3954 4216 3952 Dl 4296 3947 4240 3929 Dl 4215 3952 4204 3948 Dl 4036 3971 4011 3973 Dl 4215 3952 4206 3975 Dl 4205 3974 4163 3968 Dl 4356 3941 4356 3939 Dl 4337 3922 4324 3917 Dl 4354 3934 4338 3923 Dl 4355 3942 4297 3947 Dl 4355 3938 4354 3934 Dl 3852 3992 3805 3990 Dl 3804 3990 3803 3960 Dl 3887 3970 3852 3992 Dl 3852 4009 3852 3992 Dl 3919 4001 3852 4009 Dl 3942 3976 3919 4001 Dl 4002 4001 3946 4008 Dl 3945 4007 3919 4001 Dl 4009 3975 4003 4000 Dl 4113 3997 4065 4008 Dl 4064 4007 4005 4001 Dl 4005 4001 4003 4000 Dl 4112 3996 4105 3985 Dl 4212 3979 4210 3990 Dl 4210 3991 4131 4001 Dl 4131 4000 4113 3996 Dl 4211 3978 4206 3975 Dl 4289 3976 4281 3978 Dl 4289 3974 4286 3954 Dl 4281 3978 4212 3978 Dl 4356 3937 4356 3939 Dl 4356 3935 4354 3934 Dl 4345 3906 4307 3903 Dl 4347 3906 4345 3906 Dl 4347 3906 4338 3911 Dl 3870 4020 3847 4014 Dl 3932 4027 3871 4020 Dl 3851 4011 3847 4014 Dl 3945 4008 3932 4027 Dl 3998 4026 3932 4033 Dl 3932 4032 3932 4027 Dl 4003 4002 3998 4025 Dl 4040 4055 4004 4033 Dl 4068 4024 4041 4056 Dl 4003 4032 3998 4025 Dl 4068 4023 4065 4008 Dl 4153 4027 4123 4029 Dl 4122 4029 4068 4024 Dl 4153 4027 4131 4001 Dl 4233 4008 4166 4032 Dl 4165 4032 4153 4027 Dl 4233 4007 4225 3998 Dl 4225 3998 4210 3990 Dl 4297 3995 4297 3998 Dl 4298 3995 4281 3978 Dl 4297 3998 4225 3998 Dl 4382 3991 4377 3991 Dl 4383 3989 4336 3960 Dl 4336 3960 4330 3958 Dl 4377 3991 4290 3975 Dl 4328 3957 4298 3950 Dl 4402 3954 4356 3942 Dl 4402 3954 4330 3958 Dl 4396 3935 4356 3936 Dl 4397 3935 4338 3923 Dl 3589 4006 3564 3968 Dl 3765 4007 3590 4007 Dl 3805 3990 3767 4007 Dl 3792 4045 3783 4045 Dl 3784 4045 3767 4007 Dl 3846 4014 3792 4044 Dl 3920 4049 3871 4020 Dl 3932 4034 3921 4050 Dl 4004 4033 3921 4050 Dl 3921 4050 1 1 De 4123 4029 4044 4062 Dl 4043 4063 4041 4056 Dl 4348 4039 4327 4047 Dl 4348 4037 4297 3998 Dl 4327 4046 4234 4008 Dl 4377 3992 4371 3998 Dl 4370 3997 4298 3994 Dl 4444 3962 4432 3970 Dl 4444 3961 4402 3953 Dl 4431 3970 4336 3960 Dl 4396 3930 4366 3918 Dl 4400 3934 4398 3931 Dl 4366 3918 4342 3915 Dl 4399 3934 4397 3934 Dl 3829 4066 3792 4044 Dl 3916 4056 3830 4067 Dl 3920 4050 3917 4055 Dl 4045 4085 3992 4095 Dl 3991 4094 3917 4055 Dl 4045 4083 4044 4062 Dl 4101 4093 4045 4084 Dl 4183 4052 4101 4093 Dl 4183 4050 4166 4032 Dl 4327 4047 4319 4065 Dl 4319 4065 4183 4051 Dl 4362 4036 4349 4038 Dl 4371 3998 4363 4035 Dl 4431 3971 4426 3992 Dl 4426 3992 4384 3990 Dl 4477 3960 4399 3935 Dl 4477 3961 4443 3962 Dl 3605 4060 3590 4007 Dl 3691 4075 3605 4060 Dl 3784 4045 3692 4075 Dl 3992 4095 3987 4098 Dl 3986 4099 3824 4119 Dl 3825 4118 3830 4067 Dl 4339 4090 4319 4065 Dl 4340 4092 4148 4124 Dl 4147 4123 4101 4093 Dl 4577 4058 4561 4048 Dl 4560 4048 4426 3992 Dl 4577 4058 4363 4035 Dl 4387 3908 4366 3918 Dl 4388 3907 4348 3906 Dl 3797 4145 3701 4136 Dl 3702 4135 3692 4075 Dl 3824 4119 3798 4145 Dl 3965 4182 3827 4194 Dl 3826 4193 3798 4145 Dl 3986 4099 3965 4181 Dl 4190 4206 4142 4244 Dl 4140 4244 3965 4181 Dl 4189 4206 4148 4124 Dl 5 R f (69)4052 4170 w 10 R f 0.1 setlinewidth 4525 4205 4190 4206 Dl 4525 4203 4340 4091 Dl 5 R f (70)4288 4168 w 10 R f 0.1 setlinewidth 4687 4105 4577 4059 Dl 4538 4208 4525 4204 Dl 4687 4106 4540 4208 Dl 5 R f (71)4475 4119 w 10 R f 0.1 setlinewidth 4560 4048 4504 3964 Dl 4503 3963 4478 3961 Dl 4521 3964 4504 3964 Dl 4521 3963 4398 3931 Dl 4408 3906 4345 3906 Dl 4408 3906 4388 3908 Dl 3590 4229 3549 4177 Dl 3549 4176 3605 4060 Dl 3700 4137 3590 4230 Dl 4309 4617 4294 4647 Dl 4293 4647 3659 4367 Dl 4308 4616 4184 4376 Dl 4183 4376 3759 4277 Dl 3759 4277 3659 4367 Dl (76)3960 4456 w 4982 4308 4687 4106 Dl 4982 4308 4709 4320 Dl 4709 4320 4540 4208 Dl 5 R f (77)4714 4242 w 10 R f 0.1 setlinewidth 4452 3903 4409 3906 Dl 4537 3965 4453 3902 Dl 4537 3965 4521 3964 Dl 3658 4366 3607 4364 Dl 3606 4365 3590 4230 Dl 3826 4194 3759 4277 Dl 5 R f (79)3671 4252 w 10 R f 0.1 setlinewidth 4184 4376 4142 4244 Dl 5 R f (80)3959 4278 w 10 R f 0.1 setlinewidth 4709 4321 4308 4617 Dl (81)4342 4379 w 4699 4011 4604 3978 Dl 4604 3977 4538 3965 Dl 4699 4011 4687 4106 Dl 3438 4212 3545 3967 Dl 3548 4177 3438 4213 Dl 5 R f (83)3508 4105 w 10 R f 0.1 setlinewidth 3402 4525 3359 4384 Dl 3360 4383 3438 4213 Dl 3606 4365 3403 4525 Dl 5 R f (84)3458 4348 w 10 R f 0.1 setlinewidth 4380 4878 3601 4878 Dl 3601 4877 3403 4525 Dl 4381 4877 4294 4647 Dl (85)3808 4687 w 5039 4878 4381 4878 Dl 5040 4327 5040 4878 Dl 5039 4326 4983 4308 Dl (86)4671 4644 w 5040 4172 5040 4326 Dl 4928 4065 4700 4011 Dl 5039 4171 4928 4064 Dl 5 R f (87)4856 4162 w 10 R f 0.1 setlinewidth 4454 3902 4453 3902 Dl 4603 3977 4454 3902 Dl 3683 3420 3359 4384 Dl 5 R f (89)3507 3927 w 10 R f 0.1 setlinewidth 5039 4078 4178 3171 Dl 5040 4170 5040 4078 Dl 4928 4063 4304 3345 Dl 5 R f (92)4677 3772 w 10 R f 0.1 setlinewidth 4454 3901 4267 3562 Dl (93)4479 3771 w (94)4205 3800 w 20 R f 16 setlinewidth 5040 4878 3024 4878 Dl 5040 2862 5040 4878 Dl 3024 2862 5040 2862 Dl 3024 4878 3024 2862 Dl 4271 3657 4032 3870 Dl 4270 3656 4229 3717 Dl 4270 3656 4205 3690 Dl 10 B f (Fig. 50:)1 322 1 1048 5076 t 10 R f (dual proj. it. 3,)3 589 1 1395 5076 t 10 I f (v)2009 5076 w 10 R f (=)2078 5076 w 10 I f (center)2159 5076 w 10 B f (Fig. 51:)1 322 1 3179 5076 t 10 R f (dual proj. it. 3,)3 589 1 3526 5076 t 10 I f (v)4140 5076 w 10 R f (=)4209 5076 w 10 I f (center)4290 5076 w 10 S f (+)4539 5076 w 10 R f (\(.2,0,0\))4594 5076 w 0.1 setlinewidth 1718 6227 1713 6228 Dl 1713 6228 1703 6230 Dl 1703 6231 1692 6233 Dl 1691 6233 1656 6239 Dl 1718 6226 1684 6228 Dl 1684 6229 1656 6239 Dl 720 5851 720 6469 Dl 1056 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1540 4475 1548 Dl 4460 1501 4444 1491 Dl 4478 1526 4461 1501 Dl 4475 1548 4378 1589 Dl 4478 1537 4478 1527 Dl 3607 1795 3544 1789 Dl 3572 1727 3544 1789 Dl 3681 1748 3607 1795 Dl 3607 1795 3588 1829 Dl 3693 1810 3588 1829 Dl 3757 1756 3693 1810 Dl 3821 1799 3725 1820 Dl 3723 1820 3693 1810 Dl 3864 1744 3821 1799 Dl 3999 1771 3906 1804 Dl 3906 1804 3823 1801 Dl 3823 1801 3821 1799 Dl 4003 1748 4000 1771 Dl 4191 1703 4171 1729 Dl 4171 1729 4024 1775 Dl 4024 1775 4000 1771 Dl 4191 1703 4186 1697 Dl 4326 1665 4308 1675 Dl 4351 1614 4327 1665 Dl 4306 1675 4191 1703 Dl 4480 1530 4478 1538 Dl 4480 1529 4478 1527 Dl 4470 1445 4416 1455 Dl 4473 1445 4471 1445 Dl 4464 1467 4474 1445 Dl 3603 1846 3578 1836 Dl 3680 1857 3603 1847 Dl 3588 1829 3578 1836 Dl 3724 1821 3681 1857 Dl 3781 1848 3674 1868 Dl 3680 1858 3674 1868 Dl 3823 1801 3782 1847 Dl 3805 1897 3780 1861 Dl 3890 1835 3805 1899 Dl 3780 1861 3782 1847 Dl 3906 1804 3890 1834 Dl 4019 1826 3967 1836 Dl 3967 1834 3890 1834 Dl 4024 1777 4020 1825 Dl 4181 1762 4032 1832 Dl 4031 1832 4020 1825 Dl 4182 1745 4182 1762 Dl 4181 1744 4171 1729 Dl 4309 1708 4302 1717 Dl 4308 1675 4309 1708 Dl 4301 1718 4182 1744 Dl 4457 1663 4446 1668 Dl 4457 1663 4423 1608 Dl 4422 1606 4415 1604 Dl 4446 1668 4327 1665 Dl 4415 1604 4375 1599 Dl 4534 1558 4475 1548 Dl 4533 1558 4415 1604 Dl 4541 1506 4481 1530 Dl 4541 1504 4461 1501 Dl 3278 1730 3274 1801 Dl 3476 1819 3274 1801 Dl 3543 1790 3476 1820 Dl 5 R f (45)3402 1763 w 10 R f 0.1 setlinewidth 3474 1891 3462 1891 Dl 3476 1820 3462 1891 Dl 3577 1836 3474 1890 Dl 3639 1897 3603 1847 Dl 3674 1868 3639 1897 Dl 3779 1862 3638 1899 Dl 3639 1898 3638 1899 Dl 3967 1836 3799 1911 Dl 3804 1899 3799 1911 Dl 4321 1788 4272 1815 Dl 4322 1787 4302 1717 Dl 4272 1816 4182 1762 Dl 4446 1669 4425 1687 Dl 4424 1687 4309 1708 Dl 4590 1561 4561 1589 Dl 4590 1560 4534 1558 Dl 4561 1590 4423 1608 Dl 4544 1495 4505 1472 Dl 4545 1504 4544 1495 Dl 4503 1473 4470 1476 Dl 4546 1505 4542 1505 Dl 3498 1926 3474 1890 Dl 3626 1909 3499 1927 Dl 3637 1899 3626 1908 Dl 3772 1949 3683 1969 Dl 3682 1968 3626 1908 Dl 3799 1912 3773 1948 Dl 3841 1955 3773 1948 Dl 4029 1865 3841 1955 Dl 4031 1832 4030 1864 Dl 4271 1815 4225 1856 Dl 4225 1856 4030 1864 Dl 4347 1779 4322 1789 Dl 4424 1687 4348 1778 Dl 4561 1589 4523 1648 Dl 4522 1649 4458 1663 Dl 4643 1537 4546 1504 Dl 4643 1539 4591 1560 Dl 3274 1801 3247 1890 Dl 3325 1928 3247 1890 Dl 3461 1891 3325 1928 Dl 5 R f (62)3333 1871 w 10 R f 0.1 setlinewidth 3683 1969 3672 1974 Dl 3671 1975 3439 2002 Dl 3498 1928 3439 2002 Dl 4224 1856 4212 1897 Dl 4212 1899 3866 1994 Dl 3865 1993 3841 1955 Dl 5 R f (64)4007 1925 w 10 R f 0.1 setlinewidth 4639 1719 4646 1736 Dl 4639 1718 4523 1648 Dl 4646 1737 4348 1778 Dl 5 R f (65)4472 1726 w 10 R f 0.1 setlinewidth 4505 1472 4527 1427 Dl 4527 1427 4474 1445 Dl 3383 2034 3286 2010 Dl 3286 2010 3325 1928 Dl 3439 2002 3383 2034 Dl 5 R f (67)3368 1973 w 10 R f 0.1 setlinewidth 3546 2082 3372 2092 Dl 3373 2091 3383 2034 Dl 3672 1975 3547 2082 Dl 5 R f (68)3478 2046 w 10 R f 0.1 setlinewidth 3806 2099 3693 2147 Dl 3693 2147 3547 2082 Dl 3865 1995 3807 2100 Dl 5 R f (69)3695 2054 w 10 R f 0.1 setlinewidth 4291 2034 3807 2100 Dl 4291 2032 4212 1897 Dl 5 R f (70)4035 2016 w 10 R f 0.1 setlinewidth 4723 1787 4646 1736 Dl 4304 2035 4292 2033 Dl 4723 1788 4304 2035 Dl (71)4381 1882 w 4676 1532 4639 1719 Dl 4676 1533 4643 1538 Dl 4700 1522 4677 1532 Dl 4699 1521 4544 1495 Dl 4550 1407 4471 1445 Dl 4550 1407 4527 1427 Dl 3118 2087 3116 2019 Dl 3247 1891 3116 2019 Dl 3286 2011 3118 2088 Dl 5 R f (75)3192 1996 w 10 R f 0.1 setlinewidth 3491 2406 3454 2417 Dl 3454 2417 3097 2215 Dl 3492 2405 3589 2259 Dl 3589 2258 3237 2160 Dl 3237 2161 3097 2215 Dl 5 R f (76)3341 2286 w 10 R f 0.1 setlinewidth 4725 1788 4697 2005 Dl 4697 2005 4329 2132 Dl 4306 2035 4329 2132 Dl 5 R f (77)4509 1989 w 10 R f 0.1 setlinewidth 4599 1370 4551 1406 Dl 4718 1515 4599 1370 Dl 4719 1515 4700 1521 Dl 5 R f (78)4579 1467 w 10 R f 0.1 setlinewidth 3097 2215 3059 2203 Dl 3059 2203 3118 2088 Dl 3371 2092 3237 2160 Dl 5 R f (79)3197 2116 w 10 R f 0.1 setlinewidth 3692 2148 3589 2259 Dl 5 R f (80)3463 2170 w 10 R f 0.1 setlinewidth 4329 2133 3492 2406 Dl (81)3861 2208 w 4787 1508 4863 1537 Dl 4786 1508 4718 1515 Dl 4863 1538 4725 1788 Dl 5 R f (82)4711 1638 w 10 R f 0.1 setlinewidth 3024 1996 3024 2001 Dl 3260 1721 3024 1995 Dl 3024 2001 3116 2019 Dl 5 R f (83)3145 1900 w 10 R f 0.1 setlinewidth 3024 2201 3024 2001 Dl 3024 2203 3059 2203 Dl 3024 2365 3024 2202 Dl 3267 2465 3024 2365 Dl 3454 2418 3267 2466 Dl 5 R f (85)3166 2357 w 10 R f 0.1 setlinewidth 4698 2005 4787 1967 Dl 4864 1536 4952 1506 Dl 4952 1507 4787 1967 Dl 5 R f (87)4784 1769 w 10 R f 0.1 setlinewidth 4600 1370 4600 1368 Dl 4787 1508 4600 1368 Dl 3024 1878 3024 1995 Dl 3569 824 3024 1878 Dl (89)3217 1534 w 4952 1506 4024 577 Dl 4600 1367 4121 758 Dl (93)4475 1179 w (94)4214 1231 w 20 R f 16 setlinewidth 5040 2502 3024 2502 Dl 5040 486 5040 2502 Dl 3024 486 5040 486 Dl 3024 2502 3024 486 Dl 4386 1935 4032 1494 Dl 4386 1934 4327 1890 Dl 4386 1935 4356 1868 Dl 10 B f (Fig. 54:)1 322 1 1048 2700 t 10 R f (dual proj. it. 5,)3 589 1 1395 2700 t 10 I f (v)2009 2700 w 10 R f (=)2078 2700 w 10 I f (center)2159 2700 w 10 B f (Fig. 55:)1 322 1 3179 2700 t 10 R f (dual proj. it. 5,)3 589 1 3526 2700 t 10 I f (v)4140 2700 w 10 R f (=)4209 2700 w 10 I f (center)4290 2700 w 10 S f (+)4539 2700 w 10 R f (\(.2,0,0\))4594 2700 w 0.1 setlinewidth 1689 3799 1684 3803 Dl 1684 3803 1674 3810 Dl 1674 3809 1663 3816 Dl 1663 3816 1627 3834 Dl 1690 3798 1653 3808 Dl 1652 3809 1627 3834 Dl 720 3049 720 3406 Dl 720 3406 1000 4136 Dl 1024 4145 1000 4136 Dl 1211 4098 1024 4145 Dl 1626 3835 1211 4098 Dl 1653 3808 720 3049 Dl (4)1075 3689 w 1648 2862 720 2862 Dl 720 2862 720 3049 Dl 1720 3769 1648 2862 Dl 1719 3770 1712 3780 Dl 1712 3780 1704 3788 Dl 1704 3789 1694 3796 Dl 1693 3796 1690 3798 Dl (5)1286 3225 w 1242 4110 1211 4098 Dl 1425 4095 1243 4110 Dl 1662 3818 1424 4096 Dl 5 R f 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1567 4215 1494 4214 Dl 1494 4214 1493 4212 Dl 1669 4153 1662 4178 Dl 1883 4085 1855 4118 Dl 1855 4119 1686 4181 Dl 1685 4180 1662 4178 Dl 1884 4084 1879 4078 Dl 2072 4013 2043 4030 Dl 2118 3938 2072 4012 Dl 2042 4030 1884 4085 Dl 2371 3750 2362 3767 Dl 2371 3748 2366 3746 Dl 2384 3574 2267 3635 Dl 2389 3571 2383 3573 Dl 2357 3633 2390 3571 Dl 1303 4257 1285 4248 Dl 1364 4267 1304 4257 Dl 1293 4242 1285 4248 Dl 1407 4235 1365 4268 Dl 1449 4259 1357 4277 Dl 1364 4267 1357 4277 Dl 1494 4214 1450 4258 Dl 1457 4308 1445 4272 Dl 1545 4246 1457 4308 Dl 1450 4259 1445 4272 Dl 1567 4215 1546 4245 Dl 1670 4233 1616 4245 Dl 1616 4245 1546 4245 Dl 1686 4181 1671 4232 Dl 1860 4154 1680 4240 Dl 1681 4239 1671 4232 Dl 1865 4134 1861 4154 Dl 1865 4133 1855 4118 Dl 2038 4072 2026 4084 Dl 2043 4030 2039 4071 Dl 2026 4085 1865 4134 Dl 2296 3971 2273 3982 Dl 2295 3969 2241 3903 Dl 2240 3904 2227 3903 Dl 2272 3982 2072 4012 Dl 2227 3903 2160 3910 Dl 2480 3766 2354 3784 Dl 2480 3767 2227 3903 Dl 2517 3659 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7254 Dl 4612 7083 4568 6973 Dl 4612 7084 4541 7254 Dl 5 R f (64)4496 7131 w 10 R f 0.1 setlinewidth 4636 6307 4598 6272 Dl 4598 6271 4424 6248 Dl 4636 6308 4531 6711 Dl 5 R f (65)4496 6429 w 10 R f 0.1 setlinewidth 4121 5835 4037 5684 Dl 4060 5792 4037 5684 Dl 4233 7254 4150 7254 Dl 4150 7253 4114 7125 Dl 4410 7254 4390 7254 Dl 4730 7254 4541 7254 Dl 4730 7253 4613 7083 Dl 4878 7254 4731 7254 Dl 4794 6314 4637 6307 Dl 4878 7253 4795 6315 Dl (71)4659 6810 w 4598 6272 4279 5765 Dl 4281 5832 4279 5765 Dl 5 R f (72)4390 6086 w 10 R f 0.1 setlinewidth 4279 5764 4261 5696 Dl 4261 5697 4173 5849 Dl 4058 5796 3999 5598 Dl 4036 5684 3999 5598 Dl 4149 7254 4057 7254 Dl 4057 7253 4047 7228 Dl 4047 7228 4031 7025 Dl 4879 7254 5040 7254 Dl 5040 7253 5040 6667 Dl 4796 6315 5040 6667 Dl 4795 6314 1 1 De (77)4880 6865 w 3999 5597 3931 5430 Dl 4251 5643 3931 5430 Dl 4261 5696 4251 5644 Dl 5 R f (78)4087 5667 w 10 R f 0.1 setlinewidth 4271 5317 4232 5470 Dl 4250 5643 4232 5470 Dl 4795 6314 4273 5317 Dl (82)4418 5890 w 3944 7126 3881 6698 Dl 4046 7228 3944 7127 Dl 5 R f (83)3942 7000 w 10 R f 0.1 setlinewidth 4057 7254 3918 7254 Dl 3918 7253 3913 7233 Dl 3944 7128 3913 7233 Dl 5039 6492 4817 5950 Dl 4238 5238 4358 5238 Dl 5040 6666 5040 6492 Dl 4273 5317 4237 5238 Dl 4818 5950 4358 5238 Dl (87)4623 5931 w 3929 5429 3926 5423 Dl 4232 5469 3926 5423 Dl 5 R f (88)4109 5522 w 10 R f 0.1 setlinewidth 3126 5238 3097 5238 Dl 3912 7233 3097 5238 Dl (89)3563 6361 w 3054 5238 3097 5238 Dl 3917 7254 3767 7254 Dl 3768 7254 3054 5238 Dl (90)3482 6454 w 4237 5238 3708 5238 Dl 3927 5423 3708 5238 Dl (93)3991 5353 w 3707 5238 3398 5238 Dl (94)3742 5615 w 20 R f 16 setlinewidth 5040 7254 3024 7254 Dl 5040 5238 5040 7254 Dl 3024 5238 5040 5238 Dl 3024 7254 3024 5238 Dl 4470 6118 4032 6246 Dl 4470 6117 4406 6154 Dl 4470 6118 4396 6120 Dl 10 B f (Fig. 58:)1 322 1 1048 7452 t 10 R f (dual proj. it. 7,)3 589 1 1395 7452 t 10 I f (v)2009 7452 w 10 R f (=)2078 7452 w 10 I f (center)2159 7452 w 10 B f (Fig. 59:)1 322 1 3179 7452 t 10 R f (dual proj. it. 7,)3 589 1 3526 7452 t 10 I f (v)4140 7452 w 10 R f (=)4209 7452 w 10 I f (center)4290 7452 w 10 S f (+)4539 7452 w 10 R f (\(.2,0,0\))4594 7452 w (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 21 22 %%Page: 22 23 /saveobj save def mark 23 pagesetup 10 R f (- 22 -)2 216 1 2772 282 t 0.1 setlinewidth 1609 1341 1609 1332 Dl 1609 1356 1609 1341 Dl 1609 1357 1609 1372 Dl 1608 1372 1601 1412 Dl 1608 1332 1591 1355 Dl 1600 1412 1591 1355 Dl 740 486 720 486 Dl 720 641 720 486 Dl 1429 2178 720 641 Dl 1461 2211 1429 2178 Dl 1569 2086 1461 2212 Dl 1600 1413 1568 2086 Dl 1591 1355 740 486 Dl (4)1219 1382 w 1145 486 740 486 Dl 1598 1270 1146 486 Dl 1605 1292 1599 1270 Dl 1607 1311 1605 1293 Dl 1608 1326 1608 1310 Dl 1609 1327 1609 1332 Dl (5)1168 826 w 1609 2127 1568 2086 Dl 1749 2097 1610 2127 Dl 1750 2097 1609 1372 Dl (7)1616 1879 w 1788 2080 1768 2120 Dl 1768 2120 1750 2097 Dl 1788 2080 1609 1357 Dl 5 R f 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10 R f 0.1 setlinewidth 1803 2475 1742 2442 Dl 1741 2442 1684 2242 Dl 1803 2324 1804 2476 Dl 1886 2502 1810 2502 Dl 1809 2501 1804 2476 Dl 1885 2501 1871 2352 Dl 1976 2502 1886 2502 Dl 1976 2501 1938 2309 Dl 2056 2502 1977 2502 Dl 2081 2392 2057 2502 Dl 2080 2391 2049 2302 Dl 5 R f (31)1983 2393 w 10 R f 0.1 setlinewidth 2154 2181 2127 2071 Dl 2153 2182 2106 2403 Dl 2106 2402 2081 2391 Dl 2126 2070 2112 2050 Dl 5 R f (32)2071 2224 w 10 R f 0.1 setlinewidth 2165 1885 2161 1831 Dl 2161 1831 2085 1620 Dl 2165 1887 2127 2071 Dl 5 R f (33)2081 1855 w 10 R f 0.1 setlinewidth 2008 1180 1991 1143 Dl 1991 1143 1984 1138 Dl 1781 941 1779 817 Dl 1780 813 1779 817 Dl 1835 923 1780 812 Dl 2140 2502 2057 2502 Dl 2139 2501 2106 2403 Dl 2203 2502 2140 2502 Dl 2213 2306 2203 2502 Dl 2214 2304 2186 2234 Dl 2186 2234 2154 2181 Dl 5 R f (40)2140 2375 w 10 R f 0.1 setlinewidth 2235 2055 2225 2014 Dl 2224 2013 2165 1886 Dl 2235 2056 2186 2234 Dl 5 R f (41)2154 2074 w 10 R f 0.1 setlinewidth 2260 1719 2259 1683 Dl 2258 1682 2120 1514 Dl 2119 1514 2109 1514 Dl 2261 1719 2161 1831 Dl 2110 1514 2075 1542 Dl 5 R f (42)2137 1677 w 10 R f 0.1 setlinewidth 2082 1158 2027 1218 Dl 2108 1513 2082 1157 Dl 5 R f (43)2045 1362 w 10 R f 0.1 setlinewidth 1991 1142 1963 941 Dl 1963 942 1918 1067 Dl 1729 2502 1670 2502 Dl 1534 2424 1461 2212 Dl 1670 2501 1534 2424 Dl 1741 2443 1729 2502 Dl (45)1554 2329 w 1809 2502 1729 2502 Dl 2400 2502 2391 2502 Dl 2400 2501 2396 2356 Dl 2396 2356 2236 2056 Dl 2391 2501 2214 2305 Dl 5 R f (50)2268 2296 w 10 R f 0.1 setlinewidth 2280 1818 2261 1719 Dl 2279 1819 2225 2014 Dl 5 R f (51)2198 1868 w 10 R f 0.1 setlinewidth 2169 1223 2124 1059 Dl 2123 1060 2082 1157 Dl 2169 1224 2120 1514 Dl 5 R f (52)2098 1278 w 10 R f 0.1 setlinewidth 1938 894 1866 879 Dl 1963 930 1938 894 Dl 1865 879 1861 951 Dl 1963 940 1963 930 Dl 2390 2502 2203 2502 Dl 5 R f (58)2245 2446 w 10 R f 0.1 setlinewidth 2397 2356 2400 2290 Dl 2400 2288 2280 1818 Dl 5 R f (59)2284 2090 w 10 R f 0.1 setlinewidth 2279 1528 2170 1224 Dl 2260 1683 2279 1530 Dl 5 R f (60)2175 1486 w 10 R f 0.1 setlinewidth 2099 854 1963 930 Dl 2124 1059 2099 854 Dl 5 R f (61)2020 1037 w 10 R f 0.1 setlinewidth 1669 2502 1553 2502 Dl 1553 2501 1534 2424 Dl 2647 1670 2578 1599 Dl 2577 1599 2279 1530 Dl 2401 2290 2647 1671 Dl (65)2379 1840 w 1865 879 1749 640 Dl 1779 813 1749 640 Dl 2735 2502 2401 2502 Dl 2736 2501 2736 1689 Dl 2735 1689 2647 1671 Dl (71)2549 2187 w 2576 1598 2098 738 Dl 2098 853 2098 738 Dl (72)2243 1280 w 2098 738 2075 622 Dl 2075 622 1938 894 Dl 5 R f (73)2010 812 w 10 R f 0.1 setlinewidth 1779 817 1697 500 Dl 1749 639 1697 500 Dl 1995 486 1692 486 Dl 1697 500 1692 486 Dl 2061 529 1996 486 Dl 2075 621 2062 529 Dl (78)1848 667 w 2422 486 2059 486 Dl 2736 1688 2736 1145 Dl 2061 529 2059 486 Dl 2735 1145 2422 486 Dl (82)2394 1020 w 1553 2502 1422 2502 Dl 1423 2501 1429 2178 Dl 5 R f (83)1446 2391 w 10 R f 0.1 setlinewidth 2423 486 2736 486 Dl 2736 1145 2736 486 Dl (87)2581 725 w 2058 486 1996 486 Dl 1422 2502 1092 2502 Dl 720 1296 720 641 Dl 1092 2501 720 1297 Dl (89)1000 1789 w 1092 2502 720 2502 Dl 720 2501 720 1297 Dl (90)793 2120 w 1692 486 1146 486 Dl (94)1482 806 w 20 R f 16 setlinewidth 2736 2502 720 2502 Dl 2736 486 2736 2502 Dl 720 486 2736 486 Dl 720 2502 720 486 Dl 10 R f 0.1 setlinewidth 3950 1389 3950 1383 Dl 3951 1399 3951 1389 Dl 3950 1401 3950 1411 Dl 3951 1411 3946 1438 Dl 3950 1384 3939 1399 Dl 3945 1437 3939 1399 Dl 3840 1931 3389 838 Dl 3859 1955 3840 1931 Dl 3926 1887 3860 1956 Dl 3945 1439 3926 1886 Dl 3939 1399 3389 838 Dl (4)3719 1452 w 3449 486 3231 486 Dl 3943 1342 3450 486 Dl 3388 838 3231 486 Dl 3948 1357 3944 1342 Dl 3950 1368 3948 1356 Dl 3950 1378 3950 1368 Dl 3950 1380 3950 1383 Dl (5)3532 875 w 3952 1915 3926 1886 Dl 4046 1905 3953 1915 Dl 4046 1905 3950 1411 Dl 5 R f (7)3962 1748 w 10 R f 0.1 setlinewidth 4073 1897 4059 1922 Dl 4059 1921 4047 1905 Dl 4073 1896 3951 1400 Dl 4102 1877 4086 1897 Dl 4085 1897 4073 1896 Dl 4102 1876 3951 1389 Dl 4126 1826 4124 1882 Dl 4124 1883 4102 1877 Dl 4128 1827 3951 1380 Dl 4153 1782 4150 1709 Dl 4152 1783 4127 1827 Dl 4150 1708 3950 1368 Dl 5 R f (11)4052 1648 w 10 R f 0.1 setlinewidth 4172 1678 4163 1529 Dl 4173 1679 4150 1709 Dl 4163 1528 3948 1356 Dl 5 R f (12)4066 1547 w 10 R f 0.1 setlinewidth 4052 1205 3944 1342 Dl 4191 1490 4140 1218 Dl 4190 1491 4185 1510 Dl 4130 1197 4052 1204 Dl 4140 1217 4132 1196 Dl 4184 1511 4163 1529 Dl 5 R f (13)4060 1360 w 10 R f 0.1 setlinewidth 4002 1995 3953 1915 Dl 4072 2033 4003 1996 Dl 4071 2033 4059 1922 Dl 4109 2053 4083 2059 Dl 4082 2059 4072 2034 Dl 4111 2037 4109 2052 Dl 4111 2036 4086 1897 Dl 4149 1972 4111 2036 Dl 4149 1971 4124 1882 Dl 4183 2005 4169 2012 Dl 4183 2004 4173 1825 Dl 4170 2012 4150 1972 Dl 4172 1825 4153 1782 Dl 4216 1798 4209 1726 Dl 4216 1799 4173 1825 Dl 4209 1726 4173 1678 Dl 4234 1693 4209 1726 Dl 4235 1693 4185 1510 Dl 4139 1199 4134 1192 Dl 4139 1218 4139 1200 Dl 4134 1192 4132 1196 Dl 4067 1128 4052 1204 Dl 4120 1134 4103 1117 Dl 4132 1191 4120 1134 Dl 4103 1118 4068 1128 Dl 4177 2050 4177 2056 Dl 4176 2057 4130 2082 Dl 4129 2081 4109 2052 Dl 4176 2049 4169 2012 Dl 4260 1891 4253 2052 Dl 4252 2051 4188 2018 Dl 4260 1890 4217 1799 Dl 4188 2017 4183 2004 Dl 5 R f (23)4192 1935 w 10 R f 0.1 setlinewidth 4268 1526 4256 1501 Dl 4275 1580 4268 1527 Dl 4276 1580 4250 1703 Dl 4256 1501 4191 1491 Dl 4249 1703 4235 1694 Dl 4188 2018 4177 2049 Dl 4297 1877 4250 1703 Dl 4296 1878 4260 1890 Dl 4231 1309 4219 1284 Dl 4159 1208 4139 1200 Dl 4202 1256 4158 1208 Dl 4255 1500 4232 1309 Dl 4219 1284 4203 1256 Dl 5 R f (27)4175 1370 w 10 R f 0.1 setlinewidth 4082 2156 4041 2129 Dl 4041 2129 4003 1996 Dl 4083 2060 4083 2157 Dl 4101 2231 4083 2157 Dl 4141 2202 4101 2232 Dl 4141 2201 4130 2082 Dl 4203 2187 4168 2230 Dl 4167 2229 4142 2201 Dl 4202 2187 4177 2056 Dl 4274 2111 4253 2198 Dl 4253 2199 4206 2192 Dl 4205 2192 4203 2187 Dl 4273 2111 4253 2052 Dl 4325 1965 4307 1891 Dl 4324 1967 4291 2118 Dl 4290 2118 4274 2111 Dl 4305 1890 4296 1877 Dl 4329 1760 4327 1723 Dl 4327 1723 4276 1580 Dl 4330 1762 4307 1891 Dl 4219 1284 4208 1260 Dl 4207 1258 4203 1256 Dl 4067 1127 4065 1050 Dl 4065 1048 4065 1050 Dl 4102 1117 4066 1048 Dl 4121 2272 4101 2245 Dl 4172 2310 4122 2273 Dl 4101 2232 4101 2245 Dl 4173 2309 4168 2230 Dl 4220 2298 4177 2334 Dl 4176 2334 4172 2310 Dl 4220 2299 4206 2192 Dl 4274 2428 4230 2333 Dl 4270 2273 4275 2429 Dl 4230 2332 4220 2298 Dl 4268 2271 4253 2198 Dl 4333 2243 4312 2273 Dl 4312 2273 4269 2273 Dl 4333 2242 4291 2118 Dl 4362 2045 4348 2261 Dl 4347 2260 4334 2242 Dl 4362 2044 4345 1999 Dl 4344 1998 4324 1965 Dl 4374 1872 4368 1845 Dl 4367 1844 4330 1761 Dl 4374 1873 4345 1999 Dl 4384 1642 4383 1619 Dl 4383 1618 4296 1508 Dl 4296 1507 4290 1507 Dl 4385 1643 4327 1723 Dl 4289 1508 4268 1527 Dl 4265 1272 4232 1309 Dl 4290 1507 4266 1272 Dl 4207 1259 4186 1131 Dl 4185 1131 4158 1208 Dl 3906 2092 3860 1956 Dl 4027 2182 3907 2093 Dl 4040 2130 4028 2182 Dl 5 R f (45)3927 2041 w 10 R f 0.1 setlinewidth 4084 2342 4078 2340 Dl 4077 2341 4028 2182 Dl 4100 2246 4084 2343 Dl 4179 2397 4122 2273 Dl 4179 2396 4177 2334 Dl 4230 2334 4180 2401 Dl 4179 2400 4179 2397 Dl 4311 2273 4281 2460 Dl 4281 2459 4275 2429 Dl 4471 2159 4469 2057 Dl 4468 2057 4374 1872 Dl 4472 2159 4362 2044 Dl 5 R f (50)4383 2031 w 10 R f 0.1 setlinewidth 4397 1708 4385 1643 Dl 4397 1709 4368 1845 Dl 4319 1317 4289 1212 Dl 4289 1213 4266 1272 Dl 4319 1319 4296 1508 Dl 4169 1101 4123 1089 Dl 4185 1124 4169 1101 Dl 4122 1090 4120 1134 Dl 4186 1130 4186 1124 Dl 4121 2430 4084 2343 Dl 4180 2421 4122 2431 Dl 4180 2401 4180 2420 Dl 4287 2502 4218 2502 Dl 4218 2501 4180 2420 Dl 4287 2501 4281 2460 Dl 4352 2502 4288 2502 Dl 4374 2348 4351 2502 Dl 4376 2346 4348 2261 Dl 5 R f (57)4304 2398 w 10 R f 0.1 setlinewidth 4485 2293 4471 2160 Dl 4486 2293 4376 2347 Dl 5 R f (58)4385 2221 w 10 R f 0.1 setlinewidth 4470 2057 4470 2013 Dl 4469 2012 4397 1709 Dl 4390 1517 4320 1319 Dl 4383 1619 4390 1517 Dl 4268 1086 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3024 4526 Dl 3516 3173 3024 4242 Dl (89)3223 3979 w 3024 3852 3024 4242 Dl 3550 3043 3024 3852 Dl (90)3169 3705 w 3024 3520 3024 3852 Dl 3618 2926 3024 3520 Dl (91)3177 3447 w 3817 2862 3695 2890 Dl 5026 2862 3818 2862 Dl 5040 3127 5040 2885 Dl 4489 3223 3787 2958 Dl (93)4442 3031 w (94)4087 3373 w 20 R f 16 setlinewidth 5040 4878 3024 4878 Dl 5040 2862 5040 4878 Dl 3024 2862 5040 2862 Dl 3024 4878 3024 2862 Dl 4160 4008 4032 3870 Dl 4160 4007 4098 3967 Dl 4160 4006 4124 3942 Dl 10 B f (Fig. 62:)1 322 1 1048 5076 t 10 R f (dual proj. it. 9,)3 589 1 1395 5076 t 10 I f (v)2009 5076 w 10 R f (=)2078 5076 w 10 I f (center)2159 5076 w 10 B f (Fig. 63:)1 322 1 3179 5076 t 10 R f (dual proj. it. 9,)3 589 1 3526 5076 t 10 I f (v)4140 5076 w 10 R f (=)4209 5076 w 10 I f (center)4290 5076 w 10 S f (+)4539 5076 w 10 R f (\(.2,0,0\))4594 5076 w 0.1 setlinewidth 1691 6201 1682 6203 Dl 1682 6203 1664 6207 Dl 1664 6208 1645 6212 Dl 1644 6212 1585 6223 Dl 1692 6201 1634 6207 Dl 1633 6208 1585 6223 Dl 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6114 Dl 2553 6103 2538 6113 Dl 2119 6251 2020 6259 Dl 5 R f (13)2106 6190 w 10 R f 0.1 setlinewidth 800 6415 777 6451 Dl 877 6471 777 6451 Dl 1042 6425 878 6472 Dl 932 6484 858 6484 Dl 877 6473 858 6484 Dl 964 6478 933 6484 Dl 1150 6417 964 6478 Dl 1174 6454 964 6478 Dl 1273 6414 1175 6454 Dl 1200 6472 1152 6473 Dl 1501 6393 1200 6472 Dl 1176 6454 1152 6473 Dl 1528 6372 1501 6392 Dl 1782 6351 1669 6384 Dl 1668 6384 1501 6392 Dl 1783 6350 1772 6327 Dl 1919 6338 1783 6351 Dl 2119 6251 1920 6337 Dl 2570 6103 2568 6100 Dl 2571 6104 2538 6113 Dl 2569 6101 2553 6103 Dl 2472 6076 2282 6114 Dl 2638 6072 2612 6066 Dl 2637 6072 2568 6100 Dl 2612 6066 2473 6076 Dl 1100 6491 1089 6493 Dl 1089 6494 928 6499 Dl 933 6484 928 6499 Dl 1150 6473 1100 6490 Dl 1613 6431 1284 6503 Dl 1284 6502 1187 6478 Dl 1669 6384 1614 6430 Dl 1199 6472 1187 6478 Dl 5 R f (23)1407 6451 w 10 R f 0.1 setlinewidth 2367 6246 2355 6258 Dl 2355 6259 2273 6284 Dl 2273 6284 1945 6342 Dl 2367 6244 2175 6241 Dl 1944 6342 1920 6337 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4009 6212 4005 6212 Dl (5)3887 6069 w 3353 6370 3345 6360 Dl 3527 6371 3354 6370 Dl 3970 6221 3528 6372 Dl 5 R f (7)3595 6329 w 10 R f 0.1 setlinewidth 3587 6370 3528 6377 Dl 3528 6372 3528 6377 Dl 3985 6218 3587 6371 Dl 3663 6367 3607 6372 Dl 3607 6372 3587 6371 Dl 3998 6215 3664 6366 Dl 3776 6352 3697 6369 Dl 3697 6368 3664 6366 Dl 4009 6211 3775 6352 Dl 3975 6316 3885 6339 Dl 3883 6340 3775 6352 Dl 4021 6207 3975 6315 Dl 4248 6257 4065 6306 Dl 4064 6306 3975 6315 Dl 4248 6255 4034 6204 Dl 4440 6149 4043 6199 Dl 4628 6148 4363 6243 Dl 4363 6243 4322 6249 Dl 4638 6141 4440 6149 Dl 4638 6141 4628 6148 Dl 4321 6250 4248 6256 Dl 5 R f (13)4305 6207 w 10 R f 0.1 setlinewidth 3354 6371 3337 6396 Dl 3408 6411 3337 6396 Dl 3527 6378 3408 6412 Dl 3448 6420 3394 6420 Dl 3408 6412 3394 6420 Dl 3471 6416 3448 6420 Dl 3606 6372 3471 6416 Dl 3624 6399 3471 6416 Dl 3697 6370 3625 6399 Dl 3643 6412 3607 6413 Dl 3864 6354 3643 6412 Dl 3625 6399 3607 6413 Dl 3884 6339 3864 6354 Dl 4072 6324 3988 6348 Dl 3988 6348 3864 6354 Dl 4073 6323 4065 6306 Dl 4173 6313 4073 6323 Dl 4322 6250 4174 6313 Dl 4652 6140 4651 6138 Dl 4652 6142 4628 6148 Dl 4651 6139 4639 6140 Dl 4578 6121 4440 6149 Dl 4701 6119 4682 6114 Dl 4701 6118 4651 6138 Dl 4681 6114 4579 6121 Dl 3569 6426 3561 6428 Dl 3561 6429 3444 6432 Dl 3447 6422 3444 6432 Dl 3606 6414 3570 6426 Dl 3946 6382 3705 6435 Dl 3705 6434 3633 6417 Dl 3988 6349 3947 6382 Dl 3642 6412 3633 6417 Dl 4503 6246 4494 6255 Dl 4494 6255 4434 6274 Dl 4433 6274 4192 6317 Dl 4504 6245 4363 6243 Dl 4192 6316 4174 6313 Dl 3633 6417 3570 6426 Dl 4192 6317 4042 6380 Dl 4041 6381 3947 6382 Dl 4736 6166 4732 6174 Dl 4690 6142 4653 6141 Dl 4733 6157 4690 6143 Dl 4731 6176 4504 6246 Dl 4736 6166 4735 6157 Dl 3267 6450 3233 6438 Dl 3336 6396 3233 6438 Dl 3393 6421 3267 6450 Dl 3266 6450 3198 6474 Dl 3303 6469 3198 6474 Dl 3443 6432 3304 6470 Dl 3427 6473 3309 6482 Dl 3308 6482 3304 6470 Dl 3561 6428 3428 6472 Dl 3661 6457 3497 6483 Dl 3497 6482 3426 6474 Dl 3428 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6143 Dl 3154 6377 3062 6418 Dl 3143 6453 3062 6418 Dl 3232 6439 3144 6453 Dl 3024 6503 3024 6506 Dl 3026 6506 3024 6506 Dl 3144 6453 3024 6503 Dl 3180 6479 3026 6507 Dl 3175 6490 3098 6536 Dl 3180 6516 3098 6536 Dl 3268 6525 3094 6538 Dl 3098 6537 3094 6538 Dl 3492 6519 3168 6575 Dl 3202 6564 3168 6575 Dl 4137 6470 3975 6509 Dl 4217 6386 4138 6469 Dl 3975 6509 3927 6446 Dl 5 R f (50)4035 6457 w 10 R f 0.1 setlinewidth 4614 6299 4538 6325 Dl 4537 6327 4245 6375 Dl 5040 6132 5040 6135 Dl 5039 6136 4965 6171 Dl 5039 6132 4883 6157 Dl 4965 6171 4595 6247 Dl 4878 6101 4773 6101 Dl 4889 6107 4879 6100 Dl 4773 6101 4702 6118 Dl 4890 6108 4880 6110 Dl 3024 6541 3024 6508 Dl 3026 6508 3024 6508 Dl 3068 6543 3024 6541 Dl 3093 6538 3068 6544 Dl 3024 6609 3024 6570 Dl 3056 6609 3024 6609 Dl 3068 6545 3024 6570 Dl 3168 6575 3056 6608 Dl 3074 6628 3056 6608 Dl 3489 6556 3075 6629 Dl 3571 6520 3489 6556 Dl 5 R f (57)3287 6579 w 10 R f 0.1 setlinewidth 3975 6509 3781 6564 Dl 3780 6564 3489 6556 Dl 5 R f (58)3742 6526 w 10 R f 0.1 setlinewidth 4215 6452 4138 6469 Dl 4538 6326 4216 6452 Dl 4965 6171 4842 6248 Dl 4841 6248 4649 6289 Dl 5040 6094 5040 6132 Dl 5039 6094 4890 6107 Dl 3024 6433 3024 6503 Dl 3062 6418 3024 6432 Dl 3024 6568 3024 6541 Dl 3024 6671 3024 6651 Dl 3780 6565 3623 6622 Dl 3623 6623 3024 6672 Dl 3075 6630 3024 6651 Dl 5 R f (64)3375 6619 w 10 R f 0.1 setlinewidth 5040 6255 5040 6324 Dl 5039 6254 4842 6248 Dl 5039 6324 4216 6452 Dl 5 R f (65)4685 6343 w 10 R f 0.1 setlinewidth 4772 6100 4782 6055 Dl 4782 6055 4687 6091 Dl 3024 6507 3024 6506 Dl 3024 6650 3024 6609 Dl 3024 6934 3024 6672 Dl 3623 6623 3024 6935 Dl (70)3174 6763 w 5040 6324 5040 6485 Dl 3024 6950 3024 6935 Dl 5040 6486 3024 6950 Dl (71)4095 6617 w 5040 6136 5040 6255 Dl 5040 6093 5040 6075 Dl 5039 6075 4879 6100 Dl 4812 6030 4682 6093 Dl 4811 6030 4782 6055 Dl 5040 6486 5040 6690 Dl 3024 7200 3024 6950 Dl 5039 6690 4208 7089 Dl 4208 7090 3024 7201 Dl (77)3974 6905 w 5040 6074 5040 5987 Dl 4874 5982 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(=)4234 7452 w 10 I f (center)4315 7452 w 10 S f (+)4564 7452 w 10 R f (\(.2,0,0\))4619 7452 w (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 22 23 %%Page: 23 24 /saveobj save def mark 24 pagesetup 10 R f (- 23 -)2 216 1 2772 282 t 0.1 setlinewidth 1694 1456 1686 1458 Dl 1685 1459 1669 1462 Dl 1669 1462 1651 1465 Dl 1650 1465 1596 1474 Dl 1694 1456 1641 1461 Dl 1640 1462 1596 1474 Dl 720 1545 720 1640 Dl 1187 1292 720 1544 Dl 821 1632 720 1640 Dl 1597 1475 821 1631 Dl 1642 1461 1187 1292 Dl (4)1109 1493 w 1824 1111 1740 1442 Dl 1825 1109 1730 1080 Dl 1730 1081 1604 1093 Dl 1604 1093 1449 1139 Dl 1449 1140 1335 1193 Dl 1335 1194 1187 1292 Dl 1740 1442 1729 1447 Dl 1728 1447 1715 1451 Dl 1714 1452 1699 1455 Dl 1699 1455 1694 1456 Dl (5)1539 1283 w 833 1642 821 1631 Dl 1076 1641 833 1643 Dl 1650 1466 1077 1640 Dl 5 R f (7)1161 1591 w 10 R f 0.1 setlinewidth 1156 1638 1077 1647 Dl 1077 1641 1077 1647 Dl 1669 1462 1158 1637 Dl 1261 1631 1185 1638 Dl 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1688 4062 1627 Dl 4102 1687 4095 1614 Dl 10 B f (Fig. 66:)1 322 1 1023 2700 t 10 R f (dual proj. it. 11,)3 639 1 1370 2700 t 10 I f (v)2034 2700 w 10 R f (=)2103 2700 w 10 I f (center)2184 2700 w 10 B f (Fig. 67:)1 322 1 3154 2700 t 10 R f (dual proj. it. 11,)3 639 1 3501 2700 t 10 I f (v)4165 2700 w 10 R f (=)4234 2700 w 10 I f (center)4315 2700 w 10 S f (+)4564 2700 w 10 R f (\(.2,0,0\))4619 2700 w 0.1 setlinewidth 1657 3793 1650 3797 Dl 1650 3797 1635 3804 Dl 1634 3805 1617 3812 Dl 1617 3813 1564 3831 Dl 1657 3793 1603 3804 Dl 1602 3805 1564 3831 Dl 720 3898 720 4160 Dl 982 3477 720 3898 Dl 843 4141 720 4160 Dl 1563 3831 843 4141 Dl 1603 3803 982 3476 Dl (4)1044 3848 w 1698 3764 1522 3114 Dl 1522 3113 1397 3062 Dl 1396 3062 1273 3090 Dl 1273 3091 1145 3183 Dl 1144 3183 1065 3286 Dl 1064 3286 982 3476 Dl 1698 3764 1689 3774 Dl 1690 3774 1678 3782 Dl 1677 3783 1663 3790 Dl 1663 3790 1658 3792 Dl (5)1342 3440 w 863 4163 843 4141 Dl 1121 4161 864 4163 Dl 1617 3812 1122 4160 Dl 5 R f 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6784 4087 6847 Dl 5 R f (56)4004 6761 w 10 R f 0.1 setlinewidth 4167 6917 4087 6847 Dl 4421 6821 4167 6918 Dl 4422 6819 4389 6732 Dl 5 R f (57)4228 6816 w 10 R f 0.1 setlinewidth 4982 6796 4955 6954 Dl 4955 6954 4422 6821 Dl (58)4638 6800 w 5040 6594 5040 6681 Dl 5039 6681 5036 6685 Dl 5039 6592 4854 6320 Dl 5 R f (59)4847 6503 w 10 R f 0.1 setlinewidth 4889 6142 4667 6028 Dl 4889 6143 4831 6243 Dl 5 R f (60)4701 6158 w 10 R f 0.1 setlinewidth 4547 5898 4343 5995 Dl 4591 5973 4547 5898 Dl 5 R f (61)4442 6006 w 10 R f 0.1 setlinewidth 3698 6444 3692 6509 Dl 3734 6573 3692 6509 Dl 3817 6588 3735 6574 Dl 3987 6819 3975 6819 Dl 3975 6818 3789 6708 Dl 3841 6647 3789 6708 Dl 4994 7139 4955 6954 Dl 4995 7140 4177 7030 Dl 4176 7030 4167 6918 Dl (64)4532 7003 w 5040 6116 5040 6593 Dl 5039 6117 4889 6143 Dl 5 R f (65)4935 6315 w 10 R f 0.1 setlinewidth 4223 6013 4105 5978 Dl 4128 6019 4105 5978 Dl 3745 6715 3699 6636 Dl 3735 6574 3699 6636 Dl 3789 6709 3746 6716 Dl 3808 6882 3708 6771 Dl 3745 6716 3708 6771 Dl 3974 6819 3808 6883 Dl 5 R f (68)3799 6806 w 10 R f 0.1 setlinewidth 3986 7216 3818 7146 Dl 3818 7145 3808 6883 Dl 4177 7031 3987 7216 Dl (69)3929 7024 w 5039 7254 4024 7254 Dl 5040 7218 5040 7254 Dl 4024 7253 3987 7216 Dl 5039 7217 4995 7140 Dl (70)4437 7189 w 5040 6682 5040 7218 Dl 5 R f (71)4984 6960 w 10 R f 0.1 setlinewidth 5040 5906 5040 6116 Dl 5039 5905 4539 5851 Dl 4546 5897 4539 5851 Dl (72)4775 6005 w 4538 5851 4494 5821 Dl 4494 5821 4309 5991 Dl 4127 6021 4062 5956 Dl 4105 5977 4062 5956 Dl 3608 6561 3593 6620 Dl 3691 6509 3608 6560 Dl 3698 6636 3593 6620 Dl 3239 7089 3229 7048 Dl 3517 6707 3229 7048 Dl 3538 7109 3240 7089 Dl 3597 6744 3538 7110 Dl 3597 6742 3518 6706 Dl (76)3395 6965 w 4061 5956 3993 5919 Dl 4464 5798 3993 5919 Dl 4494 5820 4465 5796 Dl 5 R f (78)4231 5921 w 10 R f 0.1 setlinewidth 3518 6706 3516 6677 Dl 3593 6621 3516 6677 Dl 3707 6771 3597 6743 Dl 5 R f (79)3611 6703 w 10 R f 0.1 setlinewidth 3818 7146 3538 7110 Dl (80)3633 6984 w 4024 7254 3285 7254 Dl 3285 7253 3240 7089 Dl (81)3525 7207 w 5040 5904 5040 5526 Dl 4389 5706 4366 5575 Dl 4463 5797 4389 5708 Dl 5039 5527 4366 5575 Dl (82)4694 5726 w 3677 6382 3554 6491 Dl 3608 6560 3554 6491 Dl 3479 6495 3437 6546 Dl 3554 6492 3480 6494 Dl 3516 6677 3437 6546 Dl 5 R f (84)3501 6582 w 10 R f 0.1 setlinewidth 3282 6501 3134 6624 Dl 3436 6546 3282 6500 Dl 3229 7048 3134 6624 Dl (85)3261 6747 w 3024 6008 3036 6120 Dl 3134 6624 3036 6120 Dl 4366 5576 3788 5627 Dl 3788 5628 3024 5724 Dl 3993 5918 3990 5918 Dl 4389 5708 3990 5918 Dl 5 R f (88)4254 5818 w 10 R f 0.1 setlinewidth 3512 6050 3480 6494 Dl 5 R f (89)3533 6328 w 10 R f 0.1 setlinewidth 3502 6022 3282 6500 Dl 5 R f (90)3398 6357 w 10 R f 0.1 setlinewidth 3506 5994 3036 6120 Dl (91)3191 6284 w 3024 5725 3024 6007 Dl 3788 5628 3525 5980 Dl (92)3282 5872 w 3989 5918 3567 5983 Dl (93)3917 5785 w (94)3845 6057 w 20 R f 16 setlinewidth 5040 7254 3024 7254 Dl 5040 5238 5040 7254 Dl 3024 5238 5040 5238 Dl 3024 7254 3024 5238 Dl 3837 6087 4032 6246 Dl 3837 6086 3903 6117 Dl 3836 6086 3880 6145 Dl 10 B f (Fig. 70:)1 322 1 1023 7452 t 10 R f (dual proj. it. 13,)3 639 1 1370 7452 t 10 I f (v)2034 7452 w 10 R f (=)2103 7452 w 10 I f (center)2184 7452 w 10 B f (Fig. 71:)1 322 1 3154 7452 t 10 R f (dual proj. it. 13,)3 639 1 3501 7452 t 10 I f (v)4165 7452 w 10 R f (=)4234 7452 w 10 I f (center)4315 7452 w 10 S f (+)4564 7452 w 10 R f (\(.2,0,0\))4619 7452 w (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 23 24 %%Page: 24 25 /saveobj save def mark 25 pagesetup 10 R f (- 24 -)2 216 1 2772 282 t 0.1 setlinewidth 1709 1479 1704 1479 Dl 1703 1480 1693 1481 Dl 1693 1481 1682 1482 Dl 1681 1483 1648 1486 Dl 1709 1479 1676 1481 Dl 1676 1481 1648 1486 Dl 1449 1426 1190 1535 Dl 1191 1537 1190 1535 Dl 1283 1534 1191 1537 Dl 1647 1487 1284 1534 Dl 1676 1481 1450 1426 Dl 5 R f (4)1421 1495 w 10 R f 0.1 setlinewidth 1835 1329 1741 1473 Dl 1835 1328 1771 1322 Dl 1770 1322 1687 1335 Dl 1688 1336 1593 1362 Dl 1592 1362 1528 1386 Dl 1527 1388 1450 1426 Dl 1741 1473 1733 1475 Dl 1733 1475 1724 1476 Dl 1723 1477 1713 1478 Dl 1713 1478 1710 1478 Dl 5 R f (5)1654 1412 w 10 R f 0.1 setlinewidth 1287 1537 1284 1534 Dl 1380 1539 1288 1537 Dl 1681 1484 1380 1540 Dl 1413 1540 1380 1542 Dl 1380 1540 1380 1542 Dl 1693 1481 1414 1540 Dl 1460 1539 1426 1540 Dl 1425 1540 1414 1540 Dl 1703 1480 1460 1539 Dl 1532 1535 1481 1540 Dl 1480 1540 1460 1539 Dl 1712 1478 1532 1534 Dl 1677 1521 1608 1530 Dl 1607 1530 1532 1534 Dl 1722 1477 1676 1520 Dl 1915 1493 1748 1516 Dl 1746 1516 1676 1520 Dl 1914 1493 1733 1475 Dl 2129 1436 1741 1473 Dl 2368 1424 2032 1483 Dl 2031 1484 1988 1488 Dl 2384 1419 2130 1434 Dl 2384 1419 2368 1424 Dl 1988 1488 1915 1492 Dl 1288 1538 1278 1546 Dl 1313 1552 1278 1546 Dl 1380 1542 1314 1552 Dl 1334 1555 1306 1555 Dl 1313 1553 1306 1555 Dl 1346 1554 1334 1555 Dl 1425 1541 1346 1554 Dl 1433 1550 1346 1554 Dl 1480 1540 1434 1550 Dl 1442 1555 1422 1555 Dl 1592 1536 1444 1555 Dl 1433 1550 1422 1555 Dl 1607 1530 1592 1535 Dl 1752 1522 1683 1532 Dl 1683 1533 1592 1535 Dl 1753 1523 1748 1516 Dl 1840 1517 1753 1522 Dl 1988 1488 1840 1517 Dl 2403 1418 2402 1417 Dl 2403 1419 2368 1424 Dl 2402 1417 2385 1419 Dl 2307 1411 2130 1434 Dl 2480 1402 2452 1401 Dl 2480 1402 2402 1417 Dl 2451 1400 2307 1411 Dl 1401 1559 1396 1559 Dl 1395 1559 1331 1559 Dl 1333 1556 1331 1559 Dl 1422 1555 1400 1558 Dl 1648 1546 1479 1563 Dl 1478 1562 1437 1556 Dl 1683 1533 1649 1545 Dl 1442 1555 1437 1556 Dl 2191 1480 2179 1485 Dl 2179 1486 2106 1496 Dl 2105 1496 1856 1519 Dl 2191 1480 2032 1483 Dl 1855 1518 1840 1517 Dl 1437 1556 1400 1558 Dl 1855 1520 1721 1545 Dl 1721 1545 1649 1545 Dl 2524 1427 2517 1432 Dl 2459 1417 2404 1419 Dl 2524 1420 2459 1416 Dl 2517 1432 2192 1480 Dl 2525 1426 2525 1421 Dl 1240 1562 1225 1558 Dl 1278 1546 1225 1558 Dl 1305 1555 1241 1562 Dl 1240 1562 1207 1568 Dl 1257 1568 1207 1568 Dl 1331 1559 1257 1569 Dl 1318 1573 1258 1573 Dl 1258 1572 1257 1569 Dl 1395 1559 1319 1571 Dl 1449 1570 1354 1576 Dl 1353 1575 1317 1572 Dl 1318 1572 1317 1572 Dl 1479 1562 1450 1569 Dl 1720 1546 1661 1556 Dl 1661 1557 1462 1571 Dl 1462 1570 1450 1569 Dl 1721 1545 1721 1547 Dl 1995 1521 1944 1527 Dl 2105 1496 1996 1521 Dl 1944 1528 1721 1547 Dl 2535 1422 2525 1427 Dl 2536 1421 2525 1421 Dl 2456 1388 2307 1411 Dl 2466 1387 2457 1388 Dl 2466 1388 2452 1401 Dl 1197 1571 1195 1573 Dl 1207 1578 1195 1573 Dl 1206 1570 1198 1570 Dl 1258 1573 1208 1578 Dl 1250 1581 1195 1581 Dl 1207 1579 1195 1581 Dl 1317 1572 1251 1581 Dl 1234 1584 1200 1594 Dl 1310 1583 1200 1594 Dl 1250 1582 1234 1584 Dl 1353 1576 1310 1583 Dl 1393 1586 1347 1586 Dl 1346 1586 1310 1583 Dl 1461 1571 1393 1585 Dl 1626 1568 1390 1588 Dl 1393 1586 1390 1588 Dl 1652 1562 1626 1568 Dl 1660 1556 1653 1561 Dl 1899 1541 1872 1545 Dl 1944 1527 1900 1540 Dl 1872 1545 1653 1561 Dl 2385 1495 2334 1500 Dl 2384 1494 2309 1477 Dl 2309 1478 2287 1478 Dl 2332 1501 1996 1521 Dl 2287 1478 2179 1485 Dl 2736 1414 2736 1412 Dl 2735 1413 2517 1432 Dl 2735 1416 2287 1478 Dl 2736 1387 2736 1385 Dl 2735 1388 2536 1421 Dl 2735 1385 2459 1416 Dl 1190 1538 1148 1549 Dl 1182 1561 1148 1549 Dl 1224 1559 1183 1561 Dl 1127 1575 1125 1575 Dl 1182 1562 1125 1575 Dl 1197 1570 1128 1575 Dl 1195 1573 1157 1585 Dl 1195 1581 1157 1585 Dl 1234 1585 1155 1585 Dl 1157 1585 1155 1585 Dl 1346 1587 1183 1597 Dl 1199 1595 1183 1597 Dl 1791 1577 1653 1589 Dl 1872 1546 1792 1576 Dl 1653 1589 1626 1568 Dl 2333 1500 2230 1514 Dl 2229 1514 1900 1540 Dl 2736 1430 2736 1415 Dl 2735 1431 2309 1477 Dl 2736 1384 2736 1376 Dl 2735 1377 2597 1385 Dl 2597 1386 2480 1402 Dl 1128 1576 1100 1583 Dl 1142 1586 1100 1583 Dl 1155 1585 1144 1586 Dl 1130 1603 1088 1602 Dl 1142 1587 1088 1602 Dl 1182 1597 1131 1604 Dl 1135 1609 1131 1604 Dl 1339 1598 1136 1610 Dl 1388 1588 1339 1597 Dl 1653 1589 1509 1604 Dl 1508 1604 1339 1597 Dl 1864 1570 1792 1576 Dl 2229 1515 1864 1570 Dl 2736 1454 2736 1430 Dl 2735 1455 2706 1461 Dl 2706 1462 2385 1494 Dl 2736 1412 2736 1388 Dl 1148 1550 1086 1563 Dl 1085 1563 1071 1573 Dl 1125 1574 1071 1573 Dl 1088 1603 1080 1603 Dl 1079 1602 1023 1592 Dl 1100 1583 1023 1592 Dl 1509 1605 1401 1619 Dl 1401 1620 1082 1620 Dl 1136 1611 1082 1620 Dl 2736 1508 2736 1460 Dl 2735 1460 2706 1461 Dl 2735 1509 1864 1570 Dl 5 R f (65)2395 1522 w 10 R f 0.1 setlinewidth 2627 1355 2597 1385 Dl 2627 1354 2466 1386 Dl 1000 1584 988 1594 Dl 1070 1574 1001 1584 Dl 1022 1593 988 1594 Dl 943 1611 932 1601 Dl 988 1594 932 1601 Dl 1079 1604 943 1612 Dl 907 1635 846 1633 Dl 943 1612 846 1633 Dl 1081 1620 908 1635 Dl 1031 1683 908 1635 Dl 1400 1619 1031 1684 Dl 2736 1586 2736 1509 Dl 1031 1684 1021 1688 Dl 2735 1587 1021 1688 Dl (71)1982 1615 w 2736 1460 2736 1455 Dl 2686 1334 2457 1388 Dl 2687 1334 2628 1354 Dl 976 1573 928 1583 Dl 1085 1563 977 1573 Dl 1000 1583 928 1583 Dl 720 1611 720 1631 Dl 825 1597 720 1610 Dl 867 1600 720 1631 Dl 866 1599 825 1596 Dl 2736 2502 720 2502 Dl 2736 1587 2736 2502 Dl 720 2501 720 1706 Dl 1021 1688 720 1706 Dl (77)1701 2093 w 2736 1375 2736 1316 Dl 2735 1318 2687 1333 Dl 836 1593 825 1596 Dl 928 1583 837 1592 Dl 931 1600 867 1599 Dl 720 1632 720 1635 Dl 846 1634 720 1635 Dl 720 1635 720 1706 Dl 5 R f (81)819 1678 w 10 R f 0.1 setlinewidth 1190 1535 977 1560 Dl 977 1561 977 1573 Dl 904 1563 835 1573 Dl 977 1562 906 1563 Dl 836 1573 837 1592 Dl 720 1568 720 1610 Dl 835 1572 720 1567 Dl 1528 1388 906 1563 Dl 5 R f (89)1183 1505 w 10 R f 0.1 setlinewidth 720 1565 720 1567 Dl 1593 1362 720 1564 Dl 5 R f (90)1060 1504 w 10 R f 0.1 setlinewidth 720 1408 720 1564 Dl 1687 1336 720 1408 Dl (91)1000 1455 w 2736 486 720 486 Dl 2736 1123 2736 486 Dl 720 486 720 1408 Dl 2735 1124 1771 1322 Dl (92)1618 917 w 2736 1290 2736 1123 Dl 2736 1292 1836 1328 Dl (93)2350 1269 w 2736 1316 2736 1291 Dl (94)2129 1390 w 20 R f 16 setlinewidth 2736 2502 720 2502 Dl 2736 486 2736 2502 Dl 720 486 2736 486 Dl 720 2502 720 486 Dl 10 R f 0.1 setlinewidth 4017 1482 4013 1482 Dl 4012 1482 4004 1483 Dl 4005 1484 3996 1485 Dl 3994 1486 3968 1488 Dl 4016 1481 3990 1483 Dl 3990 1484 3968 1488 Dl 3810 1440 3599 1527 Dl 3599 1529 3599 1527 Dl 3675 1527 3600 1529 Dl 3969 1488 3676 1526 Dl 3990 1483 3810 1440 Dl 4116 1364 4042 1477 Dl 4117 1364 4066 1359 Dl 4065 1359 4000 1369 Dl 3999 1370 3925 1390 Dl 3924 1390 3873 1409 Dl 3872 1410 3810 1440 Dl 4042 1477 4036 1478 Dl 4036 1479 4029 1480 Dl 4027 1480 4020 1481 Dl 4019 1481 4017 1481 Dl 5 R f (5)3970 1432 w 10 R f 0.1 setlinewidth 3678 1528 3676 1526 Dl 3753 1530 3679 1529 Dl 3995 1484 3754 1530 Dl 3780 1531 3753 1532 Dl 3753 1531 3753 1532 Dl 4004 1484 3781 1530 Dl 3818 1530 3790 1531 Dl 3790 1530 3781 1530 Dl 4013 1483 3818 1530 Dl 3875 1526 3834 1531 Dl 3833 1531 3818 1530 Dl 4020 1482 3876 1526 Dl 3990 1515 3936 1522 Dl 3936 1523 3876 1526 Dl 4028 1480 3991 1514 Dl 4178 1494 4047 1512 Dl 4047 1511 3991 1514 Dl 4179 1492 4036 1478 Dl 4345 1448 4042 1477 Dl 4530 1440 4271 1486 Dl 4270 1486 4237 1489 Dl 4542 1436 4347 1447 Dl 4542 1437 4530 1440 Dl 4236 1490 4179 1493 Dl 3678 1528 3670 1535 Dl 3698 1540 3670 1535 Dl 3753 1532 3699 1540 Dl 3715 1542 3692 1542 Dl 3698 1540 3692 1542 Dl 3725 1543 3715 1543 Dl 3790 1531 3726 1542 Dl 3797 1539 3726 1542 Dl 3834 1532 3797 1539 Dl 3804 1542 3787 1542 Dl 3923 1527 3804 1542 Dl 3796 1539 3787 1542 Dl 3936 1523 3924 1527 Dl 4050 1517 3996 1524 Dl 3996 1525 3924 1527 Dl 4050 1517 4047 1512 Dl 4120 1513 4051 1517 Dl 4235 1489 4120 1512 Dl 4556 1434 4555 1434 Dl 4556 1436 4530 1440 Dl 4554 1435 4542 1436 Dl 4483 1429 4347 1447 Dl 4614 1423 4593 1422 Dl 4614 1423 4555 1434 Dl 4592 1421 4482 1429 Dl 3769 1546 3765 1546 Dl 3764 1546 3713 1546 Dl 3715 1544 3713 1546 Dl 3787 1543 3769 1545 Dl 3969 1535 3833 1549 Dl 3833 1548 3800 1543 Dl 3996 1525 3969 1535 Dl 3805 1542 3800 1543 Dl 4394 1484 4385 1487 Dl 4384 1487 4328 1495 Dl 4328 1496 4133 1514 Dl 4395 1484 4271 1486 Dl 4132 1512 4120 1512 Dl 3799 1543 3769 1545 Dl 4132 1514 4026 1534 Dl 4026 1535 3969 1535 Dl 4649 1442 4644 1445 Dl 4597 1434 4556 1435 Dl 4649 1437 4599 1434 Dl 4643 1446 4395 1483 Dl 4649 1441 4649 1437 Dl 3639 1548 3627 1545 Dl 3670 1535 3627 1545 Dl 3693 1543 3640 1549 Dl 3640 1549 3612 1554 Dl 3653 1554 3612 1554 Dl 3713 1547 3653 1554 Dl 3702 1557 3654 1557 Dl 3653 1556 3653 1554 Dl 3764 1546 3703 1556 Dl 3808 1555 3731 1560 Dl 3731 1559 3702 1557 Dl 3702 1557 1 1 De 3832 1549 3809 1554 Dl 4026 1537 3979 1544 Dl 3978 1543 3819 1555 Dl 3819 1555 3809 1554 Dl 4026 1534 4026 1535 Dl 4244 1515 4203 1520 Dl 4327 1496 4243 1515 Dl 4202 1520 4026 1535 Dl 4656 1438 4649 1442 Dl 4657 1437 4649 1437 Dl 4595 1411 4482 1429 Dl 4603 1411 4596 1411 Dl 4603 1412 4593 1422 Dl 3604 1556 3602 1558 Dl 3612 1563 3602 1558 Dl 3612 1555 3605 1555 Dl 3653 1557 3612 1562 Dl 3647 1564 3602 1564 Dl 3612 1563 3602 1564 Dl 3702 1557 3648 1564 Dl 3634 1568 3606 1575 Dl 3696 1566 3606 1575 Dl 3647 1565 3634 1567 Dl 3732 1561 3696 1566 Dl 3763 1568 3726 1568 Dl 3726 1568 3696 1566 Dl 3818 1556 3763 1567 Dl 3950 1553 3760 1569 Dl 3762 1567 3760 1569 Dl 3972 1548 3951 1553 Dl 3978 1545 3972 1548 Dl 4167 1532 4146 1535 Dl 4202 1521 4168 1531 Dl 4146 1536 3972 1548 Dl 4543 1495 4505 1499 Dl 4543 1494 4485 1481 Dl 4484 1481 4468 1481 Dl 4504 1499 4243 1515 Dl 4467 1482 4385 1487 Dl 4844 1427 4644 1445 Dl 4843 1428 4468 1481 Dl 4843 1406 4657 1437 Dl 4844 1406 4599 1434 Dl 3599 1529 3564 1538 Dl 3592 1547 3564 1538 Dl 3625 1546 3592 1548 Dl 3547 1559 3545 1559 Dl 3592 1549 3545 1559 Dl 3604 1556 3548 1560 Dl 3602 1558 3571 1568 Dl 3602 1565 3571 1568 Dl 3633 1568 3569 1568 Dl 3570 1568 3569 1568 Dl 3725 1568 3592 1577 Dl 3605 1575 3592 1577 Dl 4082 1560 3972 1570 Dl 4147 1535 4083 1559 Dl 3972 1570 3951 1553 Dl 4504 1498 4425 1509 Dl 4425 1511 4168 1531 Dl 5040 1414 5040 1408 Dl 5039 1415 4970 1427 Dl 5039 1408 4844 1428 Dl 4971 1428 4485 1481 Dl 4844 1402 4703 1410 Dl 4858 1403 4844 1401 Dl 4703 1410 4615 1422 Dl 4859 1404 4844 1406 Dl 3548 1560 3525 1566 Dl 3560 1568 3525 1566 Dl 3569 1568 3560 1568 Dl 3550 1582 3515 1581 Dl 3560 1569 3515 1581 Dl 3591 1578 3549 1583 Dl 3552 1588 3549 1583 Dl 3720 1578 3553 1588 Dl 3760 1570 3720 1577 Dl 3972 1570 3857 1582 Dl 3856 1582 3720 1577 Dl 4140 1554 4083 1559 Dl 4425 1511 4140 1554 Dl 4971 1427 4787 1468 Dl 4786 1469 4543 1494 Dl 5040 1408 5040 1388 Dl 5039 1389 4859 1404 Dl 3564 1539 3513 1549 Dl 3513 1550 3501 1558 Dl 3544 1558 3501 1558 Dl 3514 1582 3507 1582 Dl 3507 1581 3461 1573 Dl 3525 1566 3461 1573 Dl 3856 1583 3769 1594 Dl 3769 1595 3508 1596 Dl 3552 1589 3508 1596 Dl 5040 1488 5040 1458 Dl 5039 1457 4787 1468 Dl 5040 1489 4140 1554 Dl 5 R f (65)4660 1509 w 10 R f 0.1 setlinewidth 4724 1387 4703 1410 Dl 4723 1387 4603 1411 Dl 3443 1567 3432 1575 Dl 3501 1558 3443 1566 Dl 3460 1574 3432 1575 Dl 3394 1589 3385 1581 Dl 3431 1576 3385 1581 Dl 3507 1582 3394 1589 Dl 3364 1608 3313 1607 Dl 3394 1589 3313 1607 Dl 3508 1596 3364 1609 Dl 3465 1648 3364 1609 Dl 3769 1594 3466 1648 Dl 5040 1550 5040 1488 Dl 3465 1648 3457 1651 Dl 5039 1551 3457 1651 Dl (71)4328 1586 w 5040 1457 5040 1414 Dl 5040 1387 5040 1379 Dl 5039 1379 4844 1401 Dl 4768 1370 4596 1411 Dl 4768 1371 4725 1386 Dl 3424 1559 3383 1566 Dl 3513 1550 3424 1558 Dl 3442 1566 3383 1566 Dl 3044 1610 3044 1612 Dl 3296 1577 3044 1610 Dl 3192 1609 3044 1612 Dl 3331 1580 3192 1609 Dl 3331 1579 3296 1577 Dl 5040 1551 5040 1623 Dl 5039 1624 3903 1709 Dl 3903 1708 3045 1678 Dl 3456 1652 3045 1678 Dl (77)4162 1660 w 5040 1378 5040 1325 Dl 4865 1337 4768 1370 Dl 5039 1325 4866 1337 Dl 5 R f (78)4868 1378 w 10 R f 0.1 setlinewidth 3306 1575 3296 1577 Dl 3382 1566 3306 1573 Dl 3386 1581 3332 1580 Dl 3312 1607 3192 1609 Dl 3044 1613 3045 1678 Dl 5 R f (81)3197 1649 w 10 R f 0.1 setlinewidth 3597 1527 3423 1548 Dl 3424 1548 3424 1558 Dl 3364 1550 3306 1558 Dl 3424 1549 3365 1550 Dl 3306 1558 3306 1573 Dl 3200 1553 3044 1573 Dl 3305 1558 3200 1553 Dl 3044 1574 3044 1610 Dl 3055 486 3044 1437 Dl 3044 1437 3044 1573 Dl 5040 1324 5040 1317 Dl 4866 1337 1 1 De 5039 1319 4866 1337 Dl 3874 1410 3365 1550 Dl 3924 1390 3200 1553 Dl 4000 1370 3044 1437 Dl (91)3323 1483 w 5039 486 3056 486 Dl 5040 1164 5040 486 Dl 5039 1164 4066 1359 Dl (92)3941 933 w 5040 1317 5040 1164 Dl 4865 1337 4116 1364 Dl (93)4650 1306 w 5 R f (94)4357 1407 w 20 R f 16 setlinewidth 5040 2502 3024 2502 Dl 5040 486 5040 2502 Dl 3024 486 5040 486 Dl 3024 2502 3024 486 Dl 4015 1694 4032 1494 Dl 4014 1693 4003 1620 Dl 4014 1692 4038 1623 Dl 10 B f (Fig. 72:)1 322 1 1023 2700 t 10 R f (dual proj. it. 14,)3 639 1 1370 2700 t 10 I f (v)2034 2700 w 10 R f (=)2103 2700 w 10 I f (center)2184 2700 w 10 B f (Fig. 73:)1 322 1 3154 2700 t 10 R f (dual proj. it. 14,)3 639 1 3501 2700 t 10 I f (v)4165 2700 w 10 R f (=)4234 2700 w 10 I f (center)4315 2700 w 10 S f (+)4564 2700 w 10 R f (\(.2,0,0\))4619 2700 w 10 B f (Pictures of the Primal Projective Algorithm)5 1859 1 720 2940 t 10 R f ( ver-)1 191( This)1 234( primal projective version of Karmarkar's LP algorithm.)7 2288(The next group of figures is for a)7 1357 4 970 3096 t ( satisfactory termina-)2 860( uses a less)3 462( It)1 118(sion uses the same step-length choice as the dual projective algorithm.)10 2880 4 720 3216 t ( stopping once)2 593(tion test,)1 349 2 720 3336 t 10 I f (c)1692 3336 w 7 R f (T)1747 3296 w 10 I f (x)1806 3336 w 7 I f (k)1861 3296 w 10 S f (+ b)1 159 1 1949 3336 t 7 I f (k)2113 3296 w 10 S f (\243)2193 3336 w 10 R f (10)2289 3336 w 7 S f (-)2400 3296 w 7 R f (7)2450 3296 w 10 S f (\357)2493 3336 w 10 I f (c)2541 3336 w 7 R f (T)2596 3296 w 10 I f (x)2655 3336 w 7 I f (k)2710 3296 w 10 S f (\357)2749 3336 w 10 R f ( also runs a separate phase 1 to find a feasible point.)11 2134(. It)1 141 2 2765 3336 t ( add a large bound on the primal variables, which makes finding an initial dual-)14 3442(\(The dual algorithms)2 878 2 720 3456 t ( one phase-1)2 520( only)1 236( LP problem of concern here is easy in this regard:)10 2098( The)1 213(feasible point straightforward.\))2 1253 5 720 3576 t ( these there are)3 615( Of)1 160( what follows we restrict our attention to the phase-2 iterations.)10 2587( In)1 139(iteration is required.)2 819 5 720 3696 t (21, and the linear objective)4 1084 1 720 3816 t 10 I f (c)1829 3816 w 7 R f (T)1884 3776 w 10 I f (x)1943 3816 w 10 R f (increases on the first two.)4 1023 1 2012 3816 t ( the one presented to the dual algorithms, but with slack variables explicitly added.)13 3323(The LP problem is)3 747 2 970 3972 t (Thus if the dual constraints \(2b\) are)6 1437 1 720 4092 t 10 I f (A)2184 4092 w 10 S f (\260)2245 4092 w 10 I f (y)2293 4092 w 10 S f (\243)2378 4092 w 10 I f (c)2474 4092 w 10 R f ( primal constraints \(1b\), ignoring bounds, are)6 1815(, then the)2 373 2 2518 4092 t 10 I f (Ax)4732 4092 w 10 S f (=)4886 4092 w 10 I f (b)4990 4092 w 10 R f (with)720 4247 w 10 I f (A)928 4247 w 10 S f (=)1038 4247 w 10 R f ([)1142 4247 w 10 I f (A)1183 4247 w 10 S f (\260)1244 4247 w 7 R f (T)1289 4207 w 10 R f (,)1348 4247 w 10 I f (I)1414 4247 w 10 R f (]; an obvious)2 532 1 1455 4247 t 10 I f (F)2017 4247 w 10 R f (with)2108 4247 w 10 I f (AF)2316 4247 w 10 S f (=)2487 4247 w 10 B f (0)2591 4247 w 10 R f (is then)1 270 1 2671 4247 t 10 I f (F)2972 4247 w 10 S f (=)3082 4247 w (\351)3194 4210 w (\353)3194 4310 w (-)3244 4307 w 10 I f (A)3315 4307 w 10 S f (\260)3376 4307 w 10 I f (I)3313 4207 w 10 S f (\371)3416 4210 w (\373)3416 4310 w 10 R f ( simple bound constraints on all)5 1305(. With)1 281 2 3454 4247 t (the variables,)1 532 1 720 4422 t 10 I f (A)1277 4422 w 10 R f (becomes)1363 4422 w (\(18\))720 4737 w 10 I f (A)2442 4737 w 10 S f (=)2552 4737 w (\351)2672 4600 w (\357)2672 4700 w (\357)2672 4800 w (\353)2672 4900 w 10 B f (0)2775 4852 w 10 I f (I)2784 4752 w (A)2722 4652 w 10 S f (\260)2783 4652 w 7 R f (T)2828 4612 w 10 I f (I)2962 4852 w 10 B f (0)2954 4752 w 10 I f (I)2953 4652 w 10 B f (0)3085 4852 w 10 I f (I)3094 4752 w 10 B f (0)3079 4652 w 10 I f (I)3231 4852 w 10 B f (0)3222 4752 w (0)3216 4652 w 10 S f (\371)3279 4600 w (\357)3279 4700 w (\357)3279 4800 w (\373)3279 4900 w 10 R f (and)720 5072 w 10 I f (F)895 5072 w 10 R f (becomes)987 5072 w 10 I f (F)1367 5072 w 10 S f (=)1477 5072 w 10 R f ([)1581 5072 w 10 I f (I)1622 5072 w 10 R f (,)1663 5072 w 10 S f (-)1737 5072 w 10 I f (A)1808 5072 w 10 S f (\260)1869 5072 w 10 R f (,)1917 5072 w 10 S f (-)1991 5072 w 10 I f (I)2062 5072 w 10 R f (,)2103 5072 w 10 I f (A)2169 5072 w 10 S f (\260)2230 5072 w 10 R f (])2278 5072 w 7 R f (T)2322 5032 w 10 R f ( simple bound constraints are)4 1199( The)1 212( orthogonalize.)1 606(, which we then)3 650 4 2373 5072 t (superfluous, but do somewhat affect the solution path and pictures.)9 2677 1 720 5192 t ( original polytope, with the primal projective path)7 2098(Figures 74\26177 show some outside views of the)7 1972 2 970 5348 t ( 74\26176 are the same as figures 30\26132; figure 77)9 1935( for this path, figures)4 855( Except)1 332(showing through from inside.)3 1198 4 720 5468 t (shows the path from yet another view direction,)7 1908 1 720 5588 t 10 I f (d)2653 5588 w 10 S f (=)2752 5588 w 10 R f (\()2856 5588 w 10 S f (-)2905 5588 w 10 R f ( halfway between that of figures 75 and 76.)8 1732(1 , 0 , 1 \),)5 298 2 2976 5588 t (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 24 25 %%Page: 25 26 /saveobj save def mark 26 pagesetup 10 R f (- 25 -)2 216 1 2772 282 t 0.1 setlinewidth 2470 921 2465 960 Dl 2464 961 2445 1034 Dl 1195 1113 1542 2153 Dl 1542 2154 1575 2224 Dl 1575 2225 1771 2378 Dl 1175 711 1152 766 Dl 1151 766 1145 827 Dl 1146 827 1149 906 Dl 1150 907 1160 977 Dl 1161 977 1194 1113 Dl 2371 711 2438 761 Dl 2439 761 2467 824 Dl 2467 824 2473 896 Dl 2473 896 2471 920 Dl 1828 2352 1771 2378 Dl 2105 2129 1829 2351 Dl 2172 2004 2121 2107 Dl 2121 2108 2106 2128 Dl 2173 2003 2445 1034 Dl 2218 1814 2187 1942 Dl 2186 1943 2172 2003 Dl 2219 1813 2465 960 Dl 2235 1556 2221 1706 Dl 2221 1707 2219 1815 Dl 2237 1556 2473 896 Dl 5 R f (10)2294 1408 w 10 R f 0.1 setlinewidth 2193 1160 2203 1316 Dl 2204 1317 2237 1556 Dl 2192 1158 2467 824 Dl (11)2260 1190 w 2044 793 2126 1023 Dl 2128 1023 2192 1159 Dl 2045 792 2438 761 Dl (12)2194 927 w 1834 560 2370 710 Dl 1972 737 1823 585 Dl 1974 738 1997 758 Dl 1815 575 1833 560 Dl 1823 586 1815 576 Dl 1997 758 2044 792 Dl 5 R f (13)2078 706 w 10 R f 0.1 setlinewidth 1895 2263 1829 2351 Dl 2032 2134 1895 2262 Dl 2033 2134 2121 2107 Dl 2064 1994 2026 2107 Dl 2026 2107 2032 2134 Dl 2078 1973 2064 1993 Dl 2079 1972 2187 1942 Dl 5 R f (15)2078 2047 w 10 R f 0.1 setlinewidth 2150 1722 2078 1972 Dl 2151 1721 2221 1706 Dl 5 R f (16)2136 1853 w 10 R f 0.1 setlinewidth 2104 1594 2116 1679 Dl 2160 1322 2104 1594 Dl 2117 1679 2151 1722 Dl 2162 1321 2203 1316 Dl 5 R f (17)2150 1550 w 10 R f 0.1 setlinewidth 2072 1027 2072 1123 Dl 2072 1123 2161 1321 Dl 2072 1026 2126 1023 Dl 5 R f (18)2114 1174 w 10 R f 0.1 setlinewidth 2011 938 2072 1026 Dl 1998 758 2010 938 Dl 5 R f (19)2026 918 w 10 R f 0.1 setlinewidth 1814 579 1812 575 Dl 1823 585 1814 580 Dl 1813 576 1815 576 Dl 1775 558 1833 560 Dl 1779 567 1770 563 Dl 1811 575 1779 568 Dl 1770 564 1775 558 Dl 2087 1687 2082 1692 Dl 2082 1692 2047 1911 Dl 2047 1912 2064 1993 Dl 2117 1679 2088 1686 Dl 2005 1147 1997 1363 Dl 1997 1363 2092 1587 Dl 2071 1123 2005 1147 Dl 2092 1589 2104 1594 Dl 5 R f (23)2048 1346 w 10 R f 0.1 setlinewidth 1892 748 1890 766 Dl 1891 766 1901 803 Dl 1901 804 1988 932 Dl 1972 738 1892 748 Dl 1989 933 2010 938 Dl 2092 1588 2088 1686 Dl 1988 932 1954 1063 Dl 1954 1063 2005 1147 Dl 5 R f (26)1991 1057 w 10 R f 0.1 setlinewidth 1812 664 1808 652 Dl 1807 598 1814 580 Dl 1805 635 1806 597 Dl 1892 747 1812 664 Dl 1808 652 1805 637 Dl 1923 2074 1863 2135 Dl 1863 2135 1895 2262 Dl 2025 2107 1923 2075 Dl 5 R f (28)1913 2163 w 10 R f 0.1 setlinewidth 1885 2004 1923 2075 Dl 1943 1884 1884 2003 Dl 2047 1911 1944 1883 Dl 5 R f (29)1955 2004 w 10 R f 0.1 setlinewidth 1974 1669 1934 1797 Dl 1935 1797 1944 1883 Dl 2082 1691 1974 1668 Dl 5 R f (30)1982 1798 w 10 R f 0.1 setlinewidth 1957 1358 1937 1489 Dl 1937 1490 1970 1660 Dl 1970 1660 1974 1668 Dl 1996 1362 1958 1357 Dl 5 R f (31)1985 1552 w 10 R f 0.1 setlinewidth 1942 1063 1918 1105 Dl 1917 1105 1936 1315 Dl 1938 1315 1958 1357 Dl 1953 1062 1941 1062 Dl 5 R f (32)1938 1222 w 10 R f 0.1 setlinewidth 1874 899 1878 924 Dl 1900 803 1874 897 Dl 1878 924 1941 1062 Dl 1808 652 1803 640 Dl 1804 640 1805 637 Dl 1775 557 1732 559 Dl 1731 559 1732 559 Dl 1770 564 1731 560 Dl 1867 1917 1872 1994 Dl 1873 1774 1866 1917 Dl 1884 2002 1872 1994 Dl 1934 1797 1875 1774 Dl 1891 1633 1861 1758 Dl 1862 1759 1875 1774 Dl 1970 1658 1892 1632 Dl 1827 1519 1872 1609 Dl 1890 1477 1826 1519 Dl 1872 1609 1892 1632 Dl 1937 1488 1891 1476 Dl 1862 1299 1864 1360 Dl 1865 1361 1891 1476 Dl 1936 1314 1862 1299 Dl 1863 1109 1848 1281 Dl 1848 1282 1862 1299 Dl 1887 1102 1864 1110 Dl 1917 1104 1887 1100 Dl 1840 962 1836 975 Dl 1879 924 1841 961 Dl 1836 975 1887 1100 Dl 1786 836 1789 846 Dl 1838 769 1785 836 Dl 1846 766 1838 768 Dl 1873 897 1789 846 Dl 1890 766 1847 766 Dl 1811 664 1770 682 Dl 1847 765 1770 682 Dl 1803 640 1752 617 Dl 1806 598 1752 617 Dl 1619 2127 1575 2224 Dl 1794 2094 1620 2126 Dl 1862 2135 1794 2094 Dl 5 R f (45)1723 2233 w 10 R f 0.1 setlinewidth 1783 1957 1776 1962 Dl 1776 1963 1794 2094 Dl 1872 1994 1784 1957 Dl 1825 1743 1866 1917 Dl 1861 1757 1825 1742 Dl 1871 1609 1823 1740 Dl 1825 1741 1823 1740 Dl 1863 1361 1814 1510 Dl 1826 1517 1814 1510 Dl 1770 1015 1771 1060 Dl 1836 976 1770 1015 Dl 1863 1109 1771 1060 Dl 1789 847 1788 877 Dl 1789 877 1841 961 Dl 1740 687 1750 725 Dl 1769 682 1739 687 Dl 1838 768 1750 725 Dl 1745 607 1753 574 Dl 1749 616 1744 607 Dl 1779 568 1753 574 Dl 1751 617 1749 617 Dl 1767 1835 1784 1957 Dl 1812 1736 1766 1835 Dl 1822 1740 1812 1735 Dl 5 R f (55)1793 1887 w 10 R f 0.1 setlinewidth 1783 1500 1765 1566 Dl 1764 1566 1812 1735 Dl 1813 1509 1783 1499 Dl 1766 1415 1783 1499 Dl 1810 1273 1766 1415 Dl 1846 1281 1810 1272 Dl 1771 1060 1756 1105 Dl 1756 1105 1810 1272 Dl 1765 995 1770 1015 Dl 1788 877 1765 994 Dl 1750 725 1754 804 Dl 1784 835 1754 804 Dl 1749 617 1710 668 Dl 1738 687 1710 668 Dl 1631 1983 1620 2126 Dl 1684 1929 1631 1983 Dl 1775 1962 1684 1929 Dl 5 R f (62)1679 2043 w 10 R f 0.1 setlinewidth 1763 1566 1758 1568 Dl 1758 1568 1702 1722 Dl 1702 1723 1766 1835 Dl 1756 1106 1726 1121 Dl 1725 1121 1725 1356 Dl 1726 1356 1766 1415 Dl 5 R f (64)1734 1270 w 10 R f 0.1 setlinewidth 1674 858 1668 869 Dl 1753 805 1674 857 Dl 1765 994 1668 869 Dl 1752 573 1684 566 Dl 1730 560 1684 566 Dl 1673 1703 1648 1780 Dl 1648 1780 1684 1929 Dl 1702 1722 1674 1702 Dl 5 R f (67)1688 1853 w 10 R f 0.1 setlinewidth 1672 1520 1647 1617 Dl 1647 1617 1674 1702 Dl 1758 1567 1672 1519 Dl 1662 1329 1643 1365 Dl 1643 1366 1672 1519 Dl 1725 1356 1662 1329 Dl 5 R f (69)1688 1457 w 10 R f 0.1 setlinewidth 1639 1098 1662 1329 Dl 1726 1121 1639 1098 Dl 5 R f (70)1663 1230 w 10 R f 0.1 setlinewidth 1667 869 1631 892 Dl 1637 1097 1635 1093 Dl 1631 893 1635 1093 Dl 5 R f (71)1669 1019 w 10 R f 0.1 setlinewidth 1691 669 1674 857 Dl 1710 667 1692 668 Dl 1691 668 1677 665 Dl 1743 608 1677 665 Dl 1732 559 1651 570 Dl 1684 566 1651 570 Dl 1576 1687 1570 1748 Dl 1570 1749 1631 1983 Dl 1647 1779 1576 1687 Dl 1554 1302 1550 1306 Dl 1551 1306 1562 1560 Dl 1593 1337 1555 1302 Dl 1593 1337 1596 1576 Dl 1596 1575 1562 1560 Dl 1631 893 1565 990 Dl 1565 990 1591 1091 Dl 1634 1093 1591 1091 Dl 1651 571 1601 579 Dl 1665 666 1601 579 Dl 1677 665 1666 666 Dl 1561 1561 1555 1578 Dl 1555 1578 1576 1687 Dl 1647 1616 1596 1576 Dl 1642 1365 1593 1337 Dl 1591 1092 1555 1302 Dl 5 R f (81)1587 1244 w 10 R f 0.1 setlinewidth 1629 688 1599 738 Dl 1665 668 1629 689 Dl 1599 738 1631 892 Dl 1514 1672 1542 2153 Dl 1568 1748 1512 1672 Dl 5 R f (83)1544 1972 w 10 R f 0.1 setlinewidth 1496 1513 1488 1557 Dl 1488 1557 1512 1672 Dl 1555 1577 1497 1512 Dl 1498 1267 1475 1337 Dl 1475 1337 1497 1512 Dl 1550 1306 1498 1266 Dl 5 R f (85)1497 1424 w 10 R f 0.1 setlinewidth 1526 978 1486 1051 Dl 1487 1051 1498 1266 Dl 1565 989 1527 977 Dl 5 R f (86)1511 1144 w 10 R f 0.1 setlinewidth 1598 739 1525 803 Dl 1526 803 1527 977 Dl 5 R f (87)1546 879 w 10 R f 0.1 setlinewidth 1601 580 1599 580 Dl 1629 688 1599 580 Dl 1488 1557 1160 977 Dl (89)1345 1583 w 1475 1336 1149 906 Dl 5 R f (90)1328 1259 w 10 R f 0.1 setlinewidth 1486 1050 1145 827 Dl (91)1303 1089 w 1525 803 1152 766 Dl 5 R f (92)1347 889 w 10 R f 0.1 setlinewidth 1599 580 1175 710 Dl 5 R f (93)1402 718 w 20 R f 16 setlinewidth 2736 2502 720 2502 Dl 2736 486 2736 2502 Dl 720 486 2736 486 Dl 720 2502 720 486 Dl 1804 1599 1855 1563 Dl 1973 1149 1804 1599 Dl 1973 1150 1965 1223 Dl 1973 1149 1931 1210 Dl 1602 1177 1974 1149 Dl 1602 1177 1672 1154 Dl 1602 1178 1675 1190 Dl 1291 1178 1602 1177 Dl 1290 1178 1362 1160 Dl 1290 1179 1362 1196 Dl 1229 1172 1290 1179 Dl 1208 1072 1228 1171 Dl 1183 982 1207 1072 Dl 1178 891 1182 981 Dl 1223 934 1178 890 Dl 1306 967 1224 936 Dl 1470 1040 1306 966 Dl 1469 1041 1397 1028 Dl 1469 1041 1411 995 Dl 1496 1046 1470 1041 Dl 1519 990 1496 1046 Dl 1525 978 1519 990 Dl 1537 983 1527 978 Dl 1553 986 1537 984 Dl 1563 989 1553 987 Dl 1565 990 1563 990 Dl 1566 990 1 1 De 10 R f 0.1 setlinewidth 4820 1590 4827 1607 Dl 4828 1607 4841 1651 Dl 4842 1652 4854 1714 Dl 4854 1715 4888 1992 Dl 3175 1952 3592 2224 Dl 3593 2225 3648 2249 Dl 3649 2248 4034 2304 Dl 4034 2304 4888 1992 Dl 3397 1473 3342 1569 Dl 3342 1569 3291 1674 Dl 3290 1674 3175 1951 Dl 4796 1556 4819 1589 Dl 4070 1485 4034 2304 Dl 4124 853 4070 1485 Dl 4125 853 4854 1714 Dl (7)4354 1709 w 4119 786 4119 824 Dl 4119 824 4124 852 Dl 4120 785 4841 1651 Dl 5 R f (8)4457 1241 w 10 R f 0.1 setlinewidth 4109 735 4114 763 Dl 4115 764 4120 785 Dl 4108 736 4827 1607 Dl 5 R f (9)4446 1185 w 10 R f 0.1 setlinewidth 4094 701 4096 712 Dl 4097 713 4108 735 Dl 4094 701 4796 1556 Dl 4070 678 4075 682 Dl 4075 683 4093 701 Dl 4054 673 4070 678 Dl 4063 1012 4070 1485 Dl 4081 817 4063 1012 Dl 4082 817 4119 824 Dl 5 R f (14)4063 1069 w 10 R f 0.1 setlinewidth 4074 762 4075 802 Dl 4075 802 4082 817 Dl 4075 756 4073 761 Dl 4077 756 4114 763 Dl 4076 709 4076 756 Dl 4076 708 4096 712 Dl 4059 695 4065 702 Dl 4063 680 4058 695 Dl 4065 703 4076 708 Dl 4065 680 4075 682 Dl 4042 669 4042 671 Dl 4042 672 4065 680 Dl 4040 670 4052 672 Dl 4028 670 4040 670 Dl 4057 704 1 1 De 4058 705 4062 743 Dl 4062 743 4073 761 Dl 4064 703 4058 704 Dl 4028 673 4029 683 Dl 4029 683 4055 694 Dl 4041 672 4028 673 Dl 4056 695 4058 695 Dl 4004 672 4006 672 Dl 4006 671 4023 669 Dl 4023 669 4027 669 Dl 4056 696 4058 704 Dl 4023 670 4017 672 Dl 4018 673 4028 673 Dl 4038 811 4025 876 Dl 4025 876 4063 1012 Dl 4075 802 4039 810 Dl 4022 793 4039 810 Dl 4032 750 4021 792 Dl 4061 743 4032 750 Dl 4031 711 4026 735 Dl 4026 735 4032 750 Dl 4057 705 4032 710 Dl 4021 686 4019 697 Dl 4019 698 4030 710 Dl 4031 710 4032 710 Dl 4028 683 4021 685 Dl 4014 674 4010 676 Dl 4011 676 4016 684 Dl 4016 685 4021 685 Dl 4016 673 4014 673 Dl 4001 674 1 1 De 4006 672 4001 674 Dl 4002 674 4014 673 Dl 4013 774 4017 793 Dl 4011 741 4013 774 Dl 4021 793 4017 793 Dl 4026 735 4011 741 Dl 4011 718 4006 741 Dl 4007 741 4011 741 Dl 4029 710 4011 717 Dl 3994 714 4006 717 Dl 4008 702 3994 714 Dl 4006 717 4011 717 Dl 4018 697 4008 701 Dl 4001 691 4001 695 Dl 4001 696 4008 701 Dl 4015 685 4000 691 Dl 3999 681 3997 691 Dl 3997 691 4000 691 Dl 4003 679 3999 681 Dl 4009 676 4004 678 Dl 3993 679 1 1 De 4001 674 3994 678 Dl 3994 678 4004 678 Dl 3984 681 1 1 De 3993 677 3983 681 Dl 3995 676 3994 676 Dl 4001 675 3984 681 Dl 4004 673 3996 676 Dl 3874 1201 3648 2249 Dl 3995 889 3875 1200 Dl 4025 876 3996 888 Dl (45)3862 1740 w 3986 812 3984 817 Dl 3985 818 3996 888 Dl 4017 794 3987 812 Dl 3997 746 4013 774 Dl 4006 741 3996 745 Dl 4006 717 3996 745 Dl 4000 695 3990 714 Dl 3992 714 3990 714 Dl 3980 687 3980 688 Dl 3993 679 3980 686 Dl 3999 681 3980 688 Dl 3983 681 1 1 De 3984 681 3994 678 Dl 3980 783 3987 812 Dl 3992 747 3980 781 Dl 3995 746 3993 747 Dl 3982 718 3978 730 Dl 3979 731 3993 747 Dl 3990 715 3983 718 Dl 3979 713 3983 718 Dl 3988 695 3978 713 Dl 3995 692 3988 695 Dl 3979 688 3976 692 Dl 3976 693 3988 695 Dl 3980 686 1 1 De 3983 681 3978 686 Dl 3983 681 3977 684 Dl 3914 954 3875 1200 Dl 3947 860 3914 954 Dl 3983 818 3947 859 Dl 3978 730 3977 732 Dl 3977 733 3959 778 Dl 3960 778 3980 781 Dl 3977 693 3970 698 Dl 3968 697 3968 715 Dl 3968 715 3978 713 Dl 3958 697 3957 698 Dl 3977 685 3959 696 Dl 3978 688 3957 698 Dl 3948 785 3936 822 Dl 3937 822 3947 859 Dl 3958 778 3949 784 Dl 3952 749 3942 776 Dl 3942 777 3949 784 Dl 3976 733 3952 749 Dl 3951 728 3945 737 Dl 3946 737 3952 749 Dl 3969 716 3952 727 Dl 3949 713 3952 727 Dl 3969 698 3948 713 Dl 3957 698 3948 705 Dl 3947 713 1 1 De 3947 706 3947 713 Dl 3907 838 3898 873 Dl 3899 873 3914 954 Dl 3936 822 3908 837 Dl 3917 759 3916 761 Dl 3915 761 3909 805 Dl 3929 750 3917 758 Dl 3930 750 3924 791 Dl 3923 791 3909 805 Dl 3947 706 3928 726 Dl 3928 726 3934 725 Dl 3946 714 3934 725 Dl 3909 806 3905 815 Dl 3906 815 3908 837 Dl 3942 776 3924 791 Dl 3945 737 3930 749 Dl 3934 725 3917 758 Dl 3867 905 3592 2224 Dl 3897 873 3867 905 Dl (83)3711 1588 w 3877 844 3866 874 Dl 3866 874 3867 905 Dl 3904 815 3877 844 Dl 3895 784 3879 814 Dl 3878 814 3877 844 Dl 3915 761 3895 783 Dl 3915 740 3898 764 Dl 3897 765 3895 783 Dl 3928 727 3916 740 Dl 3866 874 3291 1674 Dl (89)3488 1681 w 3879 814 3342 1569 Dl 5 R f (90)3582 1226 w 10 R f 0.1 setlinewidth 3897 765 3397 1473 Dl 20 R f 16 setlinewidth 5040 2502 3024 2502 Dl 5040 486 5040 2502 Dl 3024 486 5040 486 Dl 3024 2502 3024 486 Dl 4095 2031 4065 1182 Dl 4095 2031 4075 1960 Dl 4096 2031 4111 1959 Dl 4348 1927 4096 2031 Dl 4347 1928 4288 1971 Dl 4347 1928 4274 1938 Dl 3794 1920 4348 1927 Dl 3793 1919 3865 1902 Dl 3792 1920 3864 1938 Dl 3332 1913 3793 1918 Dl 3332 1914 3404 1897 Dl 3332 1915 3404 1933 Dl 3252 1896 3332 1914 Dl 3312 1730 3250 1895 Dl 3383 1553 3314 1729 Dl 3383 1553 3373 1626 Dl 3383 1553 3340 1613 Dl 3487 1362 3384 1553 Dl 3486 1361 3468 1433 Dl 3487 1362 3437 1416 Dl 3608 1193 3487 1361 Dl 3608 1193 3581 1262 Dl 3608 1194 3552 1241 Dl 3764 961 3609 1193 Dl 3764 961 3739 1030 Dl 3763 961 3709 1010 Dl 3890 778 3764 960 Dl 3889 778 3864 847 Dl 3889 779 3834 827 Dl 3902 760 3890 778 Dl 3912 744 3902 759 Dl 3915 740 3913 743 Dl 3919 737 3916 740 Dl 3923 731 3918 736 Dl 3926 727 3924 730 Dl 3927 727 1 1 De 10 B f (Fig. 74:)1 322 1 1114 2700 t 10 R f (primal projective path)2 882 1 1461 2700 t 10 B f (Fig. 75:)1 322 1 3286 2700 t 10 I f (d)3633 2700 w 10 R f (= \(0,0,1\), 30)2 497 1 3708 2700 t 10 S f (\260)4205 2700 w 10 R f (outside view)1 508 1 4270 2700 t 0.1 setlinewidth 872 4429 2414 4342 Dl 2415 4341 2481 4336 Dl 2482 4336 2584 4309 Dl 949 3737 938 3790 Dl 937 3790 927 3859 Dl 927 3860 914 3968 Dl 913 3970 901 4091 Dl 901 4090 871 4428 Dl 2290 3875 2584 4309 Dl 2068 3562 2290 3875 Dl 1956 3414 2067 3561 Dl 1907 3365 1944 3400 Dl 1944 3401 1955 3414 Dl 1654 3252 1653 3252 Dl 1646 3254 1643 3255 Dl 1653 3252 1648 3253 Dl 1839 3309 1 1 De 1839 3310 1885 3347 Dl 1886 3347 1906 3365 Dl 1756 3265 1786 3279 Dl 1786 3281 1821 3299 Dl 1695 3249 1697 3249 Dl 1698 3250 1704 3250 Dl 1705 3250 1725 3255 Dl 1822 3299 1838 3309 Dl 1725 3255 1743 3260 Dl 1744 3260 1756 3265 Dl 1674 3250 1672 3250 Dl 1658 3251 1654 3251 Dl 1667 3250 1658 3250 Dl 1694 3249 1675 3249 Dl 1671 3250 1668 3250 Dl 1940 3402 1977 3453 Dl 1977 3453 2067 3561 Dl 1943 3401 1939 3402 Dl 1918 3384 1939 3402 Dl 1882 3348 1918 3384 Dl 1885 3347 1882 3348 Dl 1836 3310 1861 3332 Dl 1863 3333 1882 3348 Dl 1839 3310 1836 3310 Dl 1785 3280 1805 3292 Dl 1805 3292 1834 3309 Dl 1835 3310 1836 3310 Dl 1785 3280 1784 3280 Dl 1743 3261 1748 3263 Dl 1748 3264 1778 3277 Dl 1778 3278 1784 3280 Dl 1716 3255 1720 3255 Dl 1705 3251 1717 3254 Dl 1721 3255 1743 3260 Dl 1670 3250 1668 3250 Dl 1668 3250 1 1 De 1643 3255 1634 3259 Dl 1893 3366 1915 3384 Dl 1857 3336 1893 3366 Dl 1916 3384 1915 3384 Dl 1862 3333 1858 3335 Dl 1829 3313 1854 3334 Dl 1856 3334 1858 3335 Dl 1834 3310 1829 3312 Dl 1809 3303 1825 3310 Dl 1802 3295 1808 3303 Dl 1825 3311 1829 3312 Dl 1804 3293 1802 3294 Dl 1774 3279 1783 3284 Dl 1784 3285 1802 3294 Dl 1778 3277 1774 3279 Dl 1747 3266 1771 3278 Dl 1772 3279 1774 3279 Dl 1746 3264 1746 3265 Dl 1747 3264 1746 3264 Dl 1724 3259 1725 3259 Dl 1721 3256 1724 3258 Dl 1726 3259 1746 3264 Dl 1702 3255 1704 3255 Dl 1695 3251 1702 3254 Dl 1716 3255 1704 3255 Dl 1697 3250 1695 3250 Dl 1675 3249 1675 3250 Dl 1695 3250 1675 3250 Dl 1668 3250 1659 3252 Dl 1659 3252 1 1 De 2083 3680 2481 4336 Dl 1970 3459 2083 3680 Dl 1976 3453 1969 3458 Dl (45)2256 3991 w 1912 3394 1914 3398 Dl 1914 3398 1969 3458 Dl 1915 3385 1911 3394 Dl 1852 3336 1893 3366 Dl 1853 3334 1851 3335 Dl 1825 3311 1851 3335 Dl 1784 3285 1807 3303 Dl 1808 3303 1807 3303 Dl 1729 3264 1735 3266 Dl 1726 3258 1728 3263 Dl 1746 3266 1735 3266 Dl 1705 3255 1709 3256 Dl 1709 3256 1724 3258 Dl 1674 3252 1681 3252 Dl 1675 3252 1674 3252 Dl 1694 3251 1681 3252 Dl 1655 3253 1647 3254 Dl 1659 3252 1656 3252 Dl 1647 3254 1 1 De 1876 3366 1911 3394 Dl 1851 3337 1876 3365 Dl 1851 3335 1 1 De 1805 3305 1816 3315 Dl 1817 3315 1851 3335 Dl 1806 3303 1804 3304 Dl 1789 3297 1804 3304 Dl 1769 3280 1789 3296 Dl 1770 3279 1768 3280 Dl 1735 3267 1740 3270 Dl 1741 3271 1768 3280 Dl 1725 3263 1728 3263 Dl 1710 3256 1725 3263 Dl 1682 3252 1695 3254 Dl 1702 3254 1695 3254 Dl 1659 3252 1666 3252 Dl 1673 3251 1666 3252 Dl 1953 3495 2083 3680 Dl 1915 3424 1953 3495 Dl 1914 3399 1914 3425 Dl 1816 3315 1816 3316 Dl 1817 3317 1850 3355 Dl 1850 3355 1876 3365 Dl 1740 3270 1740 3273 Dl 1741 3275 1777 3295 Dl 1778 3295 1789 3296 Dl 1696 3263 1697 3263 Dl 1696 3254 1696 3261 Dl 1724 3263 1697 3263 Dl 1647 3255 1630 3262 Dl 1634 3260 1630 3262 Dl 1845 3358 1867 3388 Dl 1868 3389 1914 3425 Dl 1849 3356 1845 3358 Dl 1805 3324 1825 3347 Dl 1825 3348 1845 3358 Dl 1816 3317 1805 3324 Dl 1769 3300 1774 3307 Dl 1775 3308 1805 3324 Dl 1776 3295 1769 3300 Dl 1730 3281 1769 3300 Dl 1740 3274 1730 3280 Dl 1697 3263 1697 3267 Dl 1729 3280 1 1 De 1697 3268 1729 3280 Dl 1666 3254 1696 3261 Dl 1666 3253 1664 3254 Dl 1663 3254 1661 3255 Dl 1656 3253 1661 3255 Dl 1629 3262 1623 3265 Dl 1843 3393 1862 3421 Dl 1863 3421 1953 3495 Dl 1867 3388 1843 3392 Dl 1755 3317 1755 3318 Dl 1755 3319 1809 3362 Dl 1765 3314 1755 3317 Dl 1766 3314 1814 3354 Dl 1814 3354 1809 3362 Dl 1697 3267 1702 3282 Dl 1703 3283 1723 3286 Dl 1728 3281 1723 3286 Dl 1623 3266 1614 3271 Dl 1660 3256 1614 3271 Dl 1661 3255 1660 3256 Dl 1810 3362 1813 3369 Dl 1814 3369 1843 3392 Dl 1824 3347 1814 3354 Dl 1774 3308 1765 3313 Dl 1724 3287 1755 3317 Dl 1658 3260 1662 3265 Dl 1660 3256 1658 3260 Dl 1663 3266 1697 3267 Dl 1839 3439 2414 4342 Dl 1862 3421 1839 3438 Dl (83)2110 3900 w 1792 3386 1802 3409 Dl 1803 3408 1839 3438 Dl 1813 3370 1792 3385 Dl 1740 3331 1748 3354 Dl 1749 3355 1792 3385 Dl 1754 3319 1738 3330 Dl 1692 3289 1694 3307 Dl 1695 3307 1738 3330 Dl 1702 3282 1692 3289 Dl 1661 3266 1656 3281 Dl 1656 3282 1692 3289 Dl 1657 3261 1613 3271 Dl 1802 3410 901 4091 Dl (89)1569 4063 w 1747 3354 914 3968 Dl (90)1282 3733 w 1694 3307 927 3859 Dl (91)1264 3648 w 1655 3281 938 3790 Dl 5 R f (92)1273 3574 w 10 R f 0.1 setlinewidth 1612 3272 949 3737 Dl 5 R f (93)1263 3531 w 20 R f 16 setlinewidth 2736 4878 720 4878 Dl 2736 2862 2736 4878 Dl 720 2862 2736 2862 Dl 720 4878 720 2862 Dl 1742 4280 1774 3650 Dl 1742 4279 1728 4207 Dl 1742 4280 1763 4209 Dl 1172 4249 1741 4280 Dl 1173 4247 1245 4234 Dl 1173 4248 1243 4270 Dl 1146 4288 1172 4248 Dl 1076 4337 1146 4288 Dl 1057 4329 1074 4338 Dl 1020 4143 1058 4328 Dl 1019 4144 1051 4210 Dl 1017 4143 1015 4217 Dl 1050 3946 1018 4143 Dl 1052 3946 1057 4020 Dl 1050 3946 1021 4014 Dl 1145 3746 1051 3946 Dl 1145 3747 1131 3819 Dl 1144 3746 1098 3803 Dl 1351 3600 1146 3746 Dl 1351 3600 1303 3656 Dl 1351 3600 1282 3627 Dl 1549 3428 1351 3600 Dl 1549 3429 1507 3489 Dl 1549 3428 1483 3461 Dl 1686 3314 1550 3427 Dl 1695 3304 1685 3314 Dl 1693 3293 1697 3304 Dl 1692 3290 1692 3292 Dl 1695 3288 1692 3289 Dl 1699 3286 1695 3288 Dl 1701 3283 1699 3284 Dl 1702 3283 1 1 De 10 R f 0.1 setlinewidth 3175 4309 4515 4380 Dl 4516 4381 4608 4384 Dl 4608 4383 4888 4376 Dl 3412 3777 3376 3819 Dl 3377 3820 3344 3874 Dl 3344 3875 3303 3959 Dl 3302 3959 3264 4053 Dl 3264 4054 3175 4309 Dl 4636 3890 4888 4376 Dl 4398 3458 4636 3889 Dl 4358 3408 4384 3438 Dl 4386 3438 4398 3458 Dl 4316 3368 4341 3391 Dl 4342 3390 4358 3407 Dl 4295 3349 4316 3367 Dl 4450 3572 4636 3889 Dl 4372 3431 4449 3571 Dl 4372 3432 4384 3438 Dl 4332 3388 4360 3419 Dl 4360 3419 4372 3431 Dl 4329 3384 4331 3387 Dl 4329 3384 4341 3391 Dl 4287 3346 4328 3384 Dl 4288 3345 4295 3348 Dl 4263 3332 4276 3339 Dl 4236 3318 4263 3332 Dl 4278 3340 4288 3345 Dl 4195 3304 4205 3306 Dl 4205 3307 4235 3317 Dl 4180 3302 4195 3304 Dl 4275 3340 1 1 De 4274 3340 4310 3372 Dl 4311 3372 4331 3387 Dl 4276 3340 4274 3340 Dl 4201 3307 4223 3317 Dl 4223 3318 4261 3331 Dl 4205 3306 4201 3306 Dl 4261 3332 4263 3332 Dl 4147 3299 4148 3299 Dl 4149 3299 4154 3299 Dl 4154 3299 4177 3300 Dl 4178 3301 4180 3301 Dl 4261 3333 4274 3340 Dl 4177 3301 4186 3304 Dl 4187 3304 4201 3306 Dl 4125 3302 4123 3302 Dl 4146 3299 4126 3301 Dl 4339 3422 4361 3470 Dl 4362 3470 4449 3571 Dl 4360 3420 4340 3422 Dl 4316 3407 4340 3422 Dl 4294 3375 4315 3407 Dl 4310 3373 4294 3375 Dl 4260 3343 4276 3362 Dl 4277 3363 4294 3375 Dl 4275 3340 4260 3342 Dl 4219 3318 4231 3328 Dl 4232 3330 4258 3342 Dl 4259 3342 4260 3342 Dl 4223 3318 4218 3318 Dl 4185 3304 4186 3306 Dl 4187 3307 4211 3317 Dl 4211 3317 4218 3318 Dl 4186 3304 4185 3304 Dl 4161 3302 4163 3302 Dl 4154 3299 4160 3301 Dl 4164 3302 4185 3304 Dl 4123 3303 4121 3303 Dl 4294 3392 4312 3407 Dl 4266 3365 4293 3391 Dl 4315 3407 4312 3407 Dl 4276 3363 4266 3365 Dl 4246 3346 4261 3364 Dl 4262 3365 4266 3365 Dl 4257 3342 4245 3345 Dl 4222 3339 4240 3344 Dl 4224 3331 4222 3339 Dl 4240 3345 4245 3345 Dl 4231 3328 4224 3330 Dl 4200 3320 4207 3324 Dl 4207 3323 4224 3330 Dl 4210 3317 4200 3319 Dl 4181 3309 4196 3319 Dl 4197 3319 4200 3319 Dl 4183 3308 4181 3309 Dl 4186 3307 4182 3308 Dl 4163 3305 1 1 De 4163 3302 4162 3304 Dl 4163 3306 4182 3308 Dl 4142 3304 4143 3304 Dl 4142 3302 4142 3304 Dl 4142 3300 1 1 De 4160 3302 4143 3304 Dl 4147 3299 4142 3300 Dl 4126 3302 4122 3303 Dl 4142 3301 4122 3303 Dl 4120 3303 4109 3306 Dl 4372 3695 4608 4384 Dl 4342 3477 4371 3693 Dl 4362 3470 4342 3476 Dl (45)4540 4035 w 4294 3418 4294 3422 Dl 4295 3422 4342 3476 Dl 4312 3407 4294 3417 Dl 4255 3366 4293 3391 Dl 4261 3364 4254 3366 Dl 4240 3345 4254 3366 Dl 4208 3324 4219 3339 Dl 4221 3339 4219 3339 Dl 4158 3311 4163 3312 Dl 4163 3305 4158 3310 Dl 4181 3310 4163 3312 Dl 4144 3304 4146 3304 Dl 4147 3304 4162 3304 Dl 4118 3304 4124 3304 Dl 4121 3303 4117 3304 Dl 4142 3301 4124 3304 Dl 4106 3307 4101 3309 Dl 4108 3307 4106 3307 Dl 4265 3393 4294 3417 Dl 4252 3368 4264 3393 Dl 4254 3367 4252 3367 Dl 4213 3341 4219 3350 Dl 4220 3351 4252 3367 Dl 4218 3340 4213 3341 Dl 4201 3336 4213 3341 Dl 4191 3321 4201 3335 Dl 4196 3319 4191 3321 Dl 4163 3312 4165 3315 Dl 4166 3316 4191 3321 Dl 4156 3310 4158 3310 Dl 4147 3304 4155 3309 Dl 4124 3305 4133 3305 Dl 4141 3304 4133 3305 Dl 4109 3306 1 1 De 4116 3304 4109 3306 Dl 4289 3516 4371 3693 Dl 4277 3449 4289 3516 Dl 4295 3423 4277 3449 Dl 4219 3351 4219 3352 Dl 4220 3352 4235 3386 Dl 4235 3387 4264 3393 Dl 4165 3316 4162 3319 Dl 4162 3319 4187 3335 Dl 4189 3335 4201 3335 Dl 4125 3313 1 1 De 4133 3305 4125 3312 Dl 4155 3310 4125 3313 Dl 4100 3310 4081 3319 Dl 4227 3389 4237 3417 Dl 4237 3418 4277 3449 Dl 4234 3386 4227 3389 Dl 4199 3361 4208 3381 Dl 4209 3381 4227 3389 Dl 4219 3351 4199 3360 Dl 4173 3342 4173 3348 Dl 4174 3348 4199 3360 Dl 4187 3336 4173 3342 Dl 4144 3328 4173 3342 Dl 4161 3320 4143 3327 Dl 4125 3313 4120 3317 Dl 4142 3327 1 1 De 4120 3318 4142 3327 Dl 4107 3308 4125 3312 Dl 4109 3307 4106 3308 Dl 4105 3308 4102 3309 Dl 4105 3307 4102 3309 Dl 4081 3319 4073 3323 Dl 4205 3425 4214 3451 Dl 4214 3451 4289 3516 Dl 4236 3418 4204 3425 Dl 4145 3361 4145 3362 Dl 4146 3363 4181 3399 Dl 4158 3356 4145 3360 Dl 4160 3356 4191 3390 Dl 4191 3391 4181 3399 Dl 4119 3318 4114 3332 Dl 4114 3333 4132 3334 Dl 4142 3328 4132 3334 Dl 4072 3323 4059 3330 Dl 4099 3312 4059 3330 Dl 4101 3310 4099 3311 Dl 4181 3399 4181 3405 Dl 4181 3406 4204 3425 Dl 4207 3382 4191 3390 Dl 4173 3348 4159 3355 Dl 4132 3334 4145 3360 Dl 4093 3315 4092 3319 Dl 4099 3311 4093 3315 Dl 4093 3319 4120 3317 Dl 4181 3471 4515 4380 Dl 4214 3452 4181 3471 Dl (83)4347 3941 w 4153 3423 4154 3445 Dl 4154 3446 4181 3471 Dl 4181 3405 4152 3422 Dl 4123 3375 4121 3397 Dl 4122 3397 4152 3422 Dl 4145 3363 4123 3375 Dl 4100 3340 4093 3357 Dl 4094 3358 4123 3375 Dl 4113 3333 4101 3340 Dl 4091 3321 4076 3336 Dl 4077 3336 4101 3340 Dl 4058 3330 1 1 De 4092 3315 4058 3330 Dl 4153 3445 3264 4053 Dl (89)3851 4048 w 4121 3397 3303 3959 Dl 5 R f (90)3690 3721 w 10 R f 0.1 setlinewidth 4094 3358 3344 3874 Dl 5 R f (91)3695 3654 w 10 R f 0.1 setlinewidth 4075 3336 3376 3819 Dl 5 R f (92)3703 3603 w 10 R f 0.1 setlinewidth 4058 3331 3413 3776 Dl 20 R f 16 setlinewidth 5040 4878 3024 4878 Dl 5040 2862 5040 4878 Dl 3024 2862 5040 2862 Dl 3024 4878 3024 2862 Dl 4225 4273 4232 3672 Dl 4223 4273 4206 4201 Dl 4224 4273 4242 4201 Dl 3984 4214 4223 4273 Dl 3984 4214 4058 4214 Dl 3984 4215 4049 4249 Dl 3691 4234 3983 4214 Dl 3692 4235 3762 4212 Dl 3692 4235 3764 4247 Dl 3387 4257 3692 4234 Dl 3387 4257 3457 4234 Dl 3387 4258 3460 4270 Dl 3327 4246 3386 4257 Dl 3343 4100 3327 4246 Dl 3404 3944 3343 4099 Dl 3519 3782 3404 3944 Dl 3520 3780 3493 3849 Dl 3520 3780 3464 3828 Dl 3713 3651 3520 3781 Dl 3713 3650 3664 3705 Dl 3713 3651 3644 3676 Dl 3926 3484 3714 3650 Dl 3925 3485 3880 3543 Dl 3925 3485 3858 3515 Dl 4082 3366 3926 3484 Dl 4083 3366 4037 3423 Dl 4083 3366 4015 3394 Dl 4096 3355 4083 3366 Dl 4099 3344 4097 3354 Dl 4100 3341 4099 3343 Dl 4105 3338 4101 3340 Dl 4109 3335 4104 3338 Dl 4113 3333 4110 3335 Dl 4114 3332 1 1 De 10 B f (Fig. 76:)1 322 1 1040 5076 t 10 I f (d)1387 5076 w 10 R f (= \(\2611,0,0\), outside view)3 955 1 1462 5076 t 10 B f (Fig. 77:)1 322 1 3344 5076 t 10 I f (d)3691 5076 w 10 R f (= \(\2611,0,1\), outside view)3 955 1 3766 5076 t ( primal projective algo-)3 958(Like the transformed polytopes of the dual projective algorithm, those of the)11 3112 2 970 5232 t ( these)1 238( 78\26198 show)2 529( Figures)1 359(rithm stay reasonably round, but they change more rapidly, especially at first.)11 3194 4 720 5352 t ( from inside; fig-)3 686(polytopes on iterations 2\26122 \(the phase-2 iterations\), with the steps taken showing through)12 3634 2 720 5472 t (ure 99 is analogous to figure 47, showing the final polytope from view direction)13 3202 1 720 5592 t 10 I f (d)3947 5592 w 10 S f (=)4046 5592 w 10 R f (\( 0 ,)2 124 1 4150 5592 t 10 S f (-)4290 5592 w 10 R f (1 , 0 \).)3 207 1 4361 5592 t (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 25 26 %%Page: 26 27 /saveobj save def mark 27 pagesetup 10 R f (- 26 -)2 216 1 2772 282 t 0.1 setlinewidth 2442 1995 2442 1998 Dl 2442 1999 2441 2012 Dl 2440 2012 2437 2033 Dl 2438 2033 2420 2126 Dl 2419 2127 2409 2142 Dl 1294 2215 1256 2350 Dl 1315 2200 1294 2215 Dl 1598 2134 1316 2200 Dl 1600 2132 2420 2126 Dl 2409 2142 1256 2350 Dl (4)1685 2228 w 1225 2210 1256 2350 Dl 2432 1981 2442 1995 Dl 1494 1684 1599 2133 Dl 1397 945 1495 1683 Dl 1396 946 2437 2033 Dl (7)1800 1747 w 1368 830 1372 891 Dl 1372 892 1396 946 Dl 1368 830 2441 2012 Dl 5 R f (8)1798 1357 w 10 R f 0.1 setlinewidth 1336 742 1350 789 Dl 1350 790 1368 830 Dl 1336 742 2442 1998 Dl 5 R f (9)1782 1290 w 10 R f 0.1 setlinewidth 1311 691 1306 696 Dl 1306 697 1336 742 Dl 1311 692 2432 1980 Dl 1281 666 1311 691 Dl 1336 1177 1495 1683 Dl 1283 855 1336 1177 Dl 1283 854 1372 891 Dl 5 R f (14)1360 1179 w 10 R f 0.1 setlinewidth 1249 753 1261 823 Dl 1262 823 1283 853 Dl 1254 747 1249 753 Dl 1255 746 1350 789 Dl 1252 671 1254 746 Dl 1252 671 1306 696 Dl 1215 647 1225 655 Dl 1252 653 1216 647 Dl 1226 656 1252 671 Dl 1252 653 1280 666 Dl 1213 646 1252 653 Dl 1210 654 1208 655 Dl 1208 656 1221 720 Dl 1222 721 1249 753 Dl 1210 655 1225 655 Dl 1177 639 1165 637 Dl 1165 637 1208 645 Dl 1179 639 1212 645 Dl 1210 646 1216 647 Dl 1210 646 1210 655 Dl 1197 838 1208 961 Dl 1209 961 1336 1177 Dl 1261 824 1197 838 Dl 5 R f (28)1238 971 w 10 R f 0.1 setlinewidth 1159 809 1197 838 Dl 1166 733 1159 808 Dl 1221 721 1167 732 Dl 1157 666 1152 707 Dl 1153 707 1167 732 Dl 1206 656 1158 666 Dl 1149 641 1141 653 Dl 1141 654 1156 666 Dl 1156 666 1158 666 Dl 1164 637 1149 640 Dl 1143 642 1149 640 Dl 1141 780 1153 810 Dl 1128 724 1140 780 Dl 1159 808 1153 810 Dl 1152 708 1127 723 Dl 1126 686 1121 725 Dl 1127 724 1121 725 Dl 1156 666 1126 685 Dl 1100 688 1118 688 Dl 1124 664 1100 688 Dl 1125 686 1118 688 Dl 1139 654 1123 664 Dl 1116 660 1116 663 Dl 1116 663 1123 664 Dl 1142 643 1117 659 Dl 1117 660 1113 662 Dl 1173 1466 1316 2200 Dl 1169 990 1173 1465 Dl 1208 961 1169 990 Dl (45)1297 1681 w 1112 854 1112 866 Dl 1113 867 1169 990 Dl 1152 810 1113 853 Dl 1106 737 1140 780 Dl 1120 725 1105 736 Dl 1117 689 1105 737 Dl 1105 737 1 1 De 1115 663 1095 691 Dl 1099 688 1095 691 Dl 1093 807 1113 853 Dl 1099 741 1092 807 Dl 1104 737 1100 740 Dl 1083 702 1078 723 Dl 1078 723 1100 740 Dl 1095 692 1084 702 Dl 1082 701 1084 702 Dl 1100 674 1080 700 Dl 1112 663 1100 673 Dl 1097 1133 1173 1465 Dl 1086 961 1097 1133 Dl 1111 866 1085 960 Dl 5 R f (62)1111 1126 w 10 R f 0.1 setlinewidth 1078 723 1077 727 Dl 1076 729 1065 816 Dl 1091 808 1065 816 Dl 1081 701 1072 716 Dl 1057 834 1057 907 Dl 1057 908 1085 960 Dl 1064 817 1056 835 Dl 1052 779 1047 830 Dl 1047 830 1056 835 Dl 1076 728 1053 779 Dl 1055 752 1049 771 Dl 1049 772 1053 779 Dl 1071 716 1055 751 Dl 1039 962 1047 1027 Dl 1048 1028 1097 1133 Dl 1057 908 1038 961 Dl 1031 841 1031 846 Dl 1031 846 1029 912 Dl 1039 810 1033 840 Dl 1038 810 1036 874 Dl 1036 875 1029 912 Dl 1028 912 1028 930 Dl 1028 931 1038 961 Dl 1046 830 1036 874 Dl 1048 772 1039 810 Dl 1045 1113 1294 2215 Dl 1047 1028 1045 1113 Dl 5 R f (83)1147 1593 w 10 R f 0.1 setlinewidth 1028 1014 1033 1072 Dl 1034 1072 1045 1113 Dl 1028 931 1027 1013 Dl 1034 1072 1224 2210 Dl 5 R f (89)1165 1876 w 20 R f 16 setlinewidth 2736 2502 720 2502 Dl 2736 486 2736 2502 Dl 720 486 2736 486 Dl 720 2502 720 486 Dl 1889 2178 1630 1598 Dl 1889 2178 1843 2120 Dl 1888 2178 1876 2106 Dl 10 R f 0.1 setlinewidth 4146 1877 4146 1893 Dl 4147 1893 4149 1939 Dl 4148 1940 4152 2007 Dl 4154 2008 4172 2309 Dl 4146 1877 4174 2303 Dl 4172 2308 4174 2303 Dl 3931 2345 3892 2309 Dl 3936 2347 3931 2345 Dl 3986 2349 3937 2347 Dl 3987 2350 4172 2309 Dl 3890 1751 3890 1900 Dl 3890 1901 3892 2309 Dl 4123 1729 4140 1836 Dl 4140 1835 4145 1876 Dl 3957 1548 3987 2350 Dl 3937 872 3956 1548 Dl 3936 871 4152 2007 Dl (7)4013 1844 w 3934 794 3934 838 Dl 3934 839 3936 871 Dl 3934 794 4149 1939 Dl 3930 734 3931 768 Dl 3932 769 3933 794 Dl 3930 734 4146 1893 Dl 3927 692 3927 705 Dl 3928 705 3930 733 Dl 3928 692 4140 1836 Dl 3924 660 3924 665 Dl 3925 665 3927 691 Dl 3924 659 4122 1728 Dl 3922 648 3924 658 Dl 3933 1041 3956 1548 Dl 3929 824 3934 1040 Dl 3927 823 3934 838 Dl 3925 758 3926 804 Dl 3925 804 3927 822 Dl 3924 752 3924 757 Dl 3924 753 3931 768 Dl 3924 696 3924 751 Dl 3924 697 3927 705 Dl 3921 676 3921 686 Dl 3922 660 3921 676 Dl 3922 687 3924 696 Dl 3922 661 3924 665 Dl 3918 643 3918 645 Dl 3919 645 3922 660 Dl 3919 643 3921 648 Dl 3918 639 3919 642 Dl 3920 688 1 1 De 3920 688 3921 734 Dl 3922 734 3924 757 Dl 3921 686 3920 686 Dl 3916 644 3916 656 Dl 3917 657 3920 676 Dl 3916 644 3918 645 Dl 3921 676 1 1 De 3914 637 3916 637 Dl 3917 638 1 1 De 3920 676 3920 686 Dl 3916 638 3915 640 Dl 3915 640 3916 643 Dl 3921 807 3921 880 Dl 3922 881 3934 1040 Dl 3926 805 3921 807 Dl 3919 784 3921 807 Dl 3917 737 3917 784 Dl 3922 734 3918 736 Dl 3916 689 3916 717 Dl 3917 718 3918 736 Dl 3919 687 3916 689 Dl 3915 658 3915 671 Dl 3915 671 3916 689 Dl 3916 689 1 1 De 3916 657 3915 657 Dl 3913 640 3913 642 Dl 3914 644 3914 655 Dl 3915 655 3915 657 Dl 3914 637 3913 638 Dl 3914 639 3915 640 Dl 3916 761 3917 784 Dl 3915 723 3916 761 Dl 3916 717 3914 721 Dl 3913 694 3913 720 Dl 3914 721 1 1 De 3915 689 3913 694 Dl 3912 685 3913 692 Dl 3912 674 3911 685 Dl 3913 694 1 1 De 3914 671 3913 673 Dl 3912 659 3912 664 Dl 3913 665 3913 673 Dl 3914 655 3912 659 Dl 3912 646 3912 658 Dl 3913 644 3913 646 Dl 3913 644 3913 645 Dl 3912 643 1 1 De 3913 639 3912 642 Dl 3913 644 3913 645 Dl 3913 638 3911 642 Dl 3917 1229 3937 2347 Dl 3917 890 3916 1229 Dl 3921 880 3918 889 Dl 5 R f (45)3920 1771 w 10 R f 0.1 setlinewidth 3913 800 3913 806 Dl 3913 806 3918 889 Dl 3916 784 3913 799 Dl 3914 725 3916 761 Dl 3914 721 3913 723 Dl 3912 694 3912 724 Dl 3912 665 3911 686 Dl 3910 649 3910 651 Dl 3913 643 3911 649 Dl 3912 647 3910 651 Dl 3911 644 1 1 De 3911 643 3911 644 Dl 3911 763 3913 799 Dl 3911 725 3911 763 Dl 3912 725 1 1 De 3910 689 3910 702 Dl 3910 703 3912 725 Dl 3910 687 3910 689 Dl 3910 682 3910 689 Dl 3911 662 3910 681 Dl 3911 659 3911 661 Dl 3910 651 3910 655 Dl 3910 655 3911 661 Dl 3911 644 3910 649 Dl 3911 643 3911 645 Dl 3910 953 3916 1229 Dl 3911 849 3911 953 Dl 3913 806 3911 848 Dl 3910 702 3910 704 Dl 3908 704 3908 754 Dl 3909 755 3911 763 Dl 3909 655 3909 660 Dl 3908 661 3908 682 Dl 3908 682 1 1 De 3908 656 3908 657 Dl 3910 646 3908 656 Dl 3909 650 3908 657 Dl 3908 761 3908 802 Dl 3909 802 3911 848 Dl 3908 755 3908 760 Dl 3907 719 3907 749 Dl 3907 749 3908 760 Dl 3909 704 3907 719 Dl 3906 692 3906 702 Dl 3907 703 3907 719 Dl 3908 682 3907 692 Dl 3907 674 3907 692 Dl 3909 661 3907 673 Dl 3908 657 3908 664 Dl 3907 664 3907 674 Dl 3906 816 3906 856 Dl 3906 857 3911 953 Dl 3907 803 3905 815 Dl 3904 723 3904 725 Dl 3904 726 3904 778 Dl 3904 715 3904 722 Dl 3906 715 3906 763 Dl 3904 764 3904 778 Dl 3908 665 3906 686 Dl 3906 675 3906 685 Dl 3904 778 3904 788 Dl 3905 788 3905 815 Dl 3907 749 3906 763 Dl 3906 702 3905 714 Dl 3905 685 3904 722 Dl 3904 890 3931 2345 Dl 3904 857 3903 890 Dl 3903 818 3903 852 Dl 3902 853 3903 890 Dl 3904 788 3903 818 Dl 3902 748 3902 782 Dl 3903 782 3903 818 Dl 3904 725 3903 748 Dl 3903 718 3903 748 Dl 3905 686 3904 717 Dl 3902 853 3890 1900 Dl 5 R f (89)3882 1822 w 10 R f 0.1 setlinewidth 3901 783 3890 1751 Dl 20 R f 16 setlinewidth 5040 2502 3024 2502 Dl 5040 486 5040 2502 Dl 3024 486 5040 486 Dl 3024 2502 3024 486 Dl 4101 2263 4038 2283 Dl 4100 2263 4038 2302 Dl 4101 2263 4027 2268 Dl 10 B f (Fig. 78:)1 322 1 926 2700 t 10 R f (primal projective iter 2, outside)4 1257 1 1273 2700 t 10 B f (Fig. 79:)1 322 1 3230 2700 t 10 R f (primal projective iter 3, outside)4 1257 1 3577 2700 t 0.1 setlinewidth 1895 4107 1895 4127 Dl 1896 4129 1897 4181 Dl 1897 4180 1899 4253 Dl 1900 4254 1907 4566 Dl 1683 4700 1591 4544 Dl 1691 4709 1683 4700 Dl 1743 4726 1691 4710 Dl 1745 4726 1907 4566 Dl 1634 3671 1612 4028 Dl 1610 4028 1604 4169 Dl 1604 4169 1591 4544 Dl 1875 3957 1890 4065 Dl 1890 4066 1895 4107 Dl 1736 3987 1744 4726 Dl 1732 3290 1735 3987 Dl 1732 3289 1899 4253 Dl (7)1777 4187 w 1730 3204 1730 3255 Dl 1731 3255 1732 3289 Dl 1730 3205 1897 4181 Dl 1727 3135 1728 3175 Dl 1729 3176 1730 3204 Dl 1727 3135 1895 4127 Dl 1725 3084 1725 3103 Dl 1725 3104 1727 3135 Dl 1725 3083 1890 4065 Dl 1721 3041 1721 3051 Dl 1722 3052 1725 3084 Dl 1720 3041 1874 3958 Dl 1715 3019 1717 3027 Dl 1718 3028 1720 3040 Dl 1713 3015 1 1 De 1714 3015 1715 3018 Dl 1725 3478 1735 3987 Dl 1725 3245 1725 3477 Dl 1724 3245 1730 3255 Dl 1722 3170 1722 3224 Dl 1723 3225 1724 3245 Dl 1722 3164 1722 3170 Dl 1722 3165 1728 3175 Dl 1722 3098 1722 3164 Dl 1722 3098 1725 3103 Dl 1718 3075 1719 3087 Dl 1719 3049 1718 3075 Dl 1719 3087 1721 3097 Dl 1719 3049 1721 3051 Dl 1715 3024 1715 3029 Dl 1715 3029 1719 3048 Dl 1715 3024 1717 3027 Dl 1713 3019 1715 3024 Dl 1713 3015 1713 3018 Dl 1718 3089 1718 3090 Dl 1719 3089 1720 3144 Dl 1720 3145 1722 3170 Dl 1719 3087 1718 3088 Dl 1713 3030 1713 3049 Dl 1713 3050 1717 3074 Dl 1715 3030 1713 3030 Dl 1718 3075 1 1 De 1710 3014 1 1 De 1710 3015 1712 3018 Dl 1710 3013 1712 3014 Dl 1713 3018 1 1 De 1718 3074 1718 3088 Dl 1712 3018 1711 3025 Dl 1711 3025 1713 3030 Dl 1709 3013 1707 3017 Dl 1716 3230 1716 3309 Dl 1717 3310 1725 3477 Dl 1722 3224 1717 3229 Dl 1715 3204 1717 3229 Dl 1714 3150 1714 3204 Dl 1720 3146 1715 3149 Dl 1713 3093 1713 3126 Dl 1714 3127 1715 3149 Dl 1718 3090 1714 3093 Dl 1712 3051 1712 3069 Dl 1712 3069 1714 3092 Dl 1714 3093 1 1 De 1713 3049 1712 3050 Dl 1710 3025 1710 3029 Dl 1711 3029 1711 3047 Dl 1712 3048 1712 3050 Dl 1709 3019 1709 3020 Dl 1709 3014 1709 3019 Dl 1708 3020 1710 3025 Dl 1712 3178 1713 3204 Dl 1712 3131 1712 3177 Dl 1713 3127 1711 3131 Dl 1710 3097 1710 3129 Dl 1711 3130 1711 3131 Dl 1712 3092 1710 3097 Dl 1708 3087 1710 3096 Dl 1709 3072 1707 3086 Dl 1710 3096 1710 3097 Dl 1711 3070 1710 3072 Dl 1709 3053 1709 3060 Dl 1709 3060 1710 3072 Dl 1710 3048 1708 3052 Dl 1708 3034 1708 3052 Dl 1708 3052 1 1 De 1708 3032 1708 3034 Dl 1709 3030 1709 3031 Dl 1707 3025 1707 3026 Dl 1708 3020 1707 3025 Dl 1708 3026 1709 3031 Dl 1708 3017 1706 3022 Dl 1708 3020 1706 3022 Dl 1709 3014 1708 3016 Dl 1706 3017 1705 3019 Dl 1707 3015 1705 3019 Dl 1699 3669 1691 4710 Dl 1711 3319 1700 3667 Dl 1716 3309 1712 3319 Dl 5 R f (45)1691 4160 w 10 R f 0.1 setlinewidth 1708 3220 1708 3227 Dl 1709 3228 1712 3319 Dl 1712 3204 1708 3220 Dl 1710 3134 1712 3177 Dl 1710 3130 1709 3133 Dl 1710 3096 1709 3133 Dl 1708 3059 1707 3086 Dl 1705 3035 1705 3038 Dl 1707 3027 1705 3034 Dl 1707 3034 1705 3038 Dl 1706 3022 1706 3024 Dl 1706 3025 1707 3025 Dl 1705 3020 1704 3022 Dl 1706 3016 1704 3021 Dl 1669 3307 1634 3669 Dl 1707 3178 1708 3220 Dl 1708 3135 1707 3178 Dl 1708 3134 1 1 De 1705 3090 1705 3106 Dl 1706 3106 1708 3134 Dl 1707 3087 1706 3089 Dl 1706 3079 1706 3089 Dl 1706 3055 1705 3079 Dl 1708 3052 1707 3054 Dl 1704 3039 1704 3044 Dl 1705 3044 1707 3054 Dl 1705 3034 1 1 De 1704 3025 1704 3034 Dl 1704 3022 1704 3024 Dl 1704 3023 1704 3024 Dl 1704 3023 1704 3025 Dl 1700 3382 1700 3667 Dl 1702 3271 1700 3381 Dl 1708 3228 1703 3271 Dl 1705 3106 1705 3108 Dl 1705 3108 1703 3166 Dl 1704 3166 1707 3178 Dl 1704 3044 1704 3049 Dl 1704 3050 1704 3078 Dl 1704 3079 1705 3079 Dl 1702 3037 1702 3038 Dl 1704 3024 1702 3036 Dl 1705 3034 1702 3038 Dl 1702 3172 1701 3218 Dl 1701 3218 1703 3271 Dl 1703 3166 1702 3171 Dl 1701 3123 1700 3157 Dl 1701 3157 1702 3171 Dl 1705 3108 1702 3122 Dl 1700 3089 1700 3100 Dl 1701 3100 1702 3122 Dl 1703 3078 1701 3088 Dl 1701 3062 1701 3088 Dl 1703 3050 1700 3062 Dl 1701 3038 1700 3045 Dl 1700 3045 1700 3062 Dl 1702 3028 1702 3036 Dl 1703 3025 1703 3027 Dl 1702 3028 1702 3030 Dl 1671 3283 1669 3308 Dl 1696 3229 1696 3272 Dl 1696 3272 1700 3381 Dl 1701 3218 1697 3228 Dl 1696 3119 1696 3121 Dl 1696 3121 1696 3184 Dl 1698 3112 1696 3119 Dl 1698 3111 1698 3170 Dl 1698 3170 1696 3184 Dl 1699 3046 1697 3070 Dl 1698 3070 1698 3073 Dl 1700 3063 1698 3073 Dl 1702 3030 1702 3032 Dl 1695 3186 1695 3196 Dl 1697 3196 1697 3228 Dl 1700 3158 1698 3170 Dl 1700 3100 1698 3111 Dl 1698 3074 1696 3119 Dl 1701 3032 1699 3047 Dl 1700 3047 1700 3045 Dl 1691 3302 1683 4700 Dl 1696 3272 1692 3302 Dl 1691 3222 1690 3258 Dl 1692 3259 1692 3302 Dl 1695 3195 1692 3222 Dl 1693 3142 1691 3178 Dl 1692 3179 1692 3222 Dl 1695 3122 1693 3142 Dl 1693 3100 1693 3142 Dl 1697 3070 1693 3099 Dl 1693 3100 1688 3128 Dl 1699 3048 1688 3128 Dl 1687 3129 1671 3283 Dl 1689 3259 1604 4169 Dl (89)1602 4160 w 1691 3180 1612 4028 Dl 20 R f 16 setlinewidth 2736 4878 720 4878 Dl 2736 2862 2736 4878 Dl 720 2862 2736 2862 Dl 720 4878 720 2862 Dl 1718 4492 1821 4505 Dl 1718 4491 1791 4483 Dl 1717 4492 1786 4519 Dl 10 R f 0.1 setlinewidth 4242 4222 4242 4238 Dl 4242 4239 4243 4281 Dl 4244 4281 4247 4340 Dl 4247 4340 4265 4585 Dl 4243 4222 4276 4566 Dl 4265 4585 4276 4566 Dl 3928 4709 3916 4578 Dl 3933 4716 3929 4709 Dl 3991 4726 3934 4717 Dl 4264 4585 3990 4726 Dl 3898 4232 3916 4578 Dl 4190 4018 4212 4093 Dl 4212 4092 4235 4186 Dl 4235 4187 4242 4222 Dl 3942 4045 3990 4726 Dl 3901 3327 3942 4044 Dl 3901 3327 4247 4340 Dl (7)4037 4211 w 3894 3233 3896 3288 Dl 3896 3288 3900 3326 Dl 3894 3233 4243 4281 Dl 5 R f (8)4047 3768 w 10 R f 0.1 setlinewidth 3888 3156 3890 3200 Dl 3892 3200 3894 3232 Dl 3888 3156 4242 4238 Dl 5 R f (9)4043 3700 w 10 R f 0.1 setlinewidth 3882 3099 3882 3119 Dl 3883 3119 3888 3155 Dl 3884 3098 4235 4186 Dl 3878 3051 3878 3061 Dl 3877 3061 3882 3098 Dl 3879 3051 4212 4093 Dl 3873 3025 3874 3034 Dl 3874 3033 3878 3049 Dl 3874 3025 4190 4017 Dl 3870 3017 3870 3018 Dl 3871 3019 3873 3024 Dl 3900 3522 3942 4044 Dl 3884 3271 3898 3522 Dl 3885 3271 3896 3288 Dl 3879 3188 3881 3247 Dl 3881 3247 3884 3270 Dl 3877 3182 3877 3188 Dl 3878 3182 3890 3200 Dl 3876 3109 3878 3181 Dl 3876 3109 3882 3119 Dl 3871 3082 3872 3096 Dl 3874 3056 3871 3081 Dl 3873 3096 3876 3108 Dl 3875 3056 3878 3061 Dl 3870 3026 3870 3031 Dl 3870 3032 3875 3055 Dl 3870 3027 3874 3034 Dl 3868 3019 3870 3026 Dl 3869 3019 3867 3019 Dl 3870 3095 3870 3096 Dl 3872 3097 3874 3158 Dl 3873 3158 3877 3188 Dl 3873 3096 3871 3096 Dl 3864 3030 3864 3050 Dl 3865 3051 3870 3080 Dl 3867 3030 3870 3031 Dl 3871 3080 3871 3081 Dl 3864 3013 3866 3018 Dl 3865 3013 3870 3017 Dl 3866 3018 3867 3019 Dl 3871 3081 3871 3096 Dl 3865 3019 3863 3024 Dl 3863 3024 3865 3030 Dl 3874 3248 3877 3335 Dl 3877 3337 3898 3522 Dl 3880 3248 3873 3249 Dl 3868 3219 3873 3249 Dl 3868 3160 3868 3219 Dl 3873 3159 3867 3159 Dl 3865 3098 3865 3134 Dl 3865 3134 3867 3159 Dl 3869 3097 3864 3097 Dl 3862 3051 3862 3070 Dl 3862 3071 3864 3096 Dl 3864 3096 3864 3097 Dl 3864 3050 3862 3050 Dl 3863 3024 3862 3027 Dl 3862 3028 3862 3047 Dl 3862 3047 3862 3050 Dl 3862 3018 1 1 De 3864 3014 3862 3017 Dl 3861 3019 3862 3024 Dl 3865 3188 3867 3218 Dl 3863 3137 3865 3188 Dl 3868 3219 1 1 De 3864 3134 3862 3137 Dl 3862 3100 3862 3135 Dl 3862 3135 3862 3137 Dl 3864 3096 3861 3100 Dl 3858 3087 3860 3098 Dl 3859 3072 3857 3086 Dl 3861 3098 3861 3100 Dl 3862 3070 3860 3072 Dl 3859 3051 3859 3058 Dl 3859 3059 3860 3072 Dl 3861 3047 3859 3050 Dl 3859 3031 3858 3049 Dl 3859 3050 1 1 De 3859 3029 3859 3031 Dl 3861 3028 3860 3029 Dl 3859 3023 3859 3024 Dl 3860 3019 3859 3023 Dl 3860 3024 3860 3029 Dl 3861 3016 3859 3020 Dl 3861 3018 3859 3020 Dl 3863 3013 3862 3015 Dl 3882 3714 3934 4717 Dl 3873 3344 3881 3713 Dl 3877 3336 3872 3344 Dl 5 R f (45)3901 4168 w 10 R f 0.1 setlinewidth 3862 3235 3862 3242 Dl 3863 3242 3872 3344 Dl 3866 3219 3862 3234 Dl 3860 3139 3865 3188 Dl 3860 3136 3859 3138 Dl 3859 3098 3859 3138 Dl 3858 3059 3857 3087 Dl 3856 3032 3856 3034 Dl 3859 3024 3857 3031 Dl 3858 3032 3856 3034 Dl 3859 3020 3859 3021 Dl 3859 3023 1 1 De 3859 3188 3862 3234 Dl 3859 3139 3859 3187 Dl 3859 3139 1 1 De 3855 3089 3855 3107 Dl 3856 3107 3859 3139 Dl 3857 3087 3856 3089 Dl 3856 3078 3856 3089 Dl 3856 3053 3855 3078 Dl 3858 3050 3857 3052 Dl 3855 3035 3855 3040 Dl 3856 3040 3857 3052 Dl 3857 3031 1 1 De 3859 3022 3857 3030 Dl 3858 3020 3858 3021 Dl 3864 3409 3881 3713 Dl 3861 3289 3864 3409 Dl 3862 3242 3860 3288 Dl 3855 3107 3855 3109 Dl 3855 3110 3855 3173 Dl 3856 3172 3859 3187 Dl 3854 3041 3854 3046 Dl 3854 3047 3854 3077 Dl 3854 3078 3855 3078 Dl 3855 3034 3855 3035 Dl 3857 3022 3855 3034 Dl 3856 3030 3855 3035 Dl 3855 3178 3855 3229 Dl 3855 3229 3860 3288 Dl 3855 3173 3854 3178 Dl 3852 3124 3852 3162 Dl 3853 3162 3854 3178 Dl 3854 3109 3852 3124 Dl 3851 3088 3851 3100 Dl 3851 3100 3852 3124 Dl 3854 3078 3852 3088 Dl 3852 3060 3852 3088 Dl 3854 3048 3852 3060 Dl 3855 3036 3854 3043 Dl 3854 3044 3852 3060 Dl 3852 3240 3854 3288 Dl 3855 3289 3864 3409 Dl 3854 3230 3852 3240 Dl 3849 3120 3849 3122 Dl 3849 3122 3850 3191 Dl 3849 3112 3849 3119 Dl 3850 3112 3851 3176 Dl 3850 3176 3850 3191 Dl 3851 3060 3851 3071 Dl 3850 3192 3850 3204 Dl 3850 3204 3852 3240 Dl 3852 3162 3851 3176 Dl 3851 3100 3850 3112 Dl 3850 3071 3849 3119 Dl 3855 3322 3929 4709 Dl 3854 3289 3854 3322 Dl 3851 3234 3852 3274 Dl 3852 3275 3854 3322 Dl 3850 3204 3850 3234 Dl 3849 3146 3849 3187 Dl 3850 3187 3850 3234 Dl 3849 3123 3849 3146 Dl 3851 3275 3898 4232 Dl 20 R f 16 setlinewidth 5040 4878 3024 4878 Dl 5040 2862 5040 4878 Dl 3024 2862 5040 2862 Dl 3024 4878 3024 2862 Dl 3944 4525 4062 4530 Dl 3945 4523 4017 4509 Dl 3944 4524 4015 4545 Dl 10 B f (Fig. 80:)1 322 1 926 5076 t 10 R f (primal projective iter 4, outside)4 1257 1 1273 5076 t 10 B f (Fig. 81:)1 322 1 3230 5076 t 10 R f (primal projective iter 5, outside)4 1257 1 3577 5076 t 0.1 setlinewidth 2117 6694 2116 6706 Dl 2116 6706 2116 6737 Dl 2116 6739 2117 6782 Dl 2118 6783 2129 6963 Dl 2119 6694 2147 6948 Dl 2129 6962 2147 6948 Dl 1450 7096 1424 6971 Dl 1461 7102 1450 7096 Dl 1601 7102 1461 7102 Dl 2129 6964 1602 7102 Dl 1406 6637 1424 6971 Dl 2047 6527 2078 6590 Dl 2078 6591 2108 6666 Dl 2109 6666 2118 6693 Dl 1539 6472 1602 7102 Dl 1493 5751 1538 6472 Dl 1493 5750 2117 6782 Dl (7)1733 6609 w 1483 5650 1484 5707 Dl 1485 5706 1493 5749 Dl 1484 5649 2116 6737 Dl 5 R f (8)1754 6178 w 10 R f 0.1 setlinewidth 1473 5565 1477 5613 Dl 1478 5613 1483 5649 Dl 1473 5566 2116 6706 Dl 5 R f (9)1749 6111 w 10 R f 0.1 setlinewidth 1464 5502 1463 5522 Dl 1464 5522 1473 5565 Dl 1465 5502 2108 6666 Dl 5 R f (10)1729 6054 w 10 R f 0.1 setlinewidth 1456 5447 1455 5457 Dl 1455 5459 1465 5502 Dl 1457 5447 2078 6590 Dl 5 R f (11)1716 5996 w 10 R f 0.1 setlinewidth 1445 5415 1447 5425 Dl 1447 5424 1457 5446 Dl 1445 5414 2046 6527 Dl 1435 5402 1437 5404 Dl 1438 5405 1445 5414 Dl 1472 5942 1538 6472 Dl 1454 5677 1471 5941 Dl 1455 5677 1484 5707 Dl 5 R f (14)1468 5984 w 10 R f 0.1 setlinewidth 1444 5586 1447 5649 Dl 1447 5650 1454 5677 Dl 1446 5580 1444 5586 Dl 1446 5580 1477 5613 Dl 1446 5503 1446 5580 Dl 1446 5503 1463 5522 Dl 1435 5469 1437 5485 Dl 1445 5448 1434 5469 Dl 1438 5485 1446 5502 Dl 1447 5447 1455 5457 Dl 1435 5411 1433 5415 Dl 1434 5417 1446 5447 Dl 1437 5413 1447 5425 Dl 1430 5402 1436 5412 Dl 1436 5403 1429 5400 Dl 1432 5484 1 1 De 1432 5485 1435 5551 Dl 1436 5551 1444 5586 Dl 1432 5483 1437 5485 Dl 1422 5409 1418 5428 Dl 1419 5428 1432 5466 Dl 1423 5408 1433 5415 Dl 1432 5467 1434 5469 Dl 1421 5390 1422 5390 Dl 1420 5389 1426 5397 Dl 1422 5390 1434 5401 Dl 1427 5398 1429 5400 Dl 1432 5467 1432 5483 Dl 1425 5398 1416 5399 Dl 1417 5399 1422 5409 Dl 1426 5642 1428 5734 Dl 1428 5735 1471 5941 Dl 1426 5642 1447 5649 Dl 1414 5605 1426 5642 Dl 1417 5544 1414 5605 Dl 1417 5544 1435 5551 Dl 1415 5478 1413 5515 Dl 1413 5516 1417 5544 Dl 1417 5477 1432 5484 Dl 1412 5426 1410 5445 Dl 1410 5445 1415 5475 Dl 1416 5476 1416 5477 Dl 1413 5426 1418 5428 Dl 1414 5398 1411 5400 Dl 1411 5400 1411 5420 Dl 1411 5420 1413 5425 Dl 1415 5399 1416 5399 Dl 1412 5391 1 1 De 1419 5390 1412 5390 Dl 1413 5391 1415 5398 Dl 1408 5570 1411 5603 Dl 1405 5515 1408 5570 Dl 1412 5604 1414 5605 Dl 1405 5515 1413 5515 Dl 1404 5475 1402 5511 Dl 1402 5513 1404 5515 Dl 1405 5475 1415 5475 Dl 1396 5457 1402 5472 Dl 1404 5445 1396 5456 Dl 1402 5472 1404 5475 Dl 1405 5445 1410 5445 Dl 1401 5420 1401 5428 Dl 1402 5430 1404 5445 Dl 1403 5420 1411 5420 Dl 1405 5401 1400 5418 Dl 1401 5419 1402 5420 Dl 1407 5401 1405 5401 Dl 1408 5400 1411 5400 Dl 1406 5394 1 1 De 1411 5391 1406 5393 Dl 1406 5394 1408 5400 Dl 1414 5389 1405 5389 Dl 1415 5389 1414 5389 Dl 1405 5390 1412 5390 Dl 1415 5389 1420 5389 Dl 1406 6117 1461 7102 Dl 1413 5738 1406 6117 Dl 1428 5734 1414 5737 Dl (45)1436 6561 w 1396 5616 1396 5623 Dl 1397 5623 1414 5737 Dl 1411 5605 1397 5615 Dl 1398 5513 1408 5570 Dl 1402 5512 1397 5512 Dl 1401 5472 1396 5512 Dl 1401 5430 1394 5456 Dl 1395 5456 1396 5456 Dl 1397 5398 1396 5400 Dl 1405 5394 1397 5397 Dl 1396 5400 1405 5401 Dl 1405 5389 1404 5390 Dl 1404 5391 1406 5393 Dl 1392 5563 1397 5615 Dl 1395 5513 1391 5562 Dl 1396 5513 1395 5513 Dl 1390 5456 1388 5474 Dl 1388 5475 1395 5513 Dl 1394 5456 1390 5456 Dl 1389 5444 1390 5456 Dl 1396 5419 1389 5443 Dl 1400 5419 1396 5419 Dl 1395 5400 1393 5405 Dl 1394 5405 1396 5419 Dl 1397 5397 1 1 De 1403 5391 1397 5396 Dl 1405 5390 1404 5390 Dl 1385 5795 1406 6117 Dl 1384 5668 1384 5794 Dl 1396 5623 1385 5667 Dl 1387 5475 1387 5477 Dl 1386 5476 1381 5541 Dl 1382 5542 1391 5562 Dl 1393 5405 1390 5410 Dl 1390 5411 1386 5441 Dl 1386 5441 1389 5443 Dl 1393 5399 1392 5399 Dl 1403 5391 1393 5398 Dl 1392 5398 1397 5396 Dl 1377 5546 1376 5600 Dl 1377 5601 1385 5667 Dl 1381 5542 1378 5546 Dl 1377 5488 1374 5527 Dl 1375 5527 1378 5546 Dl 1387 5477 1378 5488 Dl 1378 5449 1376 5461 Dl 1377 5462 1378 5488 Dl 1384 5442 1378 5449 Dl 1380 5421 1378 5449 Dl 1389 5410 1381 5420 Dl 1392 5399 1388 5405 Dl 1387 5405 1381 5420 Dl 1367 5608 1368 5660 Dl 1369 5661 1384 5794 Dl 1376 5601 1368 5608 Dl 1368 5480 1368 5482 Dl 1367 5482 1365 5555 Dl 1371 5473 1368 5479 Dl 1371 5472 1369 5540 Dl 1368 5540 1365 5555 Dl 1380 5420 1377 5430 Dl 1364 5556 1364 5568 Dl 1366 5569 1368 5608 Dl 1374 5528 1369 5540 Dl 1375 5462 1371 5472 Dl 1377 5431 1368 5479 Dl 1365 5695 1450 7096 Dl 1368 5661 1364 5694 Dl 5 R f (83)1387 6379 w 10 R f 0.1 setlinewidth 1360 5599 1360 5642 Dl 1361 5643 1364 5694 Dl 1363 5569 1360 5599 Dl 1364 5506 1362 5549 Dl 1361 5549 1360 5599 Dl 1367 5483 1365 5506 Dl 1361 5643 1404 6636 Dl 20 R f 16 setlinewidth 2736 7254 720 7254 Dl 2736 5238 2736 7254 Dl 720 5238 2736 5238 Dl 720 7254 720 5238 Dl 1435 6898 1500 6919 Dl 1435 6898 1509 6903 Dl 1436 6898 1498 6937 Dl 10 R f 0.1 setlinewidth 4877 6630 4872 6635 Dl 4871 6636 4864 6651 Dl 4863 6650 4857 6672 Dl 4856 6672 4844 6762 Dl 4878 6630 4888 6757 Dl 4845 6762 4888 6757 Dl 3236 6853 3208 6851 Dl 3627 6844 3236 6854 Dl 3628 6842 4844 6762 Dl 4783 6540 4826 6575 Dl 4828 6575 4866 6615 Dl 4867 6615 4878 6629 Dl 3562 6441 3628 6843 Dl 3564 5935 3561 6441 Dl 3565 5934 4857 6672 Dl (7)4016 6525 w 3556 5860 3548 5901 Dl 3548 5900 3565 5934 Dl 3557 5859 4864 6651 Dl 5 R f (8)4093 6227 w 10 R f 0.1 setlinewidth 3544 5792 3546 5829 Dl 3546 5830 3556 5858 Dl 3543 5793 4872 6635 Dl 5 R f (9)4092 6179 w 10 R f 0.1 setlinewidth 3534 5742 3523 5756 Dl 3523 5757 3543 5793 Dl 3535 5742 4866 6615 Dl 5 R f (10)4071 6136 w 10 R f 0.1 setlinewidth 3524 5696 3515 5703 Dl 3516 5704 3535 5742 Dl 3525 5697 4826 6575 Dl 5 R f (11)4058 6096 w 10 R f 0.1 setlinewidth 3498 5665 3499 5674 Dl 3500 5674 3525 5696 Dl 3498 5665 4782 6539 Dl 3470 5649 3477 5652 Dl 3478 5653 3498 5664 Dl 3462 6063 3561 6441 Dl 3460 5865 3462 6062 Dl 3461 5865 3548 5901 Dl 5 R f (14)3495 6095 w 10 R f 0.1 setlinewidth 3445 5793 3443 5841 Dl 3443 5842 3459 5865 Dl 3452 5790 3445 5793 Dl 3454 5788 3546 5829 Dl 3471 5732 3453 5788 Dl 3472 5733 3523 5756 Dl 3443 5699 3448 5713 Dl 3488 5691 3443 5700 Dl 3448 5713 3471 5731 Dl 3489 5691 3515 5703 Dl 3466 5658 3456 5659 Dl 3457 5659 3489 5690 Dl 3466 5658 3499 5674 Dl 3448 5645 3466 5657 Dl 3449 5645 3477 5652 Dl 3432 5709 3430 5709 Dl 3430 5711 3427 5762 Dl 3426 5763 3445 5793 Dl 3433 5709 3448 5713 Dl 3422 5647 3402 5659 Dl 3401 5659 3436 5696 Dl 3422 5647 3456 5659 Dl 3437 5698 3443 5700 Dl 3424 5630 3429 5631 Dl 3424 5630 3422 5630 Dl 3422 5631 3439 5641 Dl 3429 5632 3470 5649 Dl 3439 5640 3448 5644 Dl 3436 5697 3432 5709 Dl 3408 5636 3439 5641 Dl 3408 5636 3422 5646 Dl 3376 5825 3366 5894 Dl 3367 5895 3462 6062 Dl 3377 5825 3443 5841 Dl 3346 5790 3377 5824 Dl 3370 5746 3345 5790 Dl 3371 5747 3427 5762 Dl 3380 5695 3363 5721 Dl 3363 5722 3370 5746 Dl 3380 5694 3430 5709 Dl 3385 5655 3370 5667 Dl 3371 5667 3378 5693 Dl 3378 5694 3380 5695 Dl 3386 5654 3402 5659 Dl 3402 5634 3389 5634 Dl 3387 5633 3378 5648 Dl 3379 5649 3384 5654 Dl 3402 5635 3407 5636 Dl 3397 5626 3395 5626 Dl 3398 5626 3422 5630 Dl 3396 5627 3402 5634 Dl 3334 5761 3338 5788 Dl 3335 5718 3334 5761 Dl 3339 5788 3345 5790 Dl 3336 5716 3363 5721 Dl 3345 5687 3329 5713 Dl 3329 5713 3335 5716 Dl 3346 5687 3378 5693 Dl 3322 5667 3337 5682 Dl 3351 5663 3321 5666 Dl 3338 5682 3345 5686 Dl 3352 5664 3370 5667 Dl 3350 5643 3348 5649 Dl 3348 5649 3351 5663 Dl 3350 5643 3378 5648 Dl 3367 5630 3346 5640 Dl 3346 5640 3350 5642 Dl 3369 5631 3378 5631 Dl 3379 5632 3389 5634 Dl 3376 5624 3373 5624 Dl 3377 5624 3395 5626 Dl 3375 5625 3378 5631 Dl 3376 5621 3406 5626 Dl 3406 5626 3409 5626 Dl 3374 5621 3397 5626 Dl 3409 5627 3424 5630 Dl 3229 6166 3236 6854 Dl 3321 5890 3229 6165 Dl 3321 5890 3366 5894 Dl (45)3344 6472 w 3289 5789 3286 5794 Dl 3287 5794 3321 5889 Dl 3338 5788 3290 5788 Dl 3312 5711 3334 5761 Dl 3312 5711 3329 5713 Dl 3337 5682 3311 5710 Dl 3312 5710 1 1 De 3347 5649 3316 5664 Dl 3316 5665 3321 5666 Dl 3343 5622 3338 5623 Dl 3343 5622 3373 5624 Dl 3339 5623 3368 5630 Dl 3375 5621 3370 5621 Dl 3370 5620 3377 5624 Dl 3283 5745 3290 5788 Dl 3306 5709 3282 5744 Dl 3306 5710 3311 5710 Dl 3302 5663 3291 5675 Dl 3291 5676 3306 5709 Dl 3304 5662 3316 5664 Dl 3303 5653 3303 5663 Dl 3332 5638 3302 5652 Dl 3333 5638 3346 5640 Dl 3338 5623 3328 5625 Dl 3327 5625 3332 5638 Dl 3345 5621 3344 5621 Dl 3369 5621 3345 5621 Dl 3370 5620 3375 5620 Dl 3218 5918 3229 6165 Dl 3240 5822 3216 5917 Dl 3286 5794 3241 5821 Dl 5 R f (62)3235 5955 w 10 R f 0.1 setlinewidth 3290 5676 3288 5677 Dl 3288 5678 3255 5724 Dl 3256 5723 3282 5744 Dl 3328 5625 3316 5626 Dl 3315 5627 3292 5648 Dl 3292 5648 3302 5652 Dl 3334 5619 3330 5619 Dl 3369 5619 3335 5619 Dl 3331 5620 3345 5621 Dl 3242 5725 3227 5765 Dl 3227 5765 3241 5821 Dl 3254 5724 3242 5725 Dl 3256 5680 3237 5708 Dl 3236 5708 3242 5725 Dl 3288 5678 3256 5680 Dl 3269 5650 3258 5657 Dl 3258 5658 3256 5680 Dl 3292 5647 3270 5649 Dl 3287 5629 3270 5649 Dl 3315 5626 3287 5628 Dl 3330 5619 3315 5621 Dl 3314 5621 3286 5628 Dl 3197 5766 3192 5807 Dl 3192 5807 3216 5917 Dl 3199 5765 3227 5765 Dl 3230 5666 3228 5668 Dl 3227 5668 3202 5724 Dl 3241 5664 3230 5666 Dl 3241 5663 3217 5714 Dl 3217 5715 3202 5724 Dl 3286 5629 3272 5634 Dl 3202 5724 3197 5733 Dl 3198 5733 3198 5766 Dl 3236 5708 3217 5714 Dl 3258 5658 3242 5663 Dl 3272 5635 3230 5666 Dl 3176 5831 3208 6851 Dl 3192 5808 3175 5831 Dl 5 R f (83)3184 6327 w 10 R f 0.1 setlinewidth 3182 5755 3175 5788 Dl 3175 5789 3175 5831 Dl 3197 5734 3182 5755 Dl 3215 5685 3198 5716 Dl 3199 5717 3182 5755 Dl 3227 5669 3216 5685 Dl 20 R f 16 setlinewidth 5040 7254 3024 7254 Dl 5040 5238 5040 7254 Dl 3024 5238 5040 5238 Dl 3024 7254 3024 5238 Dl 3307 6601 3299 6735 Dl 3310 6601 3322 6673 Dl 3309 6601 3286 6671 Dl 10 B f (Fig. 82:)1 322 1 926 7452 t 10 R f (primal projective iter 6, outside)4 1257 1 1273 7452 t 10 B f (Fig. 83:)1 322 1 3230 7452 t 10 R f (primal projective iter 7, outside)4 1257 1 3577 7452 t (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 26 27 %%Page: 27 28 /saveobj save def mark 28 pagesetup 10 R f (- 27 -)2 216 1 2772 282 t 0.1 setlinewidth 2584 1664 2579 1668 Dl 2578 1668 2568 1678 Dl 2567 1679 2557 1691 Dl 2557 1691 2527 1740 Dl 2584 1664 2566 1730 Dl 2565 1731 2527 1740 Dl 1052 1887 1026 1884 Dl 1413 1870 1052 1887 Dl 2527 1740 1414 1869 Dl 2514 1617 2548 1635 Dl 2548 1636 2576 1656 Dl 2577 1657 2584 1664 Dl 1343 1655 1414 1869 Dl 1330 1321 1342 1655 Dl 1331 1321 2557 1691 Dl (7)1758 1657 w 1316 1263 1309 1296 Dl 1309 1296 1329 1320 Dl 1318 1264 2568 1678 Dl 5 R f (8)1816 1461 w 10 R f 0.1 setlinewidth 1299 1212 1304 1241 Dl 1305 1240 1317 1262 Dl 1300 1211 2579 1668 Dl 5 R f (9)1812 1424 w 10 R f 0.1 setlinewidth 1286 1170 1274 1182 Dl 1274 1183 1299 1211 Dl 1286 1169 2576 1656 Dl 5 R f (10)1787 1391 w 10 R f 0.1 setlinewidth 1271 1131 1261 1138 Dl 1261 1139 1286 1170 Dl 1272 1130 2548 1635 Dl 5 R f (11)1775 1361 w 10 R f 0.1 setlinewidth 1239 1102 1241 1112 Dl 1242 1112 1272 1130 Dl 1238 1103 2513 1617 Dl 1203 1091 1212 1093 Dl 1212 1094 1237 1102 Dl 1223 1419 1342 1655 Dl 1208 1274 1223 1418 Dl 1208 1275 1309 1296 Dl 5 R f (14)1259 1430 w 10 R f 0.1 setlinewidth 1188 1219 1188 1257 Dl 1188 1258 1208 1275 Dl 1195 1215 1187 1218 Dl 1196 1216 1304 1241 Dl 1212 1167 1195 1215 Dl 1213 1167 1274 1182 Dl 1177 1141 1184 1153 Dl 1228 1129 1176 1141 Dl 1185 1154 1213 1167 Dl 1229 1129 1261 1138 Dl 1200 1101 1188 1103 Dl 1188 1103 1229 1128 Dl 1201 1101 1241 1112 Dl 1177 1090 1200 1100 Dl 1211 1092 1177 1090 Dl 1164 1151 1162 1151 Dl 1162 1151 1162 1194 Dl 1162 1195 1187 1218 Dl 1165 1151 1184 1153 Dl 1146 1096 1123 1108 Dl 1123 1109 1168 1139 Dl 1147 1096 1188 1103 Dl 1169 1139 1176 1141 Dl 1147 1078 1152 1078 Dl 1146 1078 1144 1078 Dl 1144 1078 1165 1087 Dl 1153 1078 1203 1090 Dl 1166 1088 1177 1090 Dl 1167 1139 1164 1150 Dl 1165 1087 1127 1086 Dl 1128 1086 1146 1095 Dl 1110 1248 1105 1301 Dl 1105 1302 1223 1418 Dl 1111 1248 1188 1257 Dl 1070 1223 1110 1248 Dl 1094 1185 1070 1222 Dl 1095 1185 1162 1194 Dl 1100 1141 1083 1164 Dl 1084 1165 1095 1185 Dl 1101 1142 1162 1151 Dl 1102 1105 1086 1117 Dl 1086 1117 1098 1139 Dl 1099 1140 1101 1141 Dl 1103 1105 1123 1108 Dl 1121 1085 1105 1085 Dl 1104 1086 1095 1100 Dl 1096 1100 1103 1104 Dl 1121 1085 1127 1086 Dl 1114 1077 1112 1077 Dl 1143 1078 1114 1077 Dl 1113 1078 1121 1085 Dl 1054 1199 1062 1221 Dl 1051 1162 1054 1198 Dl 1063 1221 1070 1222 Dl 1050 1162 1083 1164 Dl 1058 1136 1042 1159 Dl 1044 1160 1051 1162 Dl 1059 1136 1098 1139 Dl 1029 1120 1049 1132 Dl 1064 1115 1028 1119 Dl 1049 1133 1059 1136 Dl 1064 1115 1086 1117 Dl 1059 1097 1057 1102 Dl 1058 1102 1064 1114 Dl 1061 1097 1095 1100 Dl 1079 1084 1055 1094 Dl 1055 1094 1060 1096 Dl 1080 1083 1091 1083 Dl 1093 1084 1105 1085 Dl 1089 1077 1085 1077 Dl 1112 1077 1090 1077 Dl 1086 1077 1091 1083 Dl 1087 1072 1124 1074 Dl 1124 1075 1128 1075 Dl 1086 1073 1114 1077 Dl 1128 1075 1146 1077 Dl 980 1497 1052 1887 Dl 1052 1300 980 1496 Dl 1053 1300 1105 1301 Dl (45)1117 1655 w 1004 1223 1002 1228 Dl 1003 1228 1052 1300 Dl 1062 1221 1006 1223 Dl 1023 1157 1054 1198 Dl 1022 1158 1042 1159 Dl 1048 1132 1020 1157 Dl 1022 1157 1 1 De 1057 1103 1021 1118 Dl 1023 1119 1028 1119 Dl 1049 1075 1044 1077 Dl 1049 1077 1085 1077 Dl 1044 1078 1080 1083 Dl 1085 1072 1080 1072 Dl 1081 1073 1090 1077 Dl 1098 1072 1124 1074 Dl 991 1188 1006 1223 Dl 1015 1158 991 1188 Dl 1015 1157 1020 1157 Dl 1005 1117 993 1128 Dl 994 1129 1015 1157 Dl 1006 1118 1021 1118 Dl 1004 1108 1005 1117 Dl 1038 1094 1004 1108 Dl 1039 1093 1055 1094 Dl 1043 1078 1031 1080 Dl 1031 1080 1038 1092 Dl 1050 1076 1049 1076 Dl 1080 1073 1051 1075 Dl 1097 1072 1080 1071 Dl 1080 1072 1086 1072 Dl 938 1324 980 1496 Dl 953 1251 938 1324 Dl 1002 1228 954 1250 Dl 5 R f (62)965 1348 w 10 R f 0.1 setlinewidth 992 1129 990 1129 Dl 990 1129 957 1170 Dl 958 1171 991 1188 Dl 1030 1080 1016 1082 Dl 1015 1082 990 1103 Dl 992 1104 1004 1108 Dl 1038 1072 1033 1072 Dl 1079 1071 1038 1072 Dl 1033 1073 1051 1075 Dl 941 1173 929 1206 Dl 930 1206 954 1250 Dl 956 1171 942 1172 Dl 951 1132 932 1157 Dl 932 1158 942 1172 Dl 990 1130 952 1132 Dl 963 1106 951 1113 Dl 952 1112 952 1132 Dl 990 1103 964 1105 Dl 982 1085 964 1105 Dl 1016 1083 982 1085 Dl 1032 1072 1014 1074 Dl 1014 1076 981 1085 Dl 894 1206 894 1238 Dl 895 1239 938 1324 Dl 896 1206 929 1206 Dl 918 1120 916 1121 Dl 916 1122 894 1170 Dl 931 1117 918 1119 Dl 931 1118 910 1163 Dl 910 1163 894 1170 Dl 980 1085 964 1090 Dl 893 1171 889 1178 Dl 890 1179 895 1206 Dl 931 1158 910 1163 Dl 950 1112 932 1117 Dl 964 1089 918 1119 Dl 878 1256 1026 1884 Dl 893 1238 877 1255 Dl 5 R f (83)941 1558 w 10 R f 0.1 setlinewidth 873 1195 871 1221 Dl 871 1222 877 1255 Dl 889 1179 874 1194 Dl 903 1135 888 1161 Dl 887 1161 874 1194 Dl 916 1122 904 1134 Dl 20 R f 16 setlinewidth 2736 2502 720 2502 Dl 2736 486 2736 2502 Dl 720 486 2736 486 Dl 720 2502 720 486 Dl 1051 1606 1089 1693 Dl 1049 1606 1095 1664 Dl 1051 1606 1063 1679 Dl 10 R f 0.1 setlinewidth 4888 1492 4883 1496 Dl 4883 1496 4873 1504 Dl 4872 1504 4862 1514 Dl 4862 1515 4831 1549 Dl 4888 1492 4861 1532 Dl 4861 1533 4831 1549 Dl 3357 1620 3501 1820 Dl 3501 1821 3538 1826 Dl 3909 1783 3538 1826 Dl 4830 1549 3910 1783 Dl 3297 1526 3358 1621 Dl 4695 1424 4843 1464 Dl 4844 1465 4867 1475 Dl 4867 1475 4884 1487 Dl 4884 1487 4888 1491 Dl 3835 1656 3910 1783 Dl 3801 1407 3834 1656 Dl 3800 1406 4862 1514 Dl (7)4174 1592 w 3781 1358 3776 1388 Dl 3777 1388 3801 1406 Dl 3781 1358 4873 1504 Dl 5 R f (8)4202 1442 w 10 R f 0.1 setlinewidth 3754 1310 3764 1338 Dl 3764 1338 3781 1357 Dl 3754 1310 4883 1496 Dl 5 R f (9)4192 1408 w 10 R f 0.1 setlinewidth 3729 1268 3719 1284 Dl 3721 1284 3754 1309 Dl 3731 1267 4884 1487 Dl 5 R f (10)4160 1377 w 10 R f 0.1 setlinewidth 3700 1222 3692 1234 Dl 3692 1234 3730 1267 Dl 3702 1222 4867 1475 Dl 5 R f (11)4142 1347 w 10 R f 0.1 setlinewidth 3647 1185 3658 1203 Dl 3658 1202 3701 1221 Dl 3647 1185 4843 1464 Dl 5 R f (12)4109 1317 w 10 R f 0.1 setlinewidth 3688 1190 4695 1424 Dl 3567 1162 3599 1172 Dl 3600 1173 3612 1176 Dl 3568 1162 3688 1189 Dl 3566 1162 1 1 De 3612 1177 3646 1185 Dl 3691 1497 3834 1656 Dl 3660 1380 3692 1496 Dl 3659 1380 3776 1388 Dl 5 R f (14)3730 1494 w 10 R f 0.1 setlinewidth 3626 1329 3633 1365 Dl 3633 1366 3659 1379 Dl 3634 1325 3625 1329 Dl 3635 1325 3764 1338 Dl 3644 1274 3634 1324 Dl 3645 1274 3719 1284 Dl 3594 1250 3606 1262 Dl 3651 1228 3593 1249 Dl 3606 1263 3644 1274 Dl 3652 1228 3692 1234 Dl 3604 1194 3592 1199 Dl 3592 1199 3651 1227 Dl 3606 1194 3658 1203 Dl 3572 1181 3605 1193 Dl 3611 1176 3572 1181 Dl 3562 1161 3564 1161 Dl 3562 1162 3566 1162 Dl 3565 1161 3567 1161 Dl 3582 1262 3579 1262 Dl 3579 1261 3589 1306 Dl 3590 1307 3625 1329 Dl 3582 1261 3606 1262 Dl 3538 1194 3515 1213 Dl 3515 1214 3583 1247 Dl 3538 1194 3592 1199 Dl 3583 1247 3593 1249 Dl 3530 1162 3523 1162 Dl 3523 1162 3521 1164 Dl 3522 1164 3556 1178 Dl 3532 1162 3599 1172 Dl 3557 1179 3572 1181 Dl 3582 1248 3582 1261 Dl 3556 1178 3509 1182 Dl 3510 1182 3538 1193 Dl 3514 1156 3511 1156 Dl 3546 1158 3562 1160 Dl 3521 1156 3545 1158 Dl 3510 1156 3530 1162 Dl 3520 1156 3515 1156 Dl 3537 1362 3538 1408 Dl 3538 1409 3692 1496 Dl 3537 1361 3633 1365 Dl 3480 1339 3536 1361 Dl 3502 1301 3480 1339 Dl 3502 1300 3589 1306 Dl 3497 1255 3482 1280 Dl 3482 1281 3502 1301 Dl 3499 1255 3579 1262 Dl 3486 1211 3470 1226 Dl 3470 1226 3495 1252 Dl 3496 1253 3499 1254 Dl 3487 1211 3515 1213 Dl 3499 1181 3479 1183 Dl 3479 1184 3474 1204 Dl 3474 1205 3486 1210 Dl 3501 1181 3509 1182 Dl 3484 1167 3482 1168 Dl 3521 1165 3484 1167 Dl 3482 1169 3500 1181 Dl 3517 1156 3515 1156 Dl 3518 1156 3520 1156 Dl 3453 1315 3469 1337 Dl 3438 1277 3452 1315 Dl 3470 1338 3480 1339 Dl 3438 1278 3482 1280 Dl 3441 1250 3426 1275 Dl 3427 1276 3438 1278 Dl 3441 1249 3495 1252 Dl 3392 1229 3425 1244 Dl 3438 1224 3391 1229 Dl 3425 1246 3440 1249 Dl 3440 1224 3470 1226 Dl 3426 1201 3425 1208 Dl 3425 1209 3439 1224 Dl 3426 1200 3474 1204 Dl 3444 1182 3417 1198 Dl 3418 1198 3426 1200 Dl 3446 1181 3461 1181 Dl 3461 1181 3479 1183 Dl 3452 1170 3447 1170 Dl 3482 1169 3452 1169 Dl 3448 1170 3461 1181 Dl 3491 1158 3441 1158 Dl 3493 1159 3498 1159 Dl 3442 1160 3484 1167 Dl 3498 1160 3523 1162 Dl 3479 1154 3511 1156 Dl 3479 1153 3498 1159 Dl 3500 1154 3518 1156 Dl 3500 1153 3545 1158 Dl 3406 1567 3538 1826 Dl 3470 1408 3406 1566 Dl 3536 1408 3470 1408 Dl (45)3576 1656 w 3394 1340 3391 1344 Dl 3391 1345 3470 1408 Dl 3468 1338 3394 1340 Dl 3398 1273 3452 1315 Dl 3398 1274 3426 1275 Dl 3425 1245 3396 1273 Dl 3396 1273 3397 1273 Dl 3424 1209 3382 1229 Dl 3383 1228 3391 1229 Dl 3396 1169 3390 1172 Dl 3446 1169 3396 1169 Dl 3391 1174 3445 1181 Dl 3441 1159 3435 1161 Dl 3435 1162 3452 1169 Dl 3456 1151 3451 1152 Dl 3457 1151 3478 1153 Dl 3451 1153 3492 1159 Dl 3499 1154 3500 1154 Dl 3364 1304 3394 1340 Dl 3387 1273 3363 1304 Dl 3389 1273 3396 1273 Dl 3358 1228 3346 1240 Dl 3347 1240 3388 1272 Dl 3359 1228 3382 1229 Dl 3353 1215 3360 1227 Dl 3393 1196 3352 1214 Dl 3393 1196 3417 1198 Dl 3389 1174 3374 1177 Dl 3375 1176 3394 1195 Dl 3396 1168 3396 1169 Dl 3434 1161 3397 1167 Dl 3450 1153 3430 1155 Dl 3431 1156 3441 1158 Dl 3448 1150 3498 1153 Dl 3448 1150 3456 1151 Dl 3319 1428 3406 1566 Dl 3325 1364 3318 1427 Dl 3390 1345 3326 1363 Dl 5 R f (62)3366 1446 w 10 R f 0.1 setlinewidth 3345 1241 3342 1241 Dl 3341 1241 3308 1284 Dl 3308 1284 3363 1304 Dl 3374 1177 3354 1178 Dl 3353 1179 3330 1208 Dl 3330 1208 3352 1214 Dl 3371 1157 3364 1157 Dl 3430 1156 3371 1156 Dl 3364 1157 3397 1167 Dl 3287 1285 3277 1318 Dl 3277 1317 3326 1363 Dl 3307 1285 3286 1285 Dl 3284 1241 3265 1267 Dl 3266 1268 3286 1285 Dl 3285 1241 3342 1241 Dl 3289 1208 3273 1215 Dl 3273 1216 3285 1241 Dl 3290 1208 3330 1208 Dl 3301 1177 3289 1207 Dl 3302 1177 3354 1178 Dl 3364 1157 3337 1158 Dl 3300 1177 3301 1177 Dl 3336 1159 3300 1177 Dl 3438 1150 3371 1156 Dl 3439 1149 3448 1149 Dl 3433 1149 3438 1149 Dl 3222 1313 3229 1343 Dl 3229 1343 3318 1427 Dl 3223 1313 3277 1318 Dl 3218 1215 3216 1216 Dl 3216 1217 3206 1274 Dl 3220 1215 3243 1216 Dl 3243 1216 3232 1269 Dl 3231 1269 3206 1274 Dl 3337 1158 3281 1170 Dl 3280 1171 3275 1179 Dl 3300 1177 3275 1179 Dl 3433 1149 3428 1149 Dl 3206 1275 3202 1282 Dl 3202 1282 3222 1312 Dl 3265 1267 3232 1269 Dl 3272 1215 3243 1216 Dl 3274 1179 3220 1215 Dl 3428 1150 3380 1152 Dl 3380 1153 3337 1158 Dl 3201 1351 3501 1820 Dl 3228 1344 3200 1351 Dl 5 R f (83)3345 1580 w 10 R f 0.1 setlinewidth 3175 1290 3176 1314 Dl 3177 1315 3200 1351 Dl 3202 1283 3175 1290 Dl 3196 1223 3178 1248 Dl 3177 1249 3175 1290 Dl 3216 1217 3195 1223 Dl 3249 1180 3195 1223 Dl 3280 1171 3250 1180 Dl 3177 1315 3296 1525 Dl 20 R f 16 setlinewidth 5040 2502 3024 2502 Dl 5040 486 5040 2502 Dl 3024 486 5040 486 Dl 3024 2502 3024 486 Dl 3312 1416 3330 1493 Dl 3313 1415 3346 1481 Dl 3311 1415 3311 1489 Dl 10 B f (Fig. 84:)1 322 1 926 2700 t 10 R f (primal projective iter 8, outside)4 1257 1 1273 2700 t 10 B f (Fig. 85:)1 322 1 3230 2700 t 10 R f (primal projective iter 9, outside)4 1257 1 3577 2700 t 0.1 setlinewidth 2583 3773 2581 3777 Dl 2581 3777 2576 3785 Dl 2576 3786 2571 3795 Dl 2570 3795 2552 3824 Dl 1160 3944 1662 4186 Dl 1663 4187 1706 4189 Dl 2000 4118 1706 4189 Dl 2551 3825 2000 4118 Dl 946 3808 992 3855 Dl 992 3856 1159 3944 Dl 2441 3722 2553 3752 Dl 2553 3753 2569 3760 Dl 2569 3760 2581 3769 Dl 2582 3770 2584 3773 Dl 1911 4046 2000 4118 Dl 1794 3851 1911 4046 Dl 2570 3795 1794 3850 Dl (7)2100 3944 w 1751 3805 1763 3836 Dl 1764 3837 1794 3850 Dl 2576 3786 1751 3805 Dl 5 R f (8)2065 3823 w 10 R f 0.1 setlinewidth 1696 3758 1724 3787 Dl 1724 3787 1751 3805 Dl 1696 3757 2581 3777 Dl 5 R f (9)2037 3791 w 10 R f 0.1 setlinewidth 1643 3710 1645 3732 Dl 1645 3732 1696 3757 Dl 1642 3710 2581 3769 Dl 5 R f (10)1983 3759 w 10 R f 0.1 setlinewidth 1570 3653 1573 3671 Dl 1573 3672 1642 3710 Dl 1569 3652 2569 3760 Dl 5 R f (11)1941 3723 w 10 R f 0.1 setlinewidth 1463 3602 1501 3630 Dl 1501 3630 1569 3652 Dl 1463 3601 2553 3752 Dl 5 R f (12)1878 3684 w 10 R f 0.1 setlinewidth 1484 3583 2440 3721 Dl 1323 3564 1391 3587 Dl 1391 3587 1411 3591 Dl 1321 3563 1483 3583 Dl 1322 3564 1 1 De 1412 3591 1463 3601 Dl 5 R f (13)1878 3663 w 10 R f 0.1 setlinewidth 1732 3944 1911 4046 Dl 1646 3844 1732 3944 Dl 1763 3837 1646 3844 Dl 5 R f (14)1751 3927 w 10 R f 0.1 setlinewidth 1579 3795 1611 3833 Dl 1612 3834 1646 3844 Dl 1584 3790 1578 3795 Dl 1724 3787 1586 3789 Dl 1560 3730 1586 3789 Dl 1560 3730 1645 3732 Dl 1480 3705 1507 3720 Dl 1523 3669 1481 3705 Dl 1508 3720 1559 3730 Dl 1524 3668 1573 3671 Dl 1431 3624 1424 3634 Dl 1426 3634 1523 3667 Dl 1432 3624 1501 3630 Dl 1376 3608 1432 3623 Dl 1411 3591 1376 3607 Dl 1316 3562 1314 3562 Dl 1315 3563 1322 3564 Dl 1317 3562 1321 3562 Dl 1296 3559 1316 3561 Dl 1478 3721 1476 3722 Dl 1476 3722 1524 3774 Dl 1524 3775 1578 3795 Dl 1507 3720 1479 3720 Dl 1352 3632 1349 3663 Dl 1349 3664 1467 3703 Dl 1352 3632 1424 3634 Dl 1468 3704 1481 3705 Dl 1292 3578 1285 3579 Dl 1286 3579 1287 3583 Dl 1287 3584 1353 3605 Dl 1294 3578 1391 3587 Dl 1353 3605 1376 3607 Dl 1467 3702 1479 3720 Dl 1352 3605 1301 3617 Dl 1301 3617 1352 3632 Dl 1254 3564 1251 3564 Dl 1292 3562 1314 3562 Dl 1292 3562 1262 3562 Dl 1251 3565 1293 3577 Dl 1261 3563 1255 3563 Dl 1504 3840 1532 3884 Dl 1532 3885 1732 3944 Dl 1612 3834 1504 3839 Dl 1424 3821 1504 3839 Dl 1418 3776 1422 3821 Dl 1524 3775 1419 3776 Dl 1373 3721 1377 3754 Dl 1378 3754 1419 3776 Dl 1373 3720 1476 3722 Dl 1309 3662 1307 3685 Dl 1308 3685 1367 3718 Dl 1368 3719 1373 3720 Dl 1311 3661 1349 3663 Dl 1289 3615 1265 3620 Dl 1265 3621 1287 3654 Dl 1286 3654 1309 3661 Dl 1289 3617 1301 3617 Dl 1244 3592 1244 3595 Dl 1287 3584 1244 3592 Dl 1245 3596 1289 3616 Dl 1257 3563 1255 3563 Dl 1261 3562 1258 3562 Dl 1371 3798 1409 3821 Dl 1319 3755 1370 3798 Dl 1409 3821 1422 3821 Dl 1377 3754 1318 3754 Dl 1293 3718 1300 3751 Dl 1300 3752 1318 3754 Dl 1294 3718 1367 3718 Dl 1207 3695 1269 3713 Dl 1262 3684 1206 3695 Dl 1269 3714 1293 3718 Dl 1264 3684 1307 3685 Dl 1217 3651 1224 3662 Dl 1224 3663 1262 3684 Dl 1217 3652 1287 3654 Dl 1213 3620 1200 3648 Dl 1201 3649 1216 3651 Dl 1236 3620 1214 3620 Dl 1237 3619 1265 3620 Dl 1203 3599 1198 3600 Dl 1244 3595 1204 3597 Dl 1198 3600 1236 3619 Dl 1169 3578 1170 3579 Dl 1237 3575 1169 3578 Dl 1239 3575 1247 3575 Dl 1171 3581 1244 3592 Dl 1247 3576 1285 3579 Dl 1203 3562 1251 3564 Dl 1204 3562 1247 3575 Dl 1226 3557 1258 3562 Dl 1226 3557 1292 3561 Dl 1470 4031 1706 4189 Dl 1457 3891 1470 4031 Dl 1532 3884 1457 3890 Dl (45)1641 4059 w 1317 3830 1317 3835 Dl 1319 3835 1457 3890 Dl 1409 3821 1319 3830 Dl 1262 3753 1370 3798 Dl 1299 3752 1261 3752 Dl 1269 3713 1259 3751 Dl 1259 3752 1261 3752 Dl 1224 3663 1192 3695 Dl 1193 3694 1206 3695 Dl 1126 3602 1124 3609 Dl 1198 3600 1127 3602 Dl 1124 3610 1214 3620 Dl 1169 3581 1164 3584 Dl 1165 3584 1204 3597 Dl 1169 3560 1167 3564 Dl 1170 3559 1203 3561 Dl 1167 3565 1237 3575 Dl 1228 3557 1267 3557 Dl 1227 3556 1223 3556 Dl 1267 3557 1296 3559 Dl 1224 3556 1226 3556 Dl 1247 3792 1319 3830 Dl 1248 3753 1246 3792 Dl 1258 3752 1247 3752 Dl 1157 3694 1154 3712 Dl 1154 3713 1247 3752 Dl 1159 3695 1192 3695 Dl 1131 3677 1158 3694 Dl 1164 3647 1131 3677 Dl 1164 3647 1200 3648 Dl 1124 3609 1107 3616 Dl 1108 3616 1164 3646 Dl 1125 3600 1127 3602 Dl 1164 3584 1125 3599 Dl 1166 3565 1146 3573 Dl 1147 3573 1169 3578 Dl 1223 3556 1152 3556 Dl 1153 3556 1170 3559 Dl 1282 3921 1470 4031 Dl 1246 3859 1282 3920 Dl 1317 3835 1246 3858 Dl 5 R f (62)1348 3927 w 10 R f 0.1 setlinewidth 1153 3712 1149 3713 Dl 1149 3714 1148 3770 Dl 1149 3772 1246 3792 Dl 1106 3617 1078 3619 Dl 1079 3619 1087 3666 Dl 1088 3667 1131 3677 Dl 1058 3576 1049 3577 Dl 1146 3574 1059 3576 Dl 1050 3578 1125 3599 Dl 1247 3557 1267 3557 Dl 1117 3772 1135 3810 Dl 1135 3810 1246 3858 Dl 1147 3772 1116 3772 Dl 1062 3714 1064 3750 Dl 1065 3751 1116 3772 Dl 1149 3714 1062 3714 Dl 1021 3666 1006 3677 Dl 1007 3677 1062 3714 Dl 1022 3666 1087 3666 Dl 992 3618 1022 3666 Dl 991 3617 1078 3619 Dl 1049 3578 1009 3580 Dl 989 3616 991 3616 Dl 1008 3580 988 3615 Dl 1136 3556 1059 3576 Dl 1137 3556 1152 3556 Dl 1128 3555 1136 3555 Dl 1127 3554 1227 3556 Dl 1190 3555 1247 3556 Dl 1044 3805 1083 3838 Dl 1084 3838 1282 3920 Dl 1044 3804 1135 3810 Dl 912 3675 910 3677 Dl 910 3676 974 3757 Dl 913 3674 956 3677 Dl 956 3677 1010 3751 Dl 1009 3752 974 3757 Dl 1009 3581 935 3600 Dl 935 3600 947 3618 Dl 988 3616 947 3618 Dl 1188 3554 1118 3553 Dl 1119 3554 1127 3554 Dl 975 3758 976 3767 Dl 977 3768 1043 3804 Dl 1064 3750 1010 3751 Dl 1005 3677 956 3677 Dl 946 3618 913 3674 Dl 1118 3554 1044 3556 Dl 1044 3557 1009 3580 Dl 1035 3842 1662 4186 Dl 1082 3838 1035 3841 Dl 5 R f (83)1340 4010 w 10 R f 0.1 setlinewidth 929 3771 956 3799 Dl 956 3799 1035 3841 Dl 975 3768 928 3771 Dl 871 3680 871 3713 Dl 871 3713 928 3771 Dl 910 3677 871 3679 Dl 877 3604 871 3679 Dl 934 3600 877 3604 Dl 889 3568 877 3604 Dl 1044 3558 890 3568 Dl 956 3799 992 3855 Dl 871 3713 944 3808 Dl 20 R f 16 setlinewidth 2736 4878 720 4878 Dl 2736 2862 2736 4878 Dl 720 2862 2736 2862 Dl 720 4878 720 2862 Dl 962 3742 962 3762 Dl 962 3741 980 3813 Dl 962 3741 944 3813 Dl 10 R f 0.1 setlinewidth 4888 3780 4886 3785 Dl 4885 3786 4880 3795 Dl 4880 3796 4874 3806 Dl 4873 3807 4849 3841 Dl 3436 3974 3911 4237 Dl 3912 4237 3958 4242 Dl 4272 4171 3958 4242 Dl 4849 3841 4273 4170 Dl 3265 3842 3301 3888 Dl 3302 3889 3435 3974 Dl 4729 3723 4855 3756 Dl 4855 3757 4873 3766 Dl 4873 3767 4885 3777 Dl 4886 3778 4888 3781 Dl 4200 4086 4273 4170 Dl 4115 3850 4199 4086 Dl 4873 3806 4114 3849 Dl (7)4397 3965 w 4077 3793 4085 3831 Dl 4085 3831 4114 3849 Dl 4880 3794 4076 3792 Dl 5 R f (8)4379 3823 w 10 R f 0.1 setlinewidth 4025 3734 4050 3770 Dl 4050 3770 4076 3792 Dl 4024 3733 4886 3785 Dl 5 R f (9)4354 3783 w 10 R f 0.1 setlinewidth 3970 3674 3972 3701 Dl 3972 3702 4023 3733 Dl 3970 3675 4885 3777 Dl 5 R f (10)4300 3743 w 10 R f 0.1 setlinewidth 3897 3606 3900 3627 Dl 3900 3627 3970 3674 Dl 3896 3605 4873 3766 Dl 5 R f (11)4258 3698 w 10 R f 0.1 setlinewidth 3784 3545 3825 3577 Dl 3825 3577 3895 3605 Dl 3785 3544 4855 3756 Dl 5 R f (12)4193 3653 w 10 R f 0.1 setlinewidth 3798 3536 4728 3723 Dl 3638 3505 3710 3527 Dl 3710 3528 3731 3533 Dl 3637 3505 3798 3535 Dl 3638 3504 1 1 De 3733 3532 3785 3544 Dl 4036 3962 4199 4086 Dl 3962 3839 4035 3962 Dl 4084 3832 3962 3838 Dl 5 R f (14)4059 3939 w 10 R f 0.1 setlinewidth 3897 3777 3926 3824 Dl 3927 3825 3962 3838 Dl 3904 3770 3897 3777 Dl 4049 3770 3905 3770 Dl 3883 3697 3905 3770 Dl 3882 3697 3972 3701 Dl 3802 3665 3829 3684 Dl 3847 3621 3801 3664 Dl 3829 3685 3882 3697 Dl 3849 3622 3900 3627 Dl 3753 3568 3746 3580 Dl 3746 3580 3847 3621 Dl 3754 3568 3825 3577 Dl 3696 3550 3754 3568 Dl 3732 3533 3696 3549 Dl 3632 3503 3630 3503 Dl 3631 3503 3638 3504 Dl 3632 3504 3637 3504 Dl 3612 3501 3632 3503 Dl 3798 3685 3795 3686 Dl 3795 3686 3841 3751 Dl 3842 3752 3897 3777 Dl 3829 3684 3799 3684 Dl 3670 3576 3665 3613 Dl 3665 3615 3787 3663 Dl 3671 3577 3746 3580 Dl 3787 3662 3801 3664 Dl 3610 3515 3602 3516 Dl 3603 3516 3604 3521 Dl 3604 3522 3672 3546 Dl 3610 3515 3710 3527 Dl 3673 3546 3696 3549 Dl 3788 3663 3799 3684 Dl 3672 3546 3618 3558 Dl 3618 3558 3670 3576 Dl 3569 3502 3566 3502 Dl 3608 3502 3630 3503 Dl 3606 3501 3576 3501 Dl 3567 3503 3610 3515 Dl 3576 3502 3570 3502 Dl 3813 3830 3836 3886 Dl 3837 3887 4035 3962 Dl 3927 3826 3813 3831 Dl 3731 3808 3813 3831 Dl 3730 3753 3730 3808 Dl 3841 3752 3730 3752 Dl 3687 3683 3688 3724 Dl 3689 3725 3730 3752 Dl 3686 3684 3795 3686 Dl 3624 3612 3620 3640 Dl 3620 3641 3680 3681 Dl 3681 3681 3686 3683 Dl 3624 3611 3665 3613 Dl 3604 3558 3579 3563 Dl 3579 3564 3600 3602 Dl 3601 3603 3624 3611 Dl 3606 3557 3618 3558 Dl 3558 3530 3558 3533 Dl 3603 3522 3558 3530 Dl 3559 3535 3605 3558 Dl 3572 3502 3570 3502 Dl 3573 3501 3576 3501 Dl 3677 3779 3715 3807 Dl 3627 3725 3677 3778 Dl 3716 3808 3730 3808 Dl 3686 3725 3625 3725 Dl 3603 3681 3607 3722 Dl 3607 3723 3625 3725 Dl 3603 3681 3680 3681 Dl 3513 3653 3577 3674 Dl 3572 3639 3512 3653 Dl 3577 3674 3602 3679 Dl 3574 3639 3620 3640 Dl 3527 3599 3534 3612 Dl 3535 3613 3573 3638 Dl 3526 3599 3600 3602 Dl 3526 3561 3511 3594 Dl 3511 3596 3526 3599 Dl 3550 3561 3527 3561 Dl 3551 3561 3579 3563 Dl 3516 3537 3511 3539 Dl 3558 3534 3517 3537 Dl 3512 3539 3550 3561 Dl 3482 3516 3483 3517 Dl 3552 3513 3481 3516 Dl 3552 3512 3561 3512 Dl 3483 3518 3558 3530 Dl 3562 3513 3602 3516 Dl 3517 3500 3566 3502 Dl 3517 3499 3561 3512 Dl 3540 3497 3573 3501 Dl 3539 3497 3607 3502 Dl 3750 4061 3958 4242 Dl 3756 3893 3749 4060 Dl 3836 3886 3756 3893 Dl (45)3921 4090 w 3619 3819 3618 3824 Dl 3618 3824 3756 3893 Dl 3715 3808 3620 3818 Dl 3567 3722 3677 3778 Dl 3607 3722 3566 3722 Dl 3576 3676 3564 3722 Dl 3564 3722 3566 3722 Dl 3535 3613 3499 3651 Dl 3498 3652 3512 3653 Dl 3435 3543 3433 3550 Dl 3511 3539 3437 3542 Dl 3435 3550 3527 3561 Dl 3481 3518 3476 3522 Dl 3477 3522 3517 3537 Dl 3481 3498 3479 3502 Dl 3483 3497 3517 3499 Dl 3480 3502 3552 3512 Dl 3542 3497 3581 3499 Dl 3541 3496 3537 3496 Dl 3581 3499 3611 3501 Dl 3538 3496 3540 3496 Dl 3548 3772 3620 3818 Dl 3552 3723 3547 3771 Dl 3563 3722 3552 3722 Dl 3463 3652 3458 3674 Dl 3458 3674 3552 3722 Dl 3464 3651 3499 3651 Dl 3437 3631 3463 3651 Dl 3472 3594 3436 3630 Dl 3473 3593 3511 3594 Dl 3433 3550 3415 3558 Dl 3416 3559 3473 3593 Dl 3435 3539 3437 3542 Dl 3476 3522 3435 3538 Dl 3478 3502 3458 3510 Dl 3458 3511 3481 3516 Dl 3465 3494 3537 3496 Dl 3464 3495 3482 3497 Dl 3572 3929 3749 4060 Dl 3541 3854 3571 3929 Dl 3617 3825 3541 3853 Dl 5 R f (62)3639 3934 w 10 R f 0.1 setlinewidth 3458 3673 3453 3675 Dl 3453 3677 3448 3746 Dl 3448 3746 3547 3771 Dl 3415 3559 3386 3563 Dl 3385 3563 3391 3619 Dl 3392 3620 3436 3630 Dl 3368 3516 3358 3517 Dl 3458 3510 3368 3515 Dl 3359 3517 3435 3538 Dl 3415 3747 3431 3795 Dl 3431 3795 3541 3853 Dl 3447 3746 3414 3747 Dl 3363 3678 3363 3721 Dl 3363 3722 3414 3747 Dl 3453 3675 3363 3677 Dl 3325 3619 3309 3633 Dl 3309 3634 3363 3677 Dl 3391 3620 3325 3620 Dl 3297 3563 3325 3620 Dl 3298 3563 3386 3563 Dl 3358 3517 3317 3521 Dl 3295 3562 3297 3562 Dl 3317 3521 3294 3561 Dl 3447 3494 3368 3515 Dl 3449 3494 3464 3494 Dl 3440 3494 3448 3494 Dl 3439 3494 3541 3496 Dl 3339 3788 3377 3829 Dl 3376 3831 3571 3929 Dl 3339 3789 3431 3795 Dl 3215 3634 3213 3636 Dl 3213 3637 3273 3733 Dl 3217 3634 3259 3636 Dl 3260 3637 3309 3725 Dl 3309 3726 3273 3733 Dl 3317 3521 3242 3546 Dl 3242 3547 3252 3566 Dl 3293 3562 3252 3566 Dl 3439 3494 3430 3494 Dl 3274 3733 3274 3744 Dl 3275 3745 3339 3788 Dl 3363 3722 3309 3725 Dl 3308 3634 3259 3636 Dl 3252 3566 3216 3633 Dl 3429 3494 3355 3499 Dl 3354 3500 3317 3521 Dl 3330 3836 3911 4237 Dl 3377 3830 3330 3836 Dl 5 R f (83)3614 4029 w 10 R f 0.1 setlinewidth 3229 3753 3254 3786 Dl 3255 3787 3330 3836 Dl 3274 3745 3228 3752 Dl 3175 3643 3175 3684 Dl 3175 3686 3228 3752 Dl 3212 3636 3175 3643 Dl 3186 3558 3175 3643 Dl 3241 3547 3186 3558 Dl 3205 3532 3186 3558 Dl 3355 3500 3206 3532 Dl 3253 3787 3301 3888 Dl 5 R f (89)3471 3987 w 10 R f 0.1 setlinewidth 3175 3685 3265 3841 Dl 20 R f 16 setlinewidth 5040 4878 3024 4878 Dl 5040 2862 5040 4878 Dl 3024 2862 5040 2862 Dl 3024 4878 3024 2862 Dl 3226 3678 3277 3759 Dl 3225 3677 3279 3728 Dl 3225 3678 3248 3748 Dl 10 B f (Fig. 86:)1 322 1 901 5076 t 10 R f (primal projective iter 10, outside)4 1307 1 1248 5076 t 10 B f (Fig. 87:)1 322 1 3205 5076 t 10 R f (primal projective iter 11, outside)4 1307 1 3552 5076 t 0.1 setlinewidth 2584 6179 2583 6181 Dl 2582 6182 2579 6187 Dl 2579 6188 2574 6193 Dl 2573 6193 2553 6211 Dl 1212 6343 1862 6494 Dl 1910 6494 1862 6494 Dl 2180 6424 1910 6492 Dl 2553 6212 2181 6425 Dl 947 6261 1011 6292 Dl 1012 6294 1212 6342 Dl 2495 6151 2570 6167 Dl 2571 6168 2579 6172 Dl 2579 6172 2584 6177 Dl 2584 6177 2584 6179 Dl 2158 6395 2181 6425 Dl 2162 6271 2157 6393 Dl 2573 6193 2162 6271 Dl 5 R f (7)2292 6308 w 10 R f 0.1 setlinewidth 2144 6237 2144 6262 Dl 2144 6263 2162 6271 Dl 2578 6188 2144 6238 Dl 2112 6201 2127 6225 Dl 2127 6226 2144 6238 Dl 2582 6182 2111 6200 Dl 2070 6160 2071 6180 Dl 2071 6180 2111 6200 Dl 2070 6159 2584 6177 Dl 1998 6106 2004 6124 Dl 2005 6124 2070 6159 Dl 1998 6106 2579 6172 Dl 1867 6054 1922 6083 Dl 1924 6083 1998 6106 Dl 1868 6053 2570 6167 Dl 1845 6040 2494 6150 Dl 1663 6011 1776 6036 Dl 1777 6037 1804 6042 Dl 1660 6010 1845 6040 Dl 1661 6011 1663 6011 Dl 1804 6042 1867 6053 Dl 2069 6345 2157 6393 Dl 2040 6278 2068 6346 Dl 2143 6263 2040 6277 Dl 1990 6241 2010 6271 Dl 2011 6272 2040 6277 Dl 1999 6235 1991 6240 Dl 2128 6225 2000 6235 Dl 1988 6182 2000 6235 Dl 2070 6180 1987 6181 Dl 1904 6160 1933 6174 Dl 1952 6121 1905 6159 Dl 1934 6174 1987 6181 Dl 1953 6122 2004 6124 Dl 1842 6076 1836 6087 Dl 1836 6088 1951 6121 Dl 1843 6076 1922 6083 Dl 1770 6059 1843 6076 Dl 1803 6042 1769 6058 Dl 1653 6009 1651 6009 Dl 1652 6009 1663 6011 Dl 1654 6010 1660 6010 Dl 1620 6007 1653 6009 Dl 1900 6176 1897 6177 Dl 1898 6177 1939 6225 Dl 1940 6225 1991 6240 Dl 1933 6174 1901 6176 Dl 1742 6086 1740 6120 Dl 1741 6120 1889 6158 Dl 1744 6085 1836 6087 Dl 1890 6159 1905 6159 Dl 1642 6024 1632 6024 Dl 1633 6024 1638 6029 Dl 1638 6029 1738 6054 Dl 1644 6023 1776 6036 Dl 1739 6055 1769 6058 Dl 1889 6159 1901 6176 Dl 1737 6056 1670 6068 Dl 1671 6067 1743 6084 Dl 1574 6007 1570 6007 Dl 1622 6007 1651 6009 Dl 1582 6006 1622 6007 Dl 1569 6007 1643 6022 Dl 1581 6006 1574 6006 Dl 1895 6286 1905 6320 Dl 1905 6321 2068 6346 Dl 2011 6272 1895 6285 Dl 1808 6276 1895 6285 Dl 1814 6235 1807 6276 Dl 1939 6226 1815 6233 Dl 1768 6181 1767 6215 Dl 1768 6214 1815 6233 Dl 1897 6178 1769 6180 Dl 1686 6118 1681 6145 Dl 1682 6146 1761 6179 Dl 1762 6179 1769 6180 Dl 1686 6119 1740 6120 Dl 1652 6066 1616 6071 Dl 1617 6072 1653 6110 Dl 1653 6111 1686 6118 Dl 1652 6067 1670 6068 Dl 1576 6037 1578 6041 Dl 1637 6029 1576 6037 Dl 1578 6041 1652 6066 Dl 1576 6006 1574 6006 Dl 1577 6006 1582 6006 Dl 1746 6258 1789 6276 Dl 1687 6220 1746 6258 Dl 1806 6276 1789 6276 Dl 1765 6214 1686 6218 Dl 1658 6181 1662 6217 Dl 1662 6217 1686 6218 Dl 1760 6179 1658 6181 Dl 1527 6161 1622 6178 Dl 1615 6146 1527 6161 Dl 1623 6178 1658 6181 Dl 1680 6145 1616 6145 Dl 1544 6108 1556 6121 Dl 1557 6122 1616 6145 Dl 1544 6108 1653 6110 Dl 1537 6071 1519 6104 Dl 1519 6104 1543 6107 Dl 1572 6071 1537 6071 Dl 1573 6069 1616 6071 Dl 1514 6044 1506 6046 Dl 1578 6042 1515 6044 Dl 1507 6047 1573 6070 Dl 1449 6021 1452 6022 Dl 1558 6018 1449 6020 Dl 1559 6019 1572 6019 Dl 1453 6022 1576 6037 Dl 1571 6019 1632 6024 Dl 1494 6003 1570 6007 Dl 1494 6003 1572 6019 Dl 1521 6000 1577 6006 Dl 1521 6000 1622 6007 Dl 1761 6431 1910 6492 Dl 1815 6333 1761 6431 Dl 1903 6320 1815 6332 Dl 5 R f (45)1929 6412 w 10 R f 0.1 setlinewidth 1668 6293 1666 6297 Dl 1666 6298 1815 6332 Dl 1788 6277 1668 6292 Dl 1607 6220 1746 6258 Dl 1662 6218 1606 6220 Dl 1623 6179 1603 6220 Dl 1603 6220 1606 6220 Dl 1556 6122 1505 6160 Dl 1505 6161 1527 6161 Dl 1384 6049 1382 6057 Dl 1505 6046 1384 6048 Dl 1382 6058 1537 6071 Dl 1451 6023 1444 6027 Dl 1444 6027 1515 6044 Dl 1436 5999 1436 6004 Dl 1437 5998 1493 6002 Dl 1436 6004 1558 6018 Dl 1521 5999 1576 6002 Dl 1522 5999 1517 5999 Dl 1578 6003 1621 6006 Dl 1517 5999 1521 5999 Dl 1575 6262 1668 6292 Dl 1585 6220 1575 6261 Dl 1602 6220 1586 6220 Dl 1448 6161 1442 6182 Dl 1443 6182 1586 6220 Dl 1505 6161 1450 6161 Dl 1404 6141 1450 6161 Dl 1458 6103 1403 6140 Dl 1458 6103 1519 6104 Dl 1381 6057 1352 6066 Dl 1353 6067 1458 6103 Dl 1379 6044 1384 6048 Dl 1444 6026 1380 6044 Dl 1435 6004 1407 6013 Dl 1408 6013 1449 6020 Dl 1404 5994 1517 5999 Dl 1404 5995 1437 5999 Dl 1581 6373 1761 6431 Dl 1557 6324 1582 6372 Dl 1665 6298 1556 6325 Dl 5 R f (62)1667 6366 w 10 R f 0.1 setlinewidth 1441 6182 1434 6184 Dl 1434 6184 1426 6247 Dl 1426 6247 1575 6261 Dl 1352 6066 1299 6070 Dl 1300 6071 1323 6130 Dl 1324 6130 1403 6140 Dl 1247 6016 1229 6017 Dl 1406 6013 1247 6015 Dl 1230 6017 1380 6044 Dl 1372 6251 1396 6289 Dl 1397 6290 1556 6325 Dl 1426 6248 1373 6251 Dl 1280 6189 1283 6230 Dl 1283 6231 1373 6251 Dl 1435 6184 1279 6189 Dl 1198 6131 1170 6146 Dl 1171 6147 1279 6189 Dl 1322 6130 1199 6131 Dl 1127 6067 1199 6131 Dl 1127 6068 1299 6070 Dl 1228 6017 1149 6020 Dl 1121 6068 1126 6068 Dl 1149 6020 1121 6066 Dl 1374 5993 1247 6015 Dl 1375 5993 1403 5994 Dl 1358 5993 1375 5993 Dl 1358 5992 1522 5999 Dl 1240 6290 1302 6319 Dl 1303 6319 1582 6372 Dl 1396 6289 1240 6289 Dl 978 6148 972 6150 Dl 973 6151 1116 6246 Dl 978 6147 1069 6149 Dl 1070 6150 1183 6236 Dl 1183 6237 1116 6246 Dl 1148 6021 999 6047 Dl 999 6048 1033 6071 Dl 1120 6067 1033 6071 Dl 1340 5992 1357 5992 Dl 1116 6246 1118 6256 Dl 1119 6256 1240 6289 Dl 1282 6231 1183 6236 Dl 1169 6147 1069 6149 Dl 1033 6071 978 6147 Dl 1340 5992 1200 5994 Dl 1200 5995 1149 6020 Dl 1215 6326 1862 6494 Dl 1302 6320 1215 6325 Dl 5 R f (83)1544 6408 w 10 R f 0.1 setlinewidth 1023 6262 1074 6289 Dl 1075 6289 1215 6325 Dl 1118 6256 1023 6262 Dl 886 6157 894 6198 Dl 895 6198 1023 6262 Dl 972 6150 886 6156 Dl 871 6056 886 6156 Dl 999 6047 871 6056 Dl 873 6019 871 6056 Dl 1200 5995 874 6019 Dl 1074 6290 1011 6292 Dl 895 6199 946 6261 Dl 20 R f 16 setlinewidth 2736 7254 720 7254 Dl 2736 5238 2736 7254 Dl 720 5238 2736 5238 Dl 720 7254 720 5238 Dl 899 6093 928 6163 Dl 899 6092 943 6151 Dl 899 6093 910 6166 Dl 10 R f 0.1 setlinewidth 4887 6185 4888 6187 Dl 4888 6187 4888 6192 Dl 4888 6193 4887 6199 Dl 3678 6449 4460 6572 Dl 4513 6570 4460 6572 Dl 4736 6476 4513 6568 Dl 3330 6279 3420 6395 Dl 3420 6395 3489 6418 Dl 3490 6420 3677 6449 Dl 4881 6177 4886 6182 Dl 4887 6182 4887 6184 Dl 4757 6448 4736 6475 Dl 4858 6304 4759 6448 Dl 4886 6200 4858 6304 Dl 4867 6261 4860 6294 Dl 4860 6294 4858 6304 Dl 4888 6193 4868 6259 Dl 4860 6209 4865 6242 Dl 4865 6242 4868 6259 Dl 4888 6188 4860 6208 Dl 4829 6149 4842 6179 Dl 4843 6180 4860 6208 Dl 4830 6149 4886 6182 Dl 4746 6069 4772 6095 Dl 4773 6095 4829 6148 Dl 4745 6068 4880 6176 Dl 4579 5991 4674 6032 Dl 4674 6032 4745 6068 Dl 4483 5959 4515 5968 Dl 4516 5969 4578 5990 Dl 4764 6407 4759 6448 Dl 4810 6322 4764 6406 Dl 4859 6294 4811 6322 Dl 4798 6274 4799 6316 Dl 4800 6317 4811 6322 Dl 4803 6266 4798 6274 Dl 4864 6242 4803 6265 Dl 4801 6184 4803 6265 Dl 4842 6179 4800 6183 Dl 4740 6151 4766 6173 Dl 4740 6089 4739 6150 Dl 4766 6173 4800 6183 Dl 4741 6090 4772 6095 Dl 4615 6015 4626 6033 Dl 4626 6034 4740 6090 Dl 4615 6016 4674 6032 Dl 4531 5985 4615 6015 Dl 4515 5969 4530 5985 Dl 4743 6178 4741 6180 Dl 4741 6181 4766 6255 Dl 4767 6255 4798 6274 Dl 4766 6173 4744 6178 Dl 4547 6026 4577 6086 Dl 4578 6088 4727 6150 Dl 4548 6026 4626 6033 Dl 4728 6150 4739 6150 Dl 4345 5927 4338 5927 Dl 4340 5927 4356 5934 Dl 4356 5935 4499 5978 Dl 4346 5928 4483 5959 Dl 4499 5978 4530 5985 Dl 4728 6150 4744 6178 Dl 4498 5978 4457 5995 Dl 4457 5996 4547 6026 Dl 4218 5909 4345 5927 Dl 4710 6347 4687 6393 Dl 4687 6394 4764 6406 Dl 4798 6317 4710 6347 Dl 4646 6344 4710 6347 Dl 4665 6278 4646 6343 Dl 4766 6255 4666 6278 Dl 4630 6192 4627 6251 Dl 4628 6252 4666 6278 Dl 4740 6180 4630 6192 Dl 4523 6085 4531 6135 Dl 4532 6136 4623 6190 Dl 4623 6190 4630 6192 Dl 4523 6085 4577 6086 Dl 4437 5992 4404 6001 Dl 4404 6002 4481 6071 Dl 4482 6072 4523 6085 Dl 4437 5993 4457 5995 Dl 4305 5944 4314 5950 Dl 4354 5935 4304 5944 Dl 4314 5951 4437 5993 Dl 4596 6323 4631 6346 Dl 4548 6266 4596 6323 Dl 4646 6344 4631 6346 Dl 4626 6251 4547 6265 Dl 4516 6203 4521 6265 Dl 4522 6265 4547 6265 Dl 4622 6190 4515 6202 Dl 4361 6175 4476 6199 Dl 4458 6140 4361 6175 Dl 4477 6200 4515 6202 Dl 4530 6136 4458 6140 Dl 4351 6072 4375 6097 Dl 4374 6098 4458 6140 Dl 4481 6071 4350 6071 Dl 4307 6001 4317 6066 Dl 4317 6066 4350 6071 Dl 4350 5999 4307 6000 Dl 4350 5999 4404 6001 Dl 4240 5955 4232 5957 Dl 4313 5951 4240 5954 Dl 4233 5958 4350 5999 Dl 4114 5914 4121 5916 Dl 4113 5914 4242 5916 Dl 4243 5918 4260 5919 Dl 4120 5917 4304 5944 Dl 4260 5918 4338 5927 Dl 4121 5899 4218 5909 Dl 4121 5899 4260 5919 Dl 4467 6535 4513 6568 Dl 4605 6420 4467 6535 Dl 4686 6394 4606 6420 Dl 5 R f (45)4600 6484 w 10 R f 0.1 setlinewidth 4509 6385 4503 6392 Dl 4504 6392 4606 6420 Dl 4630 6346 4510 6384 Dl 4462 6276 4596 6323 Dl 4521 6266 4461 6276 Dl 4476 6200 4457 6276 Dl 4460 6276 4457 6276 Dl 4374 6098 4333 6175 Dl 4360 6175 4333 6175 Dl 4072 5962 4080 5978 Dl 4231 5958 4070 5962 Dl 4081 5978 4307 6000 Dl 4119 5917 4117 5924 Dl 4117 5924 4240 5954 Dl 4042 5891 4054 5895 Dl 4041 5891 4120 5898 Dl 4054 5894 4242 5916 Dl 3262 6181 3329 6278 Dl 4420 6348 4510 6384 Dl 4438 6279 4420 6348 Dl 4456 6277 4438 6279 Dl 4261 6182 4259 6224 Dl 4259 6225 4438 6279 Dl 4333 6175 4262 6181 Dl 4186 6146 4262 6181 Dl 4234 6067 4186 6146 Dl 4317 6066 4235 6066 Dl 4079 5978 4047 5997 Dl 4048 5997 4235 6066 Dl 4057 5955 4070 5962 Dl 4117 5925 4057 5955 Dl 4053 5896 4040 5904 Dl 4041 5904 4113 5914 Dl 3982 5889 4041 5891 Dl 4356 6499 4467 6535 Dl 4368 6444 4356 6499 Dl 4503 6392 4368 6444 Dl 5 R f (62)4444 6469 w 10 R f 0.1 setlinewidth 4259 6224 4249 6228 Dl 4248 6228 4240 6343 Dl 4241 6343 4420 6348 Dl 5 R f (63)4304 6306 w 10 R f 0.1 setlinewidth 4047 5997 3968 6009 Dl 3968 6009 4060 6132 Dl 4061 6133 4186 6146 Dl 5 R f (64)4079 6083 w 10 R f 0.1 setlinewidth 3799 5912 3774 5914 Dl 4039 5904 3800 5911 Dl 3775 5914 4057 5955 Dl 4170 6357 4193 6415 Dl 4194 6415 4368 6444 Dl 4240 6344 4170 6356 Dl 5 R f (67)4303 6398 w 10 R f 0.1 setlinewidth 4024 6258 4042 6334 Dl 4044 6334 4170 6356 Dl 4248 6230 4025 6258 Dl 5 R f (68)4121 6304 w 10 R f 0.1 setlinewidth 3864 6149 3829 6185 Dl 3830 6186 4025 6258 Dl 4059 6133 3864 6149 Dl 5 R f (69)4033 6201 w 10 R f 0.1 setlinewidth 3674 6020 3864 6149 Dl 3967 6009 3674 6019 Dl 5 R f (70)3861 6084 w 10 R f 0.1 setlinewidth 3774 5914 3645 5925 Dl 3663 6018 3674 6019 Dl 3645 5926 3663 6018 Dl 5 R f (71)3810 5980 w 10 R f 0.1 setlinewidth 3936 5888 3800 5911 Dl 3937 5888 3981 5888 Dl 3937 5888 3907 5889 Dl 3253 6168 3262 6181 Dl 3981 6436 4053 6468 Dl 4054 6469 4356 6499 Dl 4192 6416 3981 6436 Dl 5 R f (75)4176 6464 w 10 R f 0.1 setlinewidth 3501 6214 3494 6221 Dl 3493 6222 3796 6382 Dl 3661 6206 3502 6214 Dl 3661 6206 3895 6357 Dl 3894 6357 3796 6382 Dl 5 R f (76)3675 6296 w 10 R f 0.1 setlinewidth 3644 5925 3413 5999 Dl 3414 5999 3510 6040 Dl 3662 6019 3510 6040 Dl 3906 5889 3879 5891 Dl 3797 6382 3804 6399 Dl 3804 6400 3981 6436 Dl 4043 6334 3895 6357 Dl 5 R f (79)3986 6396 w 10 R f 0.1 setlinewidth 3829 6185 3661 6205 Dl 5 R f (80)3851 6277 w 10 R f 0.1 setlinewidth 3510 6040 3502 6214 Dl 5 R f (81)3626 6134 w 10 R f 0.1 setlinewidth 3879 5892 3664 5908 Dl 3663 5907 3644 5925 Dl 3922 6484 4460 6572 Dl 4053 6468 3921 6483 Dl 5 R f (83)4222 6525 w 10 R f 0.1 setlinewidth 3653 6421 3730 6452 Dl 3730 6453 3921 6483 Dl 3804 6400 3653 6420 Dl 5 R f (84)3828 6452 w 10 R f 0.1 setlinewidth 3351 6251 3407 6330 Dl 3407 6330 3653 6420 Dl 3494 6222 3350 6251 Dl 5 R f (85)3538 6335 w 10 R f 0.1 setlinewidth 3200 6059 3350 6251 Dl 3412 5999 3198 6058 Dl 5 R f (86)3357 6129 w 10 R f 0.1 setlinewidth 3175 6046 3198 6058 Dl 3664 5908 3175 6046 Dl 3175 6047 3252 6167 Dl 3491 6419 3730 6452 Dl 3407 6331 3420 6395 Dl 20 R f 16 setlinewidth 5040 7254 3024 7254 Dl 5040 5238 5040 7254 Dl 3024 5238 5040 5238 Dl 3024 7254 3024 5238 Dl 3270 6101 3290 6137 Dl 3269 6101 3320 6155 Dl 3269 6101 3289 6172 Dl 10 B f (Fig. 88:)1 322 1 901 7452 t 10 R f (primal projective iter 12, outside)4 1307 1 1248 7452 t 10 B f (Fig. 89:)1 322 1 3205 7452 t 10 R f (primal projective iter 13, outside)4 1307 1 3552 7452 t (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 27 28 %%Page: 28 29 /saveobj save def mark 29 pagesetup 10 R f (- 28 -)2 216 1 2772 282 t 0.1 setlinewidth 2582 1528 2583 1528 Dl 2581 1527 2580 1527 Dl 2579 1529 2574 1529 Dl 2583 1529 2576 1531 Dl 2574 1529 2576 1531 Dl 2386 1551 2340 1653 Dl 2395 1546 2387 1551 Dl 2464 1527 2396 1545 Dl 2465 1528 2574 1529 Dl 2576 1531 2340 1653 Dl 2296 1686 2303 1693 Dl 2305 1678 2295 1686 Dl 2340 1654 2306 1677 Dl 2576 1535 2303 1693 Dl 2583 1530 2576 1535 Dl 2584 1529 1 1 De 2457 1519 2464 1527 Dl 2465 1490 2458 1518 Dl 2465 1490 2580 1527 Dl 2461 1483 2458 1486 Dl 2459 1487 2464 1491 Dl 2462 1483 2581 1527 Dl 2456 1475 2458 1479 Dl 2458 1480 2462 1483 Dl 2456 1476 2583 1528 Dl 2444 1469 2449 1469 Dl 2444 1469 2456 1475 Dl 2449 1469 2584 1528 Dl 2431 1464 2449 1469 Dl 2430 1502 2458 1518 Dl 2418 1479 2429 1501 Dl 2417 1479 2458 1486 Dl 2399 1469 2405 1476 Dl 2405 1476 2417 1479 Dl 2403 1468 2399 1468 Dl 2404 1468 2458 1479 Dl 2406 1460 2404 1468 Dl 2407 1458 2444 1468 Dl 2369 1449 2381 1452 Dl 2369 1449 2407 1457 Dl 2381 1452 2406 1459 Dl 2407 1457 2431 1463 Dl 2361 1448 2363 1448 Dl 2360 1448 2376 1460 Dl 2377 1461 2399 1468 Dl 2363 1449 2381 1452 Dl 2275 1429 2360 1447 Dl 2361 1446 2369 1448 Dl 2361 1446 2363 1448 Dl 2354 1473 2363 1486 Dl 2364 1486 2429 1501 Dl 2354 1474 2405 1476 Dl 2307 1465 2353 1472 Dl 2308 1455 2306 1465 Dl 2310 1453 2376 1460 Dl 2281 1437 2280 1445 Dl 2280 1445 2309 1453 Dl 2281 1437 2360 1448 Dl 2231 1422 2221 1424 Dl 2221 1424 2276 1436 Dl 2276 1437 2281 1437 Dl 2231 1422 2274 1429 Dl 2204 1418 2230 1422 Dl 2270 1457 2297 1464 Dl 2225 1442 2270 1457 Dl 2297 1465 2306 1465 Dl 2225 1441 2280 1445 Dl 2200 1429 2206 1439 Dl 2205 1439 2224 1441 Dl 2199 1429 2276 1436 Dl 2068 1410 2168 1424 Dl 2068 1411 2162 1417 Dl 2168 1425 2198 1428 Dl 2164 1418 2221 1424 Dl 2093 1404 2105 1407 Dl 2105 1408 2162 1417 Dl 2091 1404 2203 1417 Dl 2064 1401 2092 1404 Dl 2332 1528 2396 1545 Dl 2326 1488 2331 1527 Dl 2363 1486 2325 1488 Dl 2227 1466 2227 1468 Dl 2228 1468 2325 1488 Dl 2296 1464 2227 1466 Dl 2160 1437 2270 1457 Dl 2160 1437 2206 1439 Dl 2168 1425 2157 1436 Dl 2158 1436 2160 1436 Dl 2104 1407 2042 1407 Dl 2042 1408 2068 1410 Dl 2183 1683 2303 1693 Dl 2149 1452 2227 1466 Dl 2143 1436 2149 1452 Dl 2143 1436 2157 1436 Dl 1968 1402 1970 1410 Dl 1970 1410 2142 1435 Dl 1969 1401 2042 1407 Dl 1895 1391 1968 1401 Dl 1980 1392 1895 1391 Dl 1981 1394 2063 1401 Dl 1819 1380 1981 1393 Dl 2223 1509 2331 1527 Dl 2173 1484 2222 1509 Dl 2226 1468 2172 1483 Dl 1970 1411 1962 1411 Dl 1962 1411 2003 1444 Dl 2003 1445 2149 1452 Dl 1710 1373 1819 1379 Dl 1710 1373 1758 1383 Dl 1759 1383 1895 1391 Dl 1949 1447 2021 1471 Dl 2021 1471 2172 1483 Dl 2002 1445 1947 1447 Dl 1740 1413 1809 1439 Dl 1809 1439 1947 1447 Dl 1961 1410 1740 1411 Dl 1485 1377 1437 1385 Dl 1438 1385 1740 1411 Dl 1486 1377 1758 1383 Dl 1218 1358 1486 1376 Dl 1218 1358 1710 1373 Dl 1216 1357 1196 1357 Dl 2162 1681 2182 1683 Dl 1878 1490 1995 1505 Dl 1995 1506 2222 1509 Dl 2019 1472 1877 1489 Dl 871 1416 871 1421 Dl 872 1421 1606 1472 Dl 1184 1400 872 1415 Dl 1185 1401 1684 1455 Dl 1684 1455 1606 1472 Dl 5 R f (76)1263 1443 w 10 R f 0.1 setlinewidth 1196 1358 888 1370 Dl 1607 1473 1645 1481 Dl 1645 1482 1877 1489 Dl 1808 1440 1684 1455 Dl 1437 1386 1185 1400 Dl 5 R f (80)1512 1427 w 10 R f 0.1 setlinewidth 888 1370 872 1415 Dl 5 R f (81)1101 1393 w 10 R f 0.1 setlinewidth 1973 1533 2387 1551 Dl 1995 1505 1973 1533 Dl 1621 1528 1789 1540 Dl 1973 1534 1789 1540 Dl 1644 1482 1620 1527 Dl 5 R f (84)1773 1522 w 10 R f 0.1 setlinewidth 871 1497 1242 1538 Dl 1620 1527 1242 1538 Dl 871 1421 871 1496 Dl 5 R f (85)1206 1496 w 10 R f 0.1 setlinewidth 871 1497 891 1529 Dl 890 1529 1728 1635 Dl 1729 1636 2161 1681 Dl 1790 1541 2306 1677 Dl 5 R f (89)2133 1597 w 10 R f 0.1 setlinewidth 1243 1539 2295 1686 Dl 5 R f (90)1756 1597 w (91)1459 1598 w 20 R f 16 setlinewidth 2736 2502 720 2502 Dl 2736 486 2736 2502 Dl 720 486 2736 486 Dl 720 2502 720 486 Dl 904 1474 898 1505 Dl 905 1474 908 1548 Dl 904 1474 873 1540 Dl 10 R f 0.1 setlinewidth 4828 1149 1 1 De 4829 1147 4829 1148 Dl 4829 1145 4829 1146 Dl 4832 1143 4831 1145 Dl 4828 1149 1 1 De 4831 1142 4827 1147 Dl 4844 1092 4630 1285 Dl 4850 1087 4845 1091 Dl 4851 1088 4860 1090 Dl 4860 1091 4832 1142 Dl 4827 1148 4630 1285 Dl 4468 1423 4268 1611 Dl 4527 1371 4468 1422 Dl 4630 1286 4528 1370 Dl 4813 1164 4268 1611 Dl 4824 1153 4813 1163 Dl 4826 1151 4825 1152 Dl 4827 1150 4826 1151 Dl 4864 1085 4860 1090 Dl 4873 1080 4865 1085 Dl 4874 1079 4831 1145 Dl 4875 1076 4875 1078 Dl 4875 1077 4873 1079 Dl 4873 1078 4829 1146 Dl 4875 1078 1 1 De 4873 1073 4865 1085 Dl 4880 1064 4873 1072 Dl 4881 1065 4875 1077 Dl 4883 1060 1 1 De 4883 1061 4882 1064 Dl 4883 1060 4883 1061 Dl 4882 1061 4875 1077 Dl 4885 1055 4884 1059 Dl 4885 1051 4880 1056 Dl 4880 1056 4873 1072 Dl 4885 1050 4883 1060 Dl 4887 1043 4885 1051 Dl 4888 1043 1 1 De 4887 1043 4885 1055 Dl 4888 1039 4888 1043 Dl 4888 1038 4888 1041 Dl 4888 1031 4888 1037 Dl 4888 1041 4888 1042 Dl 4888 1031 4888 1038 Dl 4888 1029 4888 1031 Dl 4860 1069 4851 1087 Dl 4878 1052 4860 1069 Dl 4879 1052 4880 1056 Dl 4885 1033 1 1 De 4884 1033 4879 1051 Dl 4887 1034 4888 1041 Dl 4888 1023 4888 1037 Dl 4888 1023 4888 1028 Dl 4268 1611 4057 1745 Dl 4885 1023 4885 1033 Dl 4887 1021 4885 1023 Dl 4888 1021 4888 1022 Dl 4883 1003 4888 1020 Dl 4865 1049 4860 1069 Dl 4876 1034 4866 1049 Dl 4884 1033 4876 1033 Dl 4882 1003 1 1 De 4882 1003 4880 1010 Dl 4879 1011 4885 1023 Dl 4875 1006 4871 1018 Dl 4871 1018 4876 1033 Dl 4876 1007 4880 1010 Dl 4866 990 4867 997 Dl 4867 996 4875 1006 Dl 4867 988 4882 1002 Dl 4836 970 4865 988 Dl 4056 1745 4013 1772 Dl 4850 1017 4850 1032 Dl 4851 1033 4866 1049 Dl 4851 1017 4871 1018 Dl 4742 951 4740 952 Dl 4741 954 4833 997 Dl 4742 951 4798 961 Dl 4799 962 4848 995 Dl 4848 996 4833 997 Dl 4648 971 4443 1040 Dl 4832 997 4832 1002 Dl 4832 1002 4850 1017 Dl 4849 996 4867 997 Dl 4799 962 4836 970 Dl 4742 952 4649 970 Dl 4825 1050 4845 1091 Dl 4849 1032 4824 1049 Dl 4788 1029 4795 1046 Dl 4796 1046 4824 1049 Dl 4831 1002 4788 1028 Dl 4637 999 4685 1035 Dl 4787 1029 4685 1035 Dl 4740 952 4636 998 Dl 4636 999 3759 1312 Dl 4444 1040 3759 1312 Dl 3758 1312 3175 2119 Dl 4013 1773 3175 2119 Dl 4795 1046 4528 1370 Dl 4684 1035 4468 1422 Dl 5 R f (90)4623 1185 w 10 R f (91)3922 1539 w 20 R f 16 setlinewidth 5040 2502 3024 2502 Dl 5040 486 5040 2502 Dl 3024 486 5040 486 Dl 3024 2502 3024 486 Dl 4242 1125 4242 1128 Dl 4243 1125 4250 1198 Dl 4242 1124 4214 1193 Dl 10 B f (Fig. 90:)1 322 1 901 2700 t 10 R f (primal projective iter 14, outside)4 1307 1 1248 2700 t 10 B f (Fig. 91:)1 322 1 3205 2700 t 10 R f (primal projective iter 15, outside)4 1307 1 3552 2700 t 0.1 setlinewidth 2508 3954 2499 3961 Dl 2059 4218 1879 4268 Dl 2118 4188 2059 4217 Dl 2580 3833 2575 3855 Dl 2584 3801 2582 3822 Dl 2582 3823 2580 3833 Dl 2576 3759 2581 3777 Dl 2581 3778 2584 3800 Dl 2584 3801 1 1 De 2574 3752 2576 3759 Dl 2576 3850 2575 3857 Dl 2580 3828 2576 3849 Dl 2575 3856 2575 3857 Dl 2582 3822 2581 3827 Dl 2583 3804 2581 3827 Dl 2584 3801 2583 3803 Dl 2579 3790 2582 3802 Dl 2579 3778 2579 3790 Dl 2583 3802 2583 3803 Dl 2580 3777 2581 3777 Dl 2568 3745 2572 3757 Dl 2572 3757 2579 3777 Dl 2568 3744 2573 3751 Dl 2546 3712 2565 3740 Dl 2566 3740 2568 3744 Dl 2522 3940 2509 3953 Dl 2568 3873 2567 3875 Dl 2573 3857 2568 3872 Dl 2578 3833 2576 3849 Dl 2581 3827 2579 3831 Dl 2581 3802 2579 3832 Dl 2573 3758 2578 3790 Dl 2578 3790 2579 3790 Dl 2497 3667 2509 3675 Dl 2509 3675 2545 3711 Dl 1878 4268 1686 4296 Dl 2569 3862 2568 3872 Dl 2577 3834 2570 3862 Dl 2578 3833 2578 3834 Dl 2574 3793 2573 3813 Dl 2573 3814 2578 3834 Dl 2577 3790 2574 3792 Dl 2566 3776 2574 3792 Dl 2560 3737 2566 3775 Dl 2560 3737 2565 3740 Dl 2510 3676 2512 3683 Dl 2513 3683 2559 3736 Dl 2488 3662 2496 3666 Dl 2530 3930 2522 3939 Dl 2549 3905 2531 3930 Dl 2567 3876 2549 3904 Dl 2572 3814 2571 3816 Dl 2570 3816 2558 3870 Dl 2569 3863 2558 3870 Dl 2511 3683 2496 3685 Dl 2497 3686 2546 3770 Dl 2547 3770 2566 3775 Dl 2298 3594 2487 3662 Dl 2549 3881 2540 3906 Dl 2548 3905 2540 3906 Dl 2558 3870 2550 3880 Dl 2541 3844 2537 3882 Dl 2550 3881 2537 3882 Dl 2571 3816 2541 3844 Dl 2505 3790 2499 3818 Dl 2499 3818 2541 3844 Dl 2546 3771 2505 3789 Dl 2364 3672 2505 3789 Dl 2363 3672 2496 3685 Dl 2175 3567 2298 3594 Dl 2353 3670 2363 3672 Dl 2174 3567 2352 3669 Dl 1686 4297 1648 4302 Dl 2504 3943 2504 3950 Dl 2530 3931 2504 3950 Dl 2540 3906 2504 3942 Dl 2341 3911 2338 3921 Dl 2339 3922 2477 3946 Dl 2433 3861 2342 3911 Dl 2434 3861 2504 3915 Dl 2503 3916 2477 3946 Dl 2173 3567 1849 3667 Dl 1850 3668 2200 3706 Dl 2352 3669 2200 3706 Dl 5 R f (77)2102 3657 w 10 R f 0.1 setlinewidth 2477 3947 2476 3954 Dl 2504 3943 2476 3954 Dl 2536 3882 2504 3915 Dl 2498 3819 2434 3862 Dl 2200 3706 2342 3911 Dl 5 R f (81)2331 3790 w 10 R f 0.1 setlinewidth 2499 3962 2463 3985 Dl 2503 3950 2463 3985 Dl 2409 4011 2421 4011 Dl 2464 3985 2421 4011 Dl 2475 3954 2409 4011 Dl 2189 4039 2263 4065 Dl 2409 4012 2263 4065 Dl 2337 3922 2188 4038 Dl 5 R f (85)2309 4001 w 10 R f 0.1 setlinewidth 2188 4039 995 4100 Dl 1848 3667 995 4100 Dl (86)1747 3927 w 995 4100 871 4354 Dl 1648 4302 871 4354 Dl 2420 4012 2118 4187 Dl 2262 4066 2059 4217 Dl (91)1469 4207 w 20 R f 16 setlinewidth 2736 4878 720 4878 Dl 2736 2862 2736 4878 Dl 720 2862 2736 2862 Dl 720 4878 720 2862 Dl 1657 3781 1562 3825 Dl 1656 3781 1599 3827 Dl 1656 3781 1584 3795 Dl 10 R f 0.1 setlinewidth 4884 3665 4883 3666 Dl 4882 3667 4880 3669 Dl 4880 3670 4878 3672 Dl 4878 3671 4869 3679 Dl 4733 3804 4666 3849 Dl 4869 3680 4734 3803 Dl 4888 3652 4888 3659 Dl 4888 3659 4887 3661 Dl 4886 3662 4885 3664 Dl 4884 3665 1 1 De 4736 3801 4734 3803 Dl 4778 3762 4736 3801 Dl 4878 3672 4778 3762 Dl 4789 3749 4777 3761 Dl 4778 3762 1 1 De 4880 3669 4790 3748 Dl 4803 3732 4793 3744 Dl 4792 3744 4790 3748 Dl 4882 3666 4802 3731 Dl 4818 3709 4805 3724 Dl 4804 3724 4802 3731 Dl 4884 3665 4818 3708 Dl 4842 3670 4829 3687 Dl 4828 3687 4818 3708 Dl 4885 3662 4842 3669 Dl 4859 3622 4844 3653 Dl 4843 3653 4842 3669 Dl 4860 3621 4888 3659 Dl 4870 3600 4888 3651 Dl 4854 3565 4854 3603 Dl 4854 3604 4855 3610 Dl 4855 3564 4870 3600 Dl 4854 3564 4854 3565 Dl 4856 3609 4860 3621 Dl 4734 3802 4727 3805 Dl 4742 3788 4727 3805 Dl 4776 3762 4743 3788 Dl 4746 3779 4737 3791 Dl 4742 3789 4737 3791 Dl 4751 3773 4746 3778 Dl 4792 3744 4752 3773 Dl 4780 3740 4752 3773 Dl 4804 3725 4781 3739 Dl 4771 3735 4770 3742 Dl 4818 3691 4772 3735 Dl 4780 3739 4770 3742 Dl 4828 3687 4818 3690 Dl 4830 3651 4816 3666 Dl 4816 3667 4818 3690 Dl 4830 3652 4844 3653 Dl 4827 3634 4830 3651 Dl 4855 3609 4826 3633 Dl 4854 3562 1 1 De 4854 3563 4854 3565 Dl 4854 3563 4854 3564 Dl 4849 3556 4854 3562 Dl 4758 3750 4756 3752 Dl 4755 3753 4739 3779 Dl 4746 3779 4739 3779 Dl 4770 3743 4758 3750 Dl 4785 3674 4746 3720 Dl 4745 3720 4767 3736 Dl 4815 3666 4785 3673 Dl 4771 3734 4767 3736 Dl 4826 3583 4821 3584 Dl 4820 3585 4815 3593 Dl 4815 3593 4819 3630 Dl 4828 3583 4854 3603 Dl 4820 3631 4826 3633 Dl 4767 3737 4758 3750 Dl 4819 3631 4774 3656 Dl 4775 3656 4785 3673 Dl 4827 3552 4824 3552 Dl 4846 3556 4853 3561 Dl 4832 3552 4846 3557 Dl 4824 3552 4827 3582 Dl 4831 3551 4827 3551 Dl 4694 3821 4687 3829 Dl 4726 3806 4687 3829 Dl 4737 3792 4695 3821 Dl 4694 3821 4666 3836 Dl 4689 3811 4666 3836 Dl 4739 3779 4690 3810 Dl 4703 3780 4680 3808 Dl 4681 3808 4690 3810 Dl 4755 3752 4704 3780 Dl 4720 3729 4691 3763 Dl 4691 3763 4701 3780 Dl 4703 3780 4701 3780 Dl 4746 3720 4721 3728 Dl 4766 3657 4740 3669 Dl 4740 3669 4712 3723 Dl 4713 3723 4721 3728 Dl 4767 3656 4774 3656 Dl 4772 3608 4767 3615 Dl 4815 3592 4772 3607 Dl 4767 3616 4767 3656 Dl 4829 3551 4827 3551 Dl 4830 3551 4831 3551 Dl 4659 3841 4649 3841 Dl 4640 3832 4649 3841 Dl 4666 3837 4659 3841 Dl 4681 3808 4640 3831 Dl 4647 3808 4627 3837 Dl 4639 3832 4627 3837 Dl 4701 3781 4648 3808 Dl 4629 3814 4574 3826 Dl 4653 3779 4574 3826 Dl 4647 3808 4629 3814 Dl 4691 3764 4653 3779 Dl 4642 3743 4637 3761 Dl 4638 3761 4653 3779 Dl 4711 3724 4643 3743 Dl 4692 3676 4628 3743 Dl 4643 3743 4628 3743 Dl 4717 3670 4692 3675 Dl 4740 3669 4717 3670 Dl 4723 3623 4713 3627 Dl 4766 3616 4723 3623 Dl 4713 3627 4717 3670 Dl 4722 3567 4721 3571 Dl 4724 3566 4797 3571 Dl 4798 3571 4803 3573 Dl 4722 3570 4772 3607 Dl 4803 3573 4821 3584 Dl 4796 3535 4824 3552 Dl 4796 3535 4803 3573 Dl 4820 3535 4830 3551 Dl 4821 3535 4846 3557 Dl 4665 3849 4629 3871 Dl 4654 3851 4629 3871 Dl 4687 3829 4655 3850 Dl 4599 3878 4597 3880 Dl 4654 3850 4597 3880 Dl 4659 3840 4600 3878 Dl 4648 3842 4592 3857 Dl 4626 3838 4592 3857 Dl 4628 3814 4590 3857 Dl 4592 3857 4590 3857 Dl 4638 3762 4556 3834 Dl 4574 3827 4556 3834 Dl 4589 3640 4564 3665 Dl 4712 3628 4589 3640 Dl 4564 3665 4692 3675 Dl 4722 3571 4705 3581 Dl 4705 3582 4723 3623 Dl 4770 3517 4757 3527 Dl 4771 3517 4795 3535 Dl 4758 3528 4797 3571 Dl 4821 3535 4839 3547 Dl 4819 3533 4821 3534 Dl 4840 3548 4849 3556 Dl 4818 3533 4819 3534 Dl 4599 3879 4558 3892 Dl 4579 3864 4558 3892 Dl 4589 3858 4579 3864 Dl 4499 3857 4481 3885 Dl 4579 3863 4481 3885 Dl 4555 3834 4500 3858 Dl 4464 3849 4500 3858 Dl 4572 3759 4464 3849 Dl 4627 3744 4572 3758 Dl 4562 3666 4501 3697 Dl 4501 3698 4572 3758 Dl 4594 3629 4589 3640 Dl 4704 3582 4593 3628 Dl 4756 3527 4708 3543 Dl 4708 3544 4723 3566 Dl 4762 3503 4818 3533 Dl 4763 3502 4771 3517 Dl 4629 3871 4564 3906 Dl 4562 3906 4543 3913 Dl 4597 3880 4543 3913 Dl 4481 3886 4473 3891 Dl 4473 3892 4456 3938 Dl 4558 3892 4456 3938 Dl 4500 3697 4403 3722 Dl 4403 3722 4363 3867 Dl 4464 3849 4363 3867 Dl 5 R f (64)4433 3789 w 10 R f 0.1 setlinewidth 4451 3513 4496 3513 Dl 4496 3514 4708 3543 Dl 4451 3513 4593 3628 Dl 4444 3958 4410 3962 Dl 4543 3914 4443 3957 Dl 4456 3939 4410 3962 Dl 4284 3976 4309 3997 Dl 4409 3962 4309 3997 Dl 4472 3891 4284 3975 Dl 4097 3955 4029 4009 Dl 4283 3975 4029 4009 Dl 4362 3868 4098 3955 Dl 5 R f (69)4254 3940 w 10 R f 0.1 setlinewidth 3831 3787 4098 3955 Dl 4403 3723 3831 3787 Dl (70)4102 3848 w 4215 3495 4451 3513 Dl 3801 3785 3831 3787 Dl 4214 3496 3800 3785 Dl (71)4191 3663 w 4747 3493 4496 3513 Dl 4747 3493 4762 3502 Dl 4740 3488 4747 3493 Dl 4740 3488 4821 3534 Dl 4408 3974 4328 4008 Dl 4563 3907 4409 3974 Dl 4443 3957 4328 4008 Dl 3244 4258 3245 4265 Dl 4117 4085 3245 4265 Dl 3721 4114 3243 4258 Dl 4195 4048 3721 4114 Dl 4195 4047 4118 4084 Dl 5 R f (76)3716 4153 w 10 R f 0.1 setlinewidth 4213 3495 3175 3644 Dl 3175 3644 3195 3875 Dl 3799 3785 3195 3875 Dl (77)3553 3708 w 4730 3484 4740 3488 Dl 4146 4077 4118 4084 Dl 4328 4009 4147 4076 Dl 4309 3998 4196 4047 Dl 4029 4010 3721 4114 Dl 5 R f (80)4039 4048 w 10 R f 0.1 setlinewidth 3195 3876 3243 4258 Dl (81)3529 4010 w 4603 3450 4731 3484 Dl 4602 3448 4214 3494 Dl 5 R f (82)4485 3496 w 20 R f 16 setlinewidth 5040 4878 3024 4878 Dl 5040 2862 5040 4878 Dl 3024 2862 5040 2862 Dl 3024 4878 3024 2862 Dl 3198 3649 3193 3659 Dl 3198 3650 3182 3722 Dl 3198 3650 3150 3706 Dl 10 B f (Fig. 92:)1 322 1 901 5076 t 10 R f (primal projective iter 16, outside)4 1307 1 1248 5076 t 10 B f (Fig. 93:)1 322 1 3205 5076 t 10 R f (primal projective iter 17, outside)4 1307 1 3552 5076 t 0.1 setlinewidth 2581 6050 2581 6053 Dl 2581 6053 2579 6060 Dl 2579 6013 2584 6035 Dl 2584 6036 2584 6041 Dl 2583 6042 2582 6048 Dl 2581 6048 2581 6050 Dl 2506 6270 2494 6300 Dl 2579 6061 2507 6269 Dl 2519 6228 2509 6258 Dl 2510 6259 2507 6269 Dl 2581 6054 2520 6228 Dl 2535 6170 2523 6211 Dl 2523 6211 2520 6228 Dl 2582 6048 2535 6169 Dl 2553 6066 2543 6112 Dl 2543 6113 2535 6169 Dl 2584 6041 2554 6066 Dl 2558 5932 2553 6022 Dl 2553 6022 2554 6066 Dl 2559 5932 2584 6035 Dl 2546 5869 2579 6013 Dl 2521 5766 2546 5879 Dl 2546 5880 2550 5898 Dl 2520 5761 2545 5869 Dl 2520 5761 2520 5765 Dl 2551 5899 2558 5932 Dl 2463 6363 2442 6399 Dl 2494 6300 2464 6363 Dl 2469 6343 2459 6371 Dl 2463 6364 2459 6371 Dl 2474 6330 2469 6342 Dl 2509 6259 2474 6330 Dl 2502 6249 2474 6330 Dl 2522 6211 2502 6248 Dl 2492 6239 2492 6258 Dl 2533 6123 2494 6238 Dl 2502 6250 2492 6258 Dl 2543 6113 2533 6123 Dl 2537 6019 2526 6060 Dl 2526 6060 2533 6123 Dl 2538 6019 2553 6022 Dl 2528 5969 2538 6017 Dl 2550 5898 2527 5969 Dl 2518 5756 1 1 De 2518 5755 2520 5765 Dl 2519 5755 2520 5760 Dl 2506 5738 2518 5756 Dl 2481 6277 2479 6281 Dl 2479 6281 2463 6343 Dl 2469 6342 2463 6343 Dl 2492 6258 2481 6276 Dl 2493 6080 2462 6202 Dl 2462 6203 2489 6243 Dl 2526 6060 2494 6080 Dl 2493 6238 2489 6243 Dl 2508 5819 2502 5824 Dl 2501 5825 2499 5851 Dl 2499 5851 2519 5960 Dl 2508 5820 2546 5879 Dl 2519 5961 2527 5969 Dl 2488 6243 2481 6276 Dl 2519 5961 2476 6034 Dl 2476 6034 2494 6080 Dl 2485 5726 2483 5728 Dl 2507 5741 2517 5755 Dl 2490 5726 2507 5741 Dl 2483 5728 2507 5820 Dl 2490 5726 2486 5726 Dl 2420 6437 2410 6454 Dl 2442 6400 2410 6454 Dl 2459 6371 2420 6436 Dl 2419 6437 2394 6471 Dl 2416 6415 2394 6471 Dl 2463 6343 2417 6415 Dl 2428 6349 2408 6411 Dl 2409 6412 2417 6415 Dl 2478 6281 2429 6348 Dl 2436 6225 2412 6309 Dl 2413 6308 2427 6349 Dl 2429 6349 2427 6349 Dl 2462 6203 2437 6224 Dl 2466 6034 2440 6069 Dl 2440 6069 2425 6212 Dl 2426 6212 2437 6224 Dl 2475 6034 2467 6034 Dl 2452 5898 2449 5920 Dl 2498 5852 2453 5898 Dl 2449 5921 2467 6034 Dl 2488 5724 2486 5726 Dl 2488 5724 2490 5726 Dl 2386 6481 2378 6481 Dl 2370 6463 2378 6481 Dl 2394 6471 2388 6480 Dl 2408 6412 2370 6462 Dl 2375 6411 2359 6474 Dl 2370 6462 2359 6474 Dl 2427 6350 2376 6411 Dl 2358 6426 2304 6451 Dl 2375 6346 2304 6451 Dl 2376 6412 2358 6426 Dl 2412 6310 2375 6346 Dl 2352 6261 2352 6304 Dl 2353 6305 2375 6346 Dl 2425 6213 2353 6261 Dl 2384 6089 2336 6261 Dl 2353 6261 2336 6261 Dl 2413 6074 2385 6089 Dl 2440 6070 2413 6073 Dl 2398 5943 2388 5955 Dl 2449 5921 2398 5942 Dl 2388 5955 2413 6073 Dl 2370 5778 2370 5791 Dl 2369 5777 2463 5786 Dl 2465 5787 2472 5792 Dl 2371 5792 2453 5898 Dl 2473 5792 2502 5824 Dl 2438 5677 2483 5728 Dl 2438 5677 2472 5792 Dl 2462 5674 2488 5723 Dl 2461 5674 2507 5741 Dl 2409 6454 2379 6498 Dl 2334 6558 2332 6561 Dl 2379 6498 2332 6561 Dl 2388 6480 2334 6557 Dl 2378 6482 2327 6515 Dl 2357 6475 2327 6515 Dl 2358 6426 2326 6517 Dl 2328 6515 2326 6517 Dl 2352 6304 2286 6467 Dl 2303 6452 2286 6467 Dl 2243 5995 2228 6064 Dl 2388 5956 2244 5995 Dl 2228 6066 2385 6089 Dl 5 R f (50)2302 6037 w 10 R f 0.1 setlinewidth 2369 5791 2354 5823 Dl 2355 5824 2398 5942 Dl 2395 5624 2385 5656 Dl 2395 5624 2437 5676 Dl 2385 5655 2463 5786 Dl 2463 5674 2488 5711 Dl 2460 5671 2462 5674 Dl 2488 5712 2505 5737 Dl 2459 5670 2461 5673 Dl 2333 6558 2297 6584 Dl 2315 6530 2297 6584 Dl 2326 6517 2316 6529 Dl 2237 6517 2225 6572 Dl 2315 6529 2225 6572 Dl 2286 6467 2237 6517 Dl 2197 6497 2237 6517 Dl 2278 6297 2196 6497 Dl 2335 6261 2279 6295 Dl 5 R f (57)2254 6398 w 10 R f 0.1 setlinewidth 2228 6065 2172 6147 Dl 2172 6147 2279 6295 Dl 5 R f (58)2257 6173 w 10 R f 0.1 setlinewidth 2244 5964 2244 5995 Dl 2353 5824 2243 5963 Dl 2384 5656 2335 5710 Dl 2336 5712 2369 5778 Dl 2371 5578 2459 5670 Dl 2371 5577 2395 5623 Dl 2331 6561 2280 6622 Dl 2225 6572 2218 6582 Dl 2217 6583 2208 6668 Dl 2297 6584 2208 6668 Dl 2171 6147 2073 6208 Dl 2074 6208 2099 6531 Dl 2196 6497 2099 6531 Dl 5 R f (64)2137 6344 w 10 R f 0.1 setlinewidth 2044 5641 1989 5643 Dl 2045 5640 2335 5710 Dl 1989 5643 2243 5963 Dl 5 R f (65)2181 5785 w 10 R f 0.1 setlinewidth 2195 6698 2170 6708 Dl 2280 6622 2196 6699 Dl 2208 6668 2170 6708 Dl 2061 6729 2088 6765 Dl 2170 6709 2088 6765 Dl 2217 6582 2060 6728 Dl 1883 6683 1847 6771 Dl 2060 6729 1847 6771 Dl 2099 6532 1883 6683 Dl 5 R f (69)2027 6648 w 10 R f 0.1 setlinewidth 1538 6340 1883 6683 Dl 2072 6208 1538 6339 Dl (70)1827 6446 w 1696 5614 1989 5643 Dl 1509 6334 1538 6339 Dl 1695 5614 1509 6334 Dl (71)1816 6001 w 2342 5550 2044 5639 Dl 2343 5550 2370 5577 Dl 5 R f (72)2237 5642 w 10 R f 0.1 setlinewidth 2328 5535 2343 5550 Dl 2195 6700 2097 6778 Dl 1373 7047 1377 7054 Dl 1940 6886 1377 7054 Dl 1640 6904 1373 7046 Dl 1997 6838 1640 6904 Dl 1997 6838 1940 6886 Dl 5 R f (76)1667 6943 w 10 R f 0.1 setlinewidth 1694 5613 871 6027 Dl 871 6027 1086 6474 Dl 1695 5613 1 1 De 1508 6333 1086 6474 Dl (77)1248 6097 w 2309 5524 2327 5535 Dl 1960 6875 1940 6886 Dl 2096 6778 1960 6874 Dl 2087 6766 1998 6837 Dl 1846 6772 1640 6904 Dl 5 R f (80)1871 6821 w 10 R f 0.1 setlinewidth 1087 6476 1373 7046 Dl (81)1428 6683 w 2103 5434 2310 5523 Dl 2102 5434 1694 5613 Dl (82)1992 5574 w 20 R f 16 setlinewidth 2736 7254 720 7254 Dl 2736 5238 2736 7254 Dl 720 5238 2736 5238 Dl 720 7254 720 5238 Dl 891 6033 894 6037 Dl 890 6033 951 6075 Dl 891 6033 924 6099 Dl 10 R f 0.1 setlinewidth 4860 6157 4850 6188 Dl 4874 6095 4867 6135 Dl 4867 6136 4861 6156 Dl 4888 5992 4884 6035 Dl 4883 6035 4875 6094 Dl 4882 5863 4888 5944 Dl 4888 5944 4888 5991 Dl 4870 5808 4875 5826 Dl 4875 5826 4881 5862 Dl 4824 6265 4812 6297 Dl 4828 6253 4824 6265 Dl 4850 6188 4829 6253 Dl 4857 6167 4829 6253 Dl 4867 6135 4857 6166 Dl 4854 6151 4852 6172 Dl 4879 6040 4854 6150 Dl 4856 6167 4852 6172 Dl 4884 6035 4880 6040 Dl 4881 5932 4876 5970 Dl 4877 5970 4880 6040 Dl 4882 5932 4888 5944 Dl 4873 5880 4881 5932 Dl 4874 5825 4872 5879 Dl 4845 6190 4844 6194 Dl 4843 6195 4823 6264 Dl 4823 6264 4824 6265 Dl 4852 6172 4845 6189 Dl 4856 5980 4836 6102 Dl 4837 6103 4852 6154 Dl 4876 5971 4857 5981 Dl 4854 6151 4852 6154 Dl 4839 5735 4837 5736 Dl 4837 5737 4839 5760 Dl 4840 5760 4866 5868 Dl 4841 5736 4870 5807 Dl 4867 5868 4872 5879 Dl 4852 6154 4845 6189 Dl 4865 5868 4842 5927 Dl 4843 5928 4857 5981 Dl 4800 5661 4840 5735 Dl 4812 6298 4780 6362 Dl 4780 6363 4762 6395 Dl 4787 6334 4762 6395 Dl 4823 6264 4787 6333 Dl 4806 6257 4783 6326 Dl 4784 6326 4787 6333 Dl 4843 6194 4806 6257 Dl 4817 6121 4797 6210 Dl 4798 6210 4805 6258 Dl 4806 6258 4805 6258 Dl 4836 6102 4818 6120 Dl 4836 5926 4817 5956 Dl 4816 5956 4809 6105 Dl 4810 6105 4818 6120 Dl 4836 5925 4842 5927 Dl 4811 5791 4811 5811 Dl 4839 5760 4811 5790 Dl 4811 5811 4836 5925 Dl 4751 6402 4756 6404 Dl 4751 6377 4751 6402 Dl 4761 6395 4756 6404 Dl 4783 6326 4751 6377 Dl 4761 6320 4741 6390 Dl 4750 6378 4741 6390 Dl 4805 6258 4762 6319 Dl 4746 6333 4703 6354 Dl 4764 6245 4703 6354 Dl 4761 6320 4747 6333 Dl 4796 6210 4766 6246 Dl 4749 6150 4748 6197 Dl 4748 6198 4766 6246 Dl 4808 6105 4749 6148 Dl 4770 5970 4734 6147 Dl 4734 6147 4749 6148 Dl 4794 5957 4771 5969 Dl 4817 5956 4794 5956 Dl 4769 5825 4762 5835 Dl 4810 5812 4769 5824 Dl 4762 5836 4794 5956 Dl 4724 5665 4726 5677 Dl 4724 5665 4802 5695 Dl 4802 5695 4809 5702 Dl 4727 5677 4811 5790 Dl 4809 5702 4837 5736 Dl 4757 5606 4800 5660 Dl 4756 5607 4809 5702 Dl 4706 6484 4703 6488 Dl 4755 6405 4707 6484 Dl 4751 6403 4715 6431 Dl 4742 6390 4715 6431 Dl 4747 6333 4713 6433 Dl 4714 6431 4713 6433 Dl 4747 6197 4688 6370 Dl 4703 6355 4688 6370 Dl 4634 5857 4625 5926 Dl 4760 5836 4633 5856 Dl 4625 5926 4771 5969 Dl 4726 5677 4716 5704 Dl 4716 5705 4769 5824 Dl 4712 5554 4712 5573 Dl 4713 5554 4756 5606 Dl 4712 5574 4802 5695 Dl 4706 6484 4680 6508 Dl 4704 6446 4680 6508 Dl 4712 6434 4704 6446 Dl 4645 6423 4630 6485 Dl 4704 6447 4630 6485 Dl 4688 6370 4645 6422 Dl 4609 6397 4645 6422 Dl 4682 6180 4608 6397 Dl 4734 6146 4684 6179 Dl 5 R f (57)4657 6294 w 10 R f 0.1 setlinewidth 4624 5926 4575 6010 Dl 4576 6010 4684 6179 Dl 5 R f (58)4654 6048 w 10 R f 0.1 setlinewidth 4629 5825 4633 5856 Dl 4715 5704 4629 5824 Dl 4712 5574 4682 5602 Dl 4682 5602 4723 5664 Dl 4679 5522 4712 5554 Dl 4703 6489 4649 6556 Dl 4630 6485 4623 6495 Dl 4623 6496 4600 6595 Dl 4680 6508 4600 6595 Dl 4576 6009 4479 6073 Dl 4479 6074 4515 6434 Dl 4609 6398 4515 6434 Dl 5 R f (64)4545 6227 w 10 R f 0.1 setlinewidth 4337 5511 4392 5513 Dl 4393 5513 4682 5602 Dl 4337 5510 4629 5824 Dl 5 R f (65)4541 5660 w 10 R f 0.1 setlinewidth 4575 6634 4561 6639 Dl 4648 6556 4576 6633 Dl 4598 6596 4561 6639 Dl 4469 6657 4486 6699 Dl 4561 6640 4486 6699 Dl 4623 6496 4469 6656 Dl 4297 6606 4260 6706 Dl 4468 6657 4260 6706 Dl 4513 6435 4297 6606 Dl 5 R f (69)4437 6566 w 10 R f 0.1 setlinewidth 3907 6223 4297 6606 Dl 4477 6073 3906 6222 Dl (70)4225 6337 w 4028 5478 4337 5510 Dl 3873 6217 3906 6222 Dl 4026 5477 3872 6217 Dl (71)4180 5873 w 4647 5501 4392 5513 Dl 4649 5501 4679 5521 Dl 4628 5494 4648 5500 Dl 4576 6633 4476 6719 Dl 3775 7028 3780 7035 Dl 4333 6834 3780 7035 Dl 4045 6862 3774 7027 Dl 4393 6779 4046 6861 Dl 4394 6778 4334 6832 Dl 5 R f (76)4066 6903 w 10 R f 0.1 setlinewidth 4026 5479 3175 5976 Dl 3175 5976 3409 6410 Dl 4027 5478 1 1 De 3872 6218 3409 6410 Dl (77)3578 6006 w 4608 5489 4628 5494 Dl 4350 6821 4334 6832 Dl 4476 6720 4350 6821 Dl 4486 6700 4394 6779 Dl 4259 6706 4046 6861 Dl 5 R f (80)4275 6762 w 10 R f 0.1 setlinewidth 3409 6410 3774 7027 Dl (81)3805 6613 w 4390 5446 4608 5489 Dl 4389 5444 4026 5477 Dl 5 R f (82)4331 5492 w 20 R f 16 setlinewidth 5040 7254 3024 7254 Dl 5040 5238 5040 7254 Dl 3024 5238 5040 5238 Dl 3024 7254 3024 5238 Dl 3187 5977 3199 5986 Dl 3188 5977 3255 6006 Dl 3187 5977 3233 6035 Dl 10 B f (Fig. 94:)1 322 1 901 7452 t 10 R f (primal projective iter 18, outside)4 1307 1 1248 7452 t 10 B f (Fig. 95:)1 322 1 3205 7452 t 10 R f (primal projective iter 19, outside)4 1307 1 3552 7452 t (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 28 29 %%Page: 29 30 /saveobj save def mark 30 pagesetup 10 R f (- 29 -)2 216 1 2772 282 t 0.1 setlinewidth 2465 1754 2465 1755 Dl 2466 1756 2466 1757 Dl 2465 1757 2467 1763 Dl 2465 1754 2468 1763 Dl 2468 1763 2467 1763 Dl 2500 1878 2561 1932 Dl 2495 1872 2499 1877 Dl 2477 1830 2494 1871 Dl 2467 1763 2477 1829 Dl 2469 1763 2561 1932 Dl 2584 1942 2579 1951 Dl 2574 1948 2579 1951 Dl 2562 1931 2574 1946 Dl 2470 1757 2584 1941 Dl 2465 1752 2470 1757 Dl 2465 1753 1 1 De 2470 1819 2477 1829 Dl 2434 1763 2468 1819 Dl 2436 1762 2466 1757 Dl 2424 1743 2430 1756 Dl 2430 1757 2435 1762 Dl 2423 1743 2465 1755 Dl 2409 1719 2417 1734 Dl 2417 1735 2422 1743 Dl 2409 1720 2465 1754 Dl 2394 1693 2396 1703 Dl 2398 1704 2409 1719 Dl 2395 1693 2465 1753 Dl 2378 1658 2378 1665 Dl 2378 1665 2394 1692 Dl 2378 1658 2465 1752 Dl 2362 1624 2362 1634 Dl 2363 1635 2378 1658 Dl 2363 1624 2465 1752 Dl 2424 1696 2470 1757 Dl 2342 1596 2363 1616 Dl 2342 1596 2347 1603 Dl 2368 1621 2424 1695 Dl 2364 1616 2368 1621 Dl 2348 1604 2363 1624 Dl 2452 1803 2468 1819 Dl 2424 1765 2452 1803 Dl 2429 1758 2424 1765 Dl 2407 1742 2419 1761 Dl 2419 1763 2424 1765 Dl 2406 1739 2406 1742 Dl 2416 1735 2405 1738 Dl 2384 1698 2405 1738 Dl 2384 1698 2396 1703 Dl 2363 1677 2372 1689 Dl 2366 1656 2363 1676 Dl 2372 1689 2383 1698 Dl 2367 1656 2378 1665 Dl 2337 1609 2333 1612 Dl 2333 1613 2366 1656 Dl 2337 1609 2362 1634 Dl 2315 1579 2337 1608 Dl 2315 1580 2347 1603 Dl 2363 1616 2365 1619 Dl 2363 1616 1 1 De 2367 1619 2368 1621 Dl 2368 1689 2368 1690 Dl 2368 1691 2396 1732 Dl 2396 1732 2406 1742 Dl 2368 1689 2372 1689 Dl 2299 1585 2309 1621 Dl 2309 1622 2359 1674 Dl 2300 1585 2333 1612 Dl 2361 1674 2363 1676 Dl 2277 1523 2287 1533 Dl 2272 1521 2277 1523 Dl 2273 1522 2303 1566 Dl 2288 1534 2342 1595 Dl 2303 1567 2315 1579 Dl 2361 1674 2368 1689 Dl 2264 1543 2303 1566 Dl 2263 1543 2299 1584 Dl 2297 1543 2306 1553 Dl 2351 1601 2363 1616 Dl 2320 1567 2350 1601 Dl 2287 1534 2297 1542 Dl 2307 1553 2319 1566 Dl 2419 1778 2437 1800 Dl 2437 1801 2452 1803 Dl 2419 1762 2419 1778 Dl 2419 1778 2411 1779 Dl 2390 1746 2411 1779 Dl 2395 1733 2389 1746 Dl 2351 1694 2374 1731 Dl 2374 1732 2389 1746 Dl 2367 1691 2351 1694 Dl 2291 1612 2311 1652 Dl 2312 1652 2349 1692 Dl 2349 1693 2351 1694 Dl 2291 1612 2309 1621 Dl 2234 1527 2252 1533 Dl 2236 1528 2275 1596 Dl 2275 1597 2291 1612 Dl 2252 1534 2262 1542 Dl 2221 1484 2219 1486 Dl 2221 1485 2271 1522 Dl 2219 1485 2252 1533 Dl 2401 1774 2411 1782 Dl 2371 1744 2400 1773 Dl 2411 1780 2411 1782 Dl 2373 1732 2370 1744 Dl 2339 1704 2368 1746 Dl 2370 1745 2368 1746 Dl 2348 1693 2338 1703 Dl 2293 1685 2330 1702 Dl 2297 1654 2293 1685 Dl 2331 1703 2338 1703 Dl 2311 1652 2297 1653 Dl 2230 1579 2254 1610 Dl 2254 1610 2297 1653 Dl 2230 1580 2275 1596 Dl 2189 1499 2213 1568 Dl 2213 1568 2229 1578 Dl 2189 1499 2210 1510 Dl 2210 1510 2234 1527 Dl 2164 1450 2172 1453 Dl 2172 1454 2219 1486 Dl 2164 1450 2210 1510 Dl 2136 1399 2135 1399 Dl 2137 1399 2245 1493 Dl 2245 1492 2252 1499 Dl 2135 1399 2221 1483 Dl 2253 1500 2277 1523 Dl 2262 1508 2297 1542 Dl 2252 1501 2262 1508 Dl 2482 1869 2494 1871 Dl 2442 1818 2481 1868 Dl 2438 1802 2442 1818 Dl 2418 1811 2420 1814 Dl 2421 1816 2442 1818 Dl 2411 1782 2417 1810 Dl 2366 1757 2400 1773 Dl 2367 1746 2365 1757 Dl 2330 1704 2365 1758 Dl 2254 1610 2286 1686 Dl 2292 1685 2286 1686 Dl 2000 1342 1998 1360 Dl 2000 1342 2164 1450 Dl 1998 1361 2188 1499 Dl 2119 1392 2135 1399 Dl 2119 1392 2172 1453 Dl 2206 1455 2234 1481 Dl 2234 1481 2262 1508 Dl 2205 1455 2245 1493 Dl 2398 1804 2417 1810 Dl 2365 1762 2398 1804 Dl 2365 1758 2365 1761 Dl 2273 1697 2307 1740 Dl 2308 1740 2365 1761 Dl 2286 1687 2273 1697 Dl 2225 1664 2273 1697 Dl 2176 1558 2224 1664 Dl 2177 1558 2213 1568 Dl 1997 1360 1969 1375 Dl 1969 1376 2176 1558 Dl 1995 1331 2000 1341 Dl 1995 1331 2118 1392 Dl 2118 1381 2204 1454 Dl 2118 1380 2136 1398 Dl 2481 1868 2466 1872 Dl 2441 1853 2466 1872 Dl 2421 1815 2441 1853 Dl 2308 1741 2310 1746 Dl 2310 1746 2389 1829 Dl 2397 1804 2389 1829 Dl 1969 1375 1900 1374 Dl 1900 1374 2175 1663 Dl 2176 1664 2224 1664 Dl 5 R f (64)2052 1527 w 10 R f 0.1 setlinewidth 1705 1109 1802 1171 Dl 1803 1171 2118 1380 Dl 1705 1109 1995 1331 Dl 2396 1851 2429 1871 Dl 2441 1854 2429 1871 Dl 2390 1829 2395 1849 Dl 2319 1822 2381 1867 Dl 2394 1850 2381 1867 Dl 2311 1747 2319 1822 Dl 2139 1747 2202 1818 Dl 2203 1819 2319 1822 Dl 2175 1664 2139 1746 Dl 5 R f (69)2206 1758 w 10 R f 0.1 setlinewidth 1104 1230 2139 1746 Dl 1104 1230 1900 1374 Dl (70)1705 1486 w 1172 849 1704 1108 Dl 1012 1205 1103 1229 Dl 1172 851 1012 1205 Dl (71)1396 1169 w 2464 1913 2449 1920 Dl 2466 1872 2464 1912 Dl 2429 1872 2449 1920 Dl 2273 2068 2291 2073 Dl 2429 1955 2291 2073 Dl 2243 1939 2271 2067 Dl 2405 1918 2243 1938 Dl 2407 1919 2430 1955 Dl 5 R f (76)2300 1992 w 10 R f 0.1 setlinewidth 871 1668 904 1717 Dl 1012 1206 871 1668 Dl 2430 1956 2440 1956 Dl 2449 1920 2440 1956 Dl 2382 1867 2406 1918 Dl 2202 1818 2243 1938 Dl 5 R f (80)2272 1887 w 10 R f 0.1 setlinewidth 871 1668 2271 2067 Dl (81)1464 1671 w 2498 1877 2487 1936 Dl 2464 1912 2487 1936 Dl 2491 1972 2481 1992 Dl 2487 1937 2492 1971 Dl 2440 1957 2481 1992 Dl 2484 2059 2428 2119 Dl 2482 1992 2485 2059 Dl 2291 2073 2428 2119 Dl 5 R f (85)2383 2053 w 10 R f 0.1 setlinewidth 2427 2120 2391 2129 Dl 905 1718 2391 2129 Dl 5 R f (86)1566 1900 w 10 R f 0.1 setlinewidth 2573 1947 2492 1971 Dl 2578 1951 2485 2059 Dl 20 R f 16 setlinewidth 2736 2502 720 2502 Dl 2736 486 2736 2502 Dl 720 486 2736 486 Dl 720 2502 720 486 Dl 914 1719 918 1709 Dl 914 1717 926 1645 Dl 913 1719 959 1661 Dl 10 R f 0.1 setlinewidth 3399 663 4830 2258 Dl 3384 648 3175 2147 Dl 3175 2147 4888 2339 Dl 3385 648 3399 663 Dl 4830 2258 4888 2339 Dl (77)3771 1731 w 20 R f 16 setlinewidth 5040 2502 3024 2502 Dl 5040 486 5040 2502 Dl 3024 486 5040 486 Dl 3024 2502 3024 486 Dl 3185 2142 3187 2138 Dl 3185 2142 3210 2073 Dl 3185 2142 3240 2094 Dl 10 B f (Fig. 96:)1 322 1 901 2700 t 10 R f (primal projective iter 20, outside)4 1307 1 1248 2700 t 10 B f (Fig. 97:)1 322 1 3205 2700 t 10 R f (primal projective iter 21, outside)4 1307 1 3552 2700 t 0.1 setlinewidth 2388 4482 2394 4487 Dl 872 3101 964 4562 Dl 871 3101 2387 4481 Dl 2394 4487 2456 4544 Dl 2456 4545 2584 4664 Dl 964 4564 2584 4664 Dl (86)1424 4129 w 20 R f 16 setlinewidth 2736 4878 720 4878 Dl 2736 2862 2736 4878 Dl 720 2862 2736 2862 Dl 720 4878 720 2862 Dl 973 4558 974 4551 Dl 972 4558 969 4484 Dl 973 4557 1004 4491 Dl 10 R f 0.1 setlinewidth 3530 3834 1 1 De 3530 3833 3529 3834 Dl 3537 3821 3509 3843 Dl 3539 3821 3538 3821 Dl 3540 3820 3539 3820 Dl 3540 3821 3530 3833 Dl 3529 3835 3509 3843 Dl 3500 3850 3492 3857 Dl 3502 3847 3500 3849 Dl 3508 3843 3503 3847 Dl 3525 3837 3492 3857 Dl 3528 3836 3526 3838 Dl 3542 3820 3540 3821 Dl 3548 3818 3543 3819 Dl 3548 3818 3530 3834 Dl 3549 3818 3548 3818 Dl 3549 3817 3530 3834 Dl 3551 3817 1 1 De 3550 3818 1 1 De 3551 3818 3530 3835 Dl 3552 3817 3551 3819 Dl 3553 3818 3551 3818 Dl 3551 3820 3529 3835 Dl 3551 3821 3549 3823 Dl 3551 3820 3551 3819 Dl 3549 3825 3529 3836 Dl 3549 3824 3543 3831 Dl 3549 3824 3549 3823 Dl 3542 3832 3528 3836 Dl 3526 3838 3525 3843 Dl 3543 3834 3528 3846 Dl 3543 3833 3543 3834 Dl 3526 3846 3525 3843 Dl 3527 3846 3526 3846 Dl 3543 3832 3543 3831 Dl 3548 3816 3543 3819 Dl 3552 3814 3547 3816 Dl 3552 3813 3549 3817 Dl 3557 3812 3555 3812 Dl 3554 3812 3553 3813 Dl 3556 3812 3551 3817 Dl 3557 3812 3556 3811 Dl 3558 3813 3553 3817 Dl 3562 3810 3561 3810 Dl 3562 3811 3555 3818 Dl 3560 3811 3558 3813 Dl 3554 3819 3552 3821 Dl 3557 3819 3554 3822 Dl 3557 3818 3555 3818 Dl 3554 3823 3549 3825 Dl 3554 3823 3554 3822 Dl 3555 3824 3543 3833 Dl 3527 3847 1 1 De 3522 3849 1 1 De 3524 3842 3522 3846 Dl 3525 3847 3523 3849 Dl 3522 3847 3522 3849 Dl 3563 3809 3559 3809 Dl 3559 3810 3557 3811 Dl 3563 3809 3561 3810 Dl 3571 3806 3566 3813 Dl 3572 3806 3564 3810 Dl 3566 3813 3558 3818 Dl 3562 3810 1 1 De 3549 3834 3547 3835 Dl 3552 3832 3549 3834 Dl 3557 3824 3553 3831 Dl 3547 3834 3543 3834 Dl 3556 3824 3555 3824 Dl 3563 3808 1 1 De 3570 3813 3557 3823 Dl 3570 3813 3566 3813 Dl 3535 3846 3533 3846 Dl 3527 3847 1 1 De 3531 3847 3528 3847 Dl 3547 3836 3535 3846 Dl 3532 3847 3530 3847 Dl 3557 3808 3553 3810 Dl 3552 3811 3547 3816 Dl 3557 3810 3555 3812 Dl 3560 3806 3557 3808 Dl 3563 3805 3561 3805 Dl 3563 3804 3559 3809 Dl 3569 3803 3567 3803 Dl 3567 3803 3564 3805 Dl 3571 3802 3564 3808 Dl 3577 3799 3577 3801 Dl 3577 3800 3571 3802 Dl 3577 3801 3572 3805 Dl 3579 3807 3573 3812 Dl 3580 3800 3579 3806 Dl 3579 3800 3577 3801 Dl 3573 3812 3571 3813 Dl 3568 3820 3566 3822 Dl 3566 3823 3553 3831 Dl 3572 3812 3569 3819 Dl 3532 3847 3531 3847 Dl 3519 3850 3518 3851 Dl 3521 3850 3518 3851 Dl 3522 3847 3520 3849 Dl 3563 3804 3561 3805 Dl 3570 3800 3564 3803 Dl 3569 3801 3567 3803 Dl 3575 3797 3571 3798 Dl 3571 3798 3570 3799 Dl 3576 3797 3571 3802 Dl 3588 3788 3578 3795 Dl 3587 3787 3582 3794 Dl 3578 3795 3576 3797 Dl 3582 3794 3577 3798 Dl 3592 3790 3589 3790 Dl 3589 3791 3582 3794 Dl 3592 3790 3580 3800 Dl 3596 3789 3590 3800 Dl 3596 3788 3593 3790 Dl 3589 3799 3584 3803 Dl 3584 3804 3579 3806 Dl 3581 3811 3579 3813 Dl 3579 3813 3569 3819 Dl 3585 3803 3583 3810 Dl 3568 3829 3566 3831 Dl 3566 3831 3550 3836 Dl 3568 3829 3566 3822 Dl 3549 3834 3549 3836 Dl 3534 3846 3533 3850 Dl 3549 3836 3533 3850 Dl 3530 3848 3523 3853 Dl 3527 3848 3523 3853 Dl 3544 3816 3539 3820 Dl 3552 3811 3543 3816 Dl 3553 3809 3553 3810 Dl 3561 3803 1 1 De 3560 3804 3553 3810 Dl 3561 3803 3561 3805 Dl 3573 3796 3564 3803 Dl 3573 3796 3571 3798 Dl 3578 3795 3573 3795 Dl 3589 3785 3589 3790 Dl 3590 3785 3588 3787 Dl 3632 3777 3623 3787 Dl 3623 3787 3583 3810 Dl 3631 3778 3590 3800 Dl 3576 3824 3569 3829 Dl 3579 3813 3575 3823 Dl 3538 3851 3530 3856 Dl 3533 3851 3530 3856 Dl 3550 3837 3538 3852 Dl 3521 3854 3521 3852 Dl 3523 3854 3522 3854 Dl 3523 3850 3521 3852 Dl 3491 3858 3486 3863 Dl 3519 3850 3486 3863 Dl 3566 3799 3561 3803 Dl 3573 3796 3567 3798 Dl 3573 3795 1 1 De 3594 3780 3588 3782 Dl 3589 3783 3574 3795 Dl 3594 3780 3589 3785 Dl 3605 3774 3595 3780 Dl 3606 3779 3605 3773 Dl 3607 3780 3597 3787 Dl 3647 3762 3632 3777 Dl 3648 3762 3607 3780 Dl 3623 3788 3620 3792 Dl 3619 3792 3575 3823 Dl 3558 3842 3538 3852 Dl 3565 3832 3558 3841 Dl 3522 3854 3520 3863 Dl 3529 3857 3520 3863 Dl 3548 3811 3543 3816 Dl 3556 3805 3549 3810 Dl 3560 3804 3556 3805 Dl 3588 3783 3571 3793 Dl 3570 3793 3567 3798 Dl 3671 3743 3648 3762 Dl 3671 3743 3617 3763 Dl 3616 3763 3605 3773 Dl 3604 3862 3584 3860 Dl 3583 3859 3558 3841 Dl 3620 3792 3605 3863 Dl 3521 3852 3514 3854 Dl 3519 3851 3514 3854 Dl 3569 3794 3561 3800 Dl 3560 3800 3556 3805 Dl 3570 3792 1 1 De 3587 3778 3574 3788 Dl 3573 3788 3570 3792 Dl 3588 3779 3588 3783 Dl 3625 3749 3612 3756 Dl 3612 3756 3587 3778 Dl 3627 3749 3617 3763 Dl 4258 3308 3627 3748 Dl 4258 3308 3671 3742 Dl 4541 4717 3605 3863 Dl 4485 3144 4258 3307 Dl 4487 3144 4541 4717 Dl (71)4148 3914 w 3583 3860 3515 3867 Dl 3520 3863 3515 3867 Dl 3515 3868 3511 3870 Dl 3521 3855 3511 3870 Dl 3486 3864 3485 3864 Dl 3505 3859 3485 3864 Dl 3512 3854 3504 3859 Dl 3556 3801 3551 3806 Dl 3551 3807 3549 3810 Dl 3561 3800 3556 3801 Dl 3586 3765 3582 3768 Dl 3581 3770 3561 3795 Dl 3598 3762 3586 3765 Dl 3597 3761 3567 3791 Dl 3566 3792 3561 3795 Dl 4541 4717 4541 4726 Dl 4481 3013 4486 3144 Dl 3506 3871 3504 3859 Dl 3510 3870 3507 3872 Dl 3560 3795 3558 3797 Dl 3558 3797 3556 3801 Dl 3573 3789 3567 3791 Dl 3612 3756 3598 3761 Dl 4480 3013 3586 3765 Dl (81)4111 3348 w 3507 3872 3481 3890 Dl 4540 4725 3481 3890 Dl (82)3840 4191 w 3543 3813 3538 3821 Dl 3550 3807 3543 3812 Dl 3543 3808 3541 3812 Dl 3543 3812 3541 3812 Dl 3558 3798 3545 3808 Dl 3542 3802 3536 3811 Dl 3544 3808 3536 3811 Dl 3581 3769 3542 3802 Dl 3542 3803 3460 3873 Dl 3466 3878 3460 3873 Dl 3480 3891 3466 3879 Dl 3484 3864 3466 3879 Dl 3541 3812 3503 3847 Dl 3535 3811 3500 3849 Dl 20 R f 16 setlinewidth 5040 4878 3024 4878 Dl 5040 2862 5040 4878 Dl 3024 2862 5040 2862 Dl 3024 4878 3024 2862 Dl 4469 3828 4469 3831 Dl 4469 3828 4492 3898 Dl 4468 3828 4456 3901 Dl 10 B f (Fig. 98:)1 322 1 901 5076 t 10 R f (primal projective iter 22, outside)4 1307 1 1248 5076 t 10 B f (Fig. 99:)1 322 1 3299 5076 t 10 R f (iter 22, outside,)2 622 1 3646 5076 t 10 I f (d)4293 5076 w 10 R f (= \(0,\2611,0\))1 397 1 4368 5076 t ( transformed)1 518( show views of the projectively)5 1301( they)1 232(Figures 100\261135 are analogous to figures 48\26173:)6 2019 4 970 5232 t (polytope in direction)2 863 1 720 5352 t 10 I f (d)1623 5352 w 10 S f (=)1722 5352 w 10 R f (\()1826 5352 w 10 S f (-)1875 5352 w 10 R f ( numbered figures are from the center, the odd numbered)9 2403( the even)2 390(1 , 0 , 0 \);)5 301 3 1946 5352 t (ones from the center plus \(0.1,0,0\) \320 cutaway views from outside the polytope.)12 3195 1 720 5472 t (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 29 30 %%Page: 30 31 /saveobj save def mark 31 pagesetup 10 R f (- 30 -)2 216 1 2772 282 t 0.1 setlinewidth 1430 2502 891 2502 Dl 2736 640 2736 2243 Dl 2735 2244 1430 2502 Dl 2735 640 952 691 Dl 892 2501 952 691 Dl (2)1782 1565 w 753 486 720 486 Dl 891 2502 720 2502 Dl 720 2502 720 486 Dl 951 691 753 486 Dl (4)795 1506 w 2735 486 753 486 Dl 2736 640 2736 486 Dl (5)1721 595 w 2735 2502 1430 2502 Dl 2736 2244 2736 2502 Dl (7)2276 2435 w 20 R f 16 setlinewidth 2736 2502 720 2502 Dl 2736 486 2736 2502 Dl 720 486 2736 486 Dl 720 2502 720 486 Dl 10 R f 0.1 setlinewidth 5040 1294 5040 1451 Dl 5039 1452 4824 1530 Dl 4824 1530 3850 1735 Dl 5039 1294 3852 1308 Dl 3850 1734 3852 1308 Dl (2)4338 1483 w 3827 2502 3660 2502 Dl 3660 2501 3636 1084 Dl 3849 1736 3827 2502 Dl 3852 1307 3636 1084 Dl (4)3718 1840 w 5040 1294 5040 1069 Dl 5040 1069 3636 1084 Dl (5)4364 1205 w 5039 2502 3827 2502 Dl 5040 1615 5040 2502 Dl 5039 1614 4824 1530 Dl (7)4436 2081 w 5040 1452 5040 1614 Dl 5 R f (8)4956 1542 w 20 R f 16 setlinewidth 5040 2502 3024 2502 Dl 5040 486 5040 2502 Dl 3024 486 5040 486 Dl 3024 2502 3024 486 Dl 4072 1509 4032 1494 Dl 4071 1510 3998 1500 Dl 4072 1509 4012 1466 Dl 10 B f (Fig. 100:)1 372 1 1055 2700 t 10 R f (pr. proj. it. 5,)3 525 1 1452 2700 t 10 I f (v)2002 2700 w 10 R f (=)2071 2700 w 10 I f (center)2152 2700 w 10 B f (Fig. 101:)1 372 1 3186 2700 t 10 R f (pr. proj. it. 5,)3 525 1 3583 2700 t 10 I f (v)4133 2700 w 10 R f (=)4202 2700 w 10 I f (center)4283 2700 w 10 S f (+)4532 2700 w 10 R f (\(.1,0,0\))4587 2700 w 0.1 setlinewidth 2736 3626 2736 3834 Dl 2735 3835 2567 3903 Dl 2566 3902 1514 4146 Dl 2735 3625 1516 3648 Dl 1514 4146 1516 3648 Dl (2)2025 3850 w 764 2862 720 2862 Dl 1477 4878 720 4878 Dl 720 4878 720 2862 Dl 1513 4147 1477 4878 Dl 1515 3648 764 2862 Dl (4)1055 4051 w 2735 2862 764 2862 Dl 2736 3625 2736 2862 Dl (5)1893 3239 w 2735 4878 1477 4878 Dl 2736 3969 2736 4878 Dl 2735 3968 2567 3903 Dl (7)2120 4464 w 2736 3835 2736 3968 Dl 20 R f 16 setlinewidth 2736 4878 720 4878 Dl 2736 2862 2736 4878 Dl 720 2862 2736 2862 Dl 720 4878 720 2862 Dl 10 R f 0.1 setlinewidth 4614 3761 4586 3790 Dl 4586 3791 4508 3839 Dl 4507 3840 4397 3884 Dl 4396 3883 3938 3990 Dl 4614 3760 3936 3770 Dl 3937 3990 3936 3770 Dl (2)4175 3866 w 3915 4878 3746 4878 Dl 3746 4877 3690 3512 Dl 3938 3991 3915 4878 Dl 3936 3769 3690 3512 Dl (4)3795 4240 w 5040 3746 5040 3492 Dl 5039 3492 3690 3512 Dl 5039 3745 4914 3750 Dl 4914 3751 4692 3758 Dl 4692 3758 4615 3760 Dl (5)4397 3647 w 5039 4878 3915 4878 Dl 5040 4152 5040 4878 Dl 5039 4151 4397 3884 Dl (7)4439 4449 w 5040 4041 5040 4151 Dl 5039 4039 4508 3839 Dl 5 R f (8)4744 3994 w 10 R f 0.1 setlinewidth 5040 3947 5040 4039 Dl 5039 3946 4586 3790 Dl 5 R f (9)4788 3918 w 10 R f 0.1 setlinewidth 5040 3870 5040 3947 Dl 5039 3869 4692 3758 Dl 5 R f (10)4810 3851 w 10 R f 0.1 setlinewidth 5040 3787 5040 3869 Dl 5039 3786 4914 3750 Dl 5 R f (11)4889 3805 w 10 R f 0.1 setlinewidth 5040 3746 5040 3787 Dl 20 R f 16 setlinewidth 5040 4878 3024 4878 Dl 5040 2862 5040 4878 Dl 3024 2862 5040 2862 Dl 3024 4878 3024 2862 Dl 4140 3868 4032 3870 Dl 4140 3867 4069 3887 Dl 4140 3866 4068 3851 Dl 10 B f (Fig. 102:)1 372 1 1055 5076 t 10 R f (pr. proj. it. 6,)3 525 1 1452 5076 t 10 I f (v)2002 5076 w 10 R f (=)2071 5076 w 10 I f (center)2152 5076 w 10 B f (Fig. 103:)1 372 1 3186 5076 t 10 R f (pr. proj. it. 6,)3 525 1 3583 5076 t 10 I f (v)4133 5076 w 10 R f (=)4202 5076 w 10 I f (center)4283 5076 w 10 S f (+)4532 5076 w 10 R f (\(.1,0,0\))4587 5076 w 0.1 setlinewidth 1973 6179 1962 6197 Dl 1961 6197 1928 6227 Dl 1927 6227 1879 6255 Dl 1879 6256 1671 6323 Dl 1973 6179 1669 6185 Dl 1671 6321 1669 6185 Dl 5 R f (2)1776 6243 w 10 R f 0.1 setlinewidth 749 5238 720 5238 Dl 1646 7254 720 7254 Dl 720 7254 720 5238 Dl 1646 7253 1671 6323 Dl 1669 6185 749 5238 Dl (4)1116 6466 w 2735 5238 749 5238 Dl 2736 6120 2736 5238 Dl 2735 6120 2677 6127 Dl 2677 6128 2217 6165 Dl 2216 6165 2116 6171 Dl 2115 6172 2009 6177 Dl 2009 6178 1973 6179 Dl (5)1915 5674 w 2735 7254 1646 7254 Dl 2736 6717 2736 7254 Dl 2735 6716 1879 6255 Dl (7)2119 6859 w 2736 6612 2736 6716 Dl 2735 6611 1928 6227 Dl (8)2340 6496 w 2736 6526 2736 6611 Dl 2735 6526 1962 6197 Dl 5 R f (9)2369 6419 w 10 R f 0.1 setlinewidth 2736 6456 2736 6526 Dl 2735 6455 2009 6177 Dl 5 R f (10)2369 6363 w 10 R f 0.1 setlinewidth 2736 6382 2736 6456 Dl 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6516 w 10 R f 0.1 setlinewidth 5040 6590 5040 6662 Dl 5039 6588 4191 6212 Dl 5 R f (9)4654 6461 w 10 R f 0.1 setlinewidth 5040 6530 5040 6589 Dl 5039 6529 4224 6199 Dl 5 R f (10)4649 6414 w 10 R f 0.1 setlinewidth 5040 6467 5040 6529 Dl 5039 6466 4294 6195 Dl 5 R f (11)4669 6375 w 10 R f 0.1 setlinewidth 5040 6418 5040 6467 Dl 5039 6417 4359 6192 Dl 5 R f (12)4694 6340 w 10 R f 0.1 setlinewidth 5040 6416 5040 6303 Dl 5039 6303 4632 6171 Dl 5 R f (13)4738 6284 w 10 R f 0.1 setlinewidth 5040 6302 5040 6114 Dl 5 R f (54)4878 6207 w 20 R f 16 setlinewidth 5040 7254 3024 7254 Dl 5040 5238 5040 7254 Dl 3024 5238 5040 5238 Dl 3024 7254 3024 5238 Dl 4708 6139 4032 6246 Dl 4708 6140 4640 6168 Dl 4708 6138 4634 6132 Dl 10 B f (Fig. 104:)1 372 1 1055 7452 t 10 R f (pr. proj. it. 7,)3 525 1 1452 7452 t 10 I f (v)2002 7452 w 10 R f (=)2071 7452 w 10 I f (center)2152 7452 w 10 B f (Fig. 105:)1 372 1 3186 7452 t 10 R f (pr. proj. it. 7,)3 525 1 3583 7452 t 10 I f (v)4133 7452 w 10 R f (=)4202 7452 w 10 I f (center)4283 7452 w 10 S f (+)4532 7452 w 10 R f (\(.1,0,0\))4587 7452 w (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 30 31 %%Page: 31 32 /saveobj save def mark 32 pagesetup 10 R f (- 31 -)2 216 1 2772 282 t 0.1 setlinewidth 1796 1427 1788 1453 Dl 1788 1454 1766 1498 Dl 1765 1498 1735 1539 Dl 1735 1539 1612 1636 Dl 1796 1427 1627 1433 Dl 1627 1433 1612 1636 Dl 5 R f (2)1676 1514 w 10 R f 0.1 setlinewidth 1500 2502 720 2502 Dl 720 885 720 2502 Dl 1611 1637 1500 2502 Dl 1627 1432 720 884 Dl (4)1093 1822 w 2736 486 720 486 Dl 2736 1190 2736 486 Dl 720 486 720 884 Dl 2735 1191 2154 1373 Dl 2154 1374 1923 1412 Dl 1923 1413 1872 1419 Dl 1871 1419 1816 1424 Dl 1815 1425 1797 1427 Dl (5)1769 907 w 2239 2502 1500 2502 Dl 2239 2501 1735 1539 Dl (7)1775 2167 w 2372 2502 2239 2502 Dl 2373 2501 1766 1498 Dl (8)2044 2100 w 2510 2502 2374 2502 Dl 2510 2501 1788 1453 Dl (9)2135 2086 w 2647 2502 2510 2502 Dl 2648 2501 1816 1424 Dl (10)2202 2074 w 2735 2502 2648 2502 Dl 2736 2400 2736 2502 Dl 2736 2399 1872 1419 Dl (11)2298 2054 w 2736 2235 2736 2399 Dl 2735 2234 1923 1412 Dl (12)2328 1954 w 2736 2235 2736 1913 Dl 2735 1913 2154 1373 Dl (13)2345 1770 w 2736 1912 2736 1190 Dl (54)2492 1512 w 20 R f 16 setlinewidth 2736 2502 720 2502 Dl 2736 486 2736 2502 Dl 720 486 2736 486 Dl 720 2502 720 486 Dl 10 R f 0.1 setlinewidth 4076 1450 4071 1467 Dl 4071 1467 4057 1496 Dl 4057 1497 4037 1523 Dl 4036 1524 3957 1586 Dl 4076 1450 3966 1454 Dl 3966 1455 3957 1586 Dl 3851 2502 3530 2502 Dl 3535 1195 3530 2502 Dl 3956 1587 3851 2502 Dl 3966 1453 3536 1194 Dl (4)3693 1899 w 5040 1177 5040 1139 Dl 5039 1138 4461 1130 Dl 4460 1130 4173 1141 Dl 4173 1142 3536 1194 Dl 5039 1178 4293 1420 Dl 4292 1421 4158 1441 Dl 4158 1442 4125 1445 Dl 4125 1445 4089 1448 Dl 4089 1449 4077 1450 Dl (5)4228 1281 w 4551 2502 3851 2502 Dl 4552 2501 4037 1523 Dl (7)4104 2169 w 4659 2502 4552 2502 Dl 4659 2501 4057 1496 Dl (8)4349 2110 w 4767 2502 4659 2502 Dl 4767 2501 4071 1467 Dl (9)4421 2102 w 4876 2502 4768 2502 Dl 4875 2501 4089 1448 Dl (10)4468 2095 w 5012 2502 4876 2502 Dl 5012 2501 4125 1445 Dl (11)4554 2092 w 5039 2502 5013 2502 Dl 5040 2392 5040 2502 Dl 5039 2390 4158 1441 Dl (12)4621 2064 w 5040 2390 5040 2203 Dl 5039 2202 4293 1420 Dl (13)4591 1895 w 5040 2202 5040 1177 Dl (54)4740 1620 w 20 R f 16 setlinewidth 5040 2502 3024 2502 Dl 5040 486 5040 2502 Dl 3024 486 5040 486 Dl 3024 2502 3024 486 Dl 4471 1553 4032 1494 Dl 4470 1552 4397 1560 Dl 4471 1552 4402 1525 Dl 10 B f (Fig. 106:)1 372 1 1055 2700 t 10 R f (pr. proj. it. 8,)3 525 1 1452 2700 t 10 I f (v)2002 2700 w 10 R f (=)2071 2700 w 10 I f (center)2152 2700 w 10 B f (Fig. 107:)1 372 1 3186 2700 t 10 R f (pr. proj. it. 8,)3 525 1 3583 2700 t 10 I f (v)4133 2700 w 10 R f (=)4202 2700 w 10 I f (center)4283 2700 w 10 S f (+)4532 2700 w 10 R f (\(.1,0,0\))4587 2700 w 0.1 setlinewidth 1729 3834 1720 3846 Dl 1719 3846 1699 3866 Dl 1699 3867 1675 3885 Dl 1675 3886 1588 3930 Dl 1729 3834 1631 3837 Dl 1631 3838 1588 3930 Dl 720 4878 1028 4878 Dl 720 3531 720 4878 Dl 1588 3931 1028 4878 Dl 1631 3836 720 3530 Dl (4)1022 4195 w 2736 2862 720 2862 Dl 2736 3474 2736 2862 Dl 720 2862 720 3530 Dl 2735 3475 1918 3804 Dl 1917 3804 1799 3825 Dl 1799 3826 1771 3829 Dl 1770 3829 1740 3832 Dl 1740 3834 1730 3834 Dl (5)1692 3301 w 1874 4878 1028 4878 Dl 1874 4877 1675 3885 Dl (7)1494 4546 w 2001 4878 1874 4878 Dl 2001 4877 1699 3866 Dl (8)1814 4501 w 2130 4878 2002 4878 Dl 2131 4877 1720 3846 Dl (9)1902 4496 w 2260 4878 2131 4878 Dl 2259 4877 1740 3832 Dl (10)1964 4492 w 2424 4878 2260 4878 Dl 2425 4877 1771 3829 Dl (11)2065 4491 w 2583 4878 2426 4878 Dl 2583 4877 1799 3825 Dl (12)2176 4491 w 2735 4878 2583 4878 Dl 2736 4776 2736 4878 Dl 2735 4775 1918 3804 Dl (13)2259 4404 w 2736 4774 2736 3474 Dl (54)2413 4038 w 20 R f 16 setlinewidth 2736 4878 720 4878 Dl 2736 2862 2736 4878 Dl 720 2862 2736 2862 Dl 720 4878 720 2862 Dl 10 R f 0.1 setlinewidth 4033 3844 4026 3852 Dl 4026 3852 4011 3867 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4878 Dl 3024 2862 5040 2862 Dl 3024 4878 3024 2862 Dl 4528 4104 4032 3870 Dl 4527 4103 4455 4089 Dl 4528 4103 4471 4057 Dl 10 B f (Fig. 108:)1 372 1 1055 5076 t 10 R f (pr. proj. it. 9,)3 525 1 1452 5076 t 10 I f (v)2002 5076 w 10 R f (=)2071 5076 w 10 I f (center)2152 5076 w 10 B f (Fig. 109:)1 372 1 3186 5076 t 10 R f (pr. proj. it. 9,)3 525 1 3583 5076 t 10 I f (v)4133 5076 w 10 R f (=)4202 5076 w 10 I f (center)4283 5076 w 10 S f (+)4532 5076 w 10 R f (\(.1,0,0\))4587 5076 w 0.1 setlinewidth 1703 6222 1693 6227 Dl 1692 6227 1673 6235 Dl 1673 6236 1651 6243 Dl 1650 6243 1579 6261 Dl 1703 6223 1630 6225 Dl 1629 6225 1579 6261 Dl 720 6034 720 6748 Dl 1579 6261 720 6748 Dl 1630 6224 720 6033 Dl (4)1001 6356 w 2736 5238 720 5238 Dl 2736 5729 2736 5238 Dl 720 5238 720 6033 Dl 2735 5729 1833 6202 Dl 1833 6202 1752 6217 Dl 1751 6217 1732 6219 Dl 1731 6219 1710 6221 Dl 1710 6222 1703 6222 Dl (5)1642 5682 w 720 7048 720 6748 Dl 1321 7206 720 7048 Dl 1650 6244 1321 7207 Dl (7)1147 6798 w 1508 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5039 5703 3643 5786 Dl 3643 5787 3304 5866 Dl 3304 5866 3024 6002 Dl 5039 5717 4111 6212 Dl 4111 6213 4050 6223 Dl 4050 6223 4035 6225 Dl 4035 6226 4019 6227 Dl 4017 6228 4012 6228 Dl (5)3955 5969 w 3294 6766 3161 6691 Dl 3770 6862 3294 6767 Dl 3971 6244 3771 6862 Dl (7)3600 6622 w 3891 6893 3804 6893 Dl 3803 6892 3771 6862 Dl 3989 6238 3892 6892 Dl 5 R f (8)3873 6659 w 10 R f 0.1 setlinewidth 4025 6928 3940 6914 Dl 3940 6913 3892 6892 Dl 4026 6928 4005 6231 Dl 5 R f (9)3960 6675 w 10 R f 0.1 setlinewidth 4172 6956 4102 6974 Dl 4101 6974 4026 6929 Dl 4173 6956 4019 6227 Dl 5 R f (10)4044 6703 w 10 R f 0.1 setlinewidth 4371 6982 4307 7003 Dl 4307 7002 4173 6955 Dl 4371 6981 4035 6225 Dl (11)4137 6731 w 4594 7041 4471 7043 Dl 4472 7042 4372 6981 Dl 4595 7040 4050 6223 Dl (12)4282 6762 w 4658 6879 4111 6212 Dl 4843 7149 4691 7125 Dl 4690 7125 4660 7102 Dl 4848 7144 4660 6880 Dl 4848 7145 4843 7150 Dl 4659 7101 4595 7040 Dl (13)4421 6762 w 3490 6934 3294 6767 Dl 3760 7027 3491 6935 Dl 3803 6894 3760 7027 Dl 5 R f (14)3570 6903 w 10 R f 0.1 setlinewidth 3900 7091 3785 7066 Dl 3784 7065 3760 7027 Dl 3919 7081 3900 7092 Dl 3940 6914 3920 7080 Dl 5 R f (15)3830 6999 w 10 R f 0.1 setlinewidth 4112 7081 3920 7080 Dl 4113 7082 4102 6974 Dl 5 R f (16)3988 7019 w 10 R f 0.1 setlinewidth 4207 7169 4150 7145 Dl 4330 7067 4208 7169 Dl 4150 7143 4113 7081 Dl 4330 7066 4307 7003 Dl 5 R f (17)4181 7064 w 10 R f 0.1 setlinewidth 4523 7139 4484 7168 Dl 4483 7168 4330 7067 Dl 4522 7138 4471 7043 Dl 5 R f (18)4391 7079 w 10 R f 0.1 setlinewidth 4612 7201 4523 7138 Dl 4660 7102 4613 7202 Dl 5 R f (19)4549 7115 w 10 R f 0.1 setlinewidth 4857 7152 4857 7158 Dl 4855 7157 4843 7150 Dl 4855 7151 4849 7144 Dl 4887 7169 4880 7151 Dl 4801 7041 4660 6880 Dl 4886 7169 4856 7151 Dl 4879 7150 4801 7041 Dl 4149 7186 4146 7191 Dl 4146 7190 3964 7152 Dl 3963 7152 3900 7092 Dl 4150 7145 4150 7186 Dl 5 R f (22)4017 7136 w 10 R f 0.1 setlinewidth 4513 7254 4297 7254 Dl 4297 7253 4215 7187 Dl 4513 7253 4484 7168 Dl 4215 7187 4208 7169 Dl 5 R f (23)4334 7189 w 10 R f 0.1 setlinewidth 4780 7254 4670 7254 Dl 4670 7253 4638 7236 Dl 4781 7253 4691 7125 Dl 4637 7236 4613 7202 Dl 4214 7187 4150 7186 Dl 4633 7254 4513 7254 Dl 4636 7237 4634 7254 Dl 4894 7254 4781 7254 Dl 4878 7202 4857 7158 Dl 4879 7203 4894 7254 Dl 3740 7199 3597 7158 Dl 3596 7158 3491 6935 Dl 3784 7067 3740 7200 Dl 5 R f (28)3626 7081 w 10 R f 0.1 setlinewidth 3953 7254 3761 7254 Dl 3760 7254 3740 7200 Dl 3963 7153 3954 7254 Dl 5 R f (29)3827 7183 w 10 R f 0.1 setlinewidth 4152 7254 3954 7254 Dl 4153 7253 4146 7191 Dl 4297 7254 4153 7254 Dl 4670 7254 4634 7254 Dl 4893 7142 4856 7099 Dl 4893 7144 4880 7151 Dl 4856 7098 4801 7041 Dl 4917 7254 4894 7254 Dl 4916 7253 4878 7202 Dl 3024 7150 3024 6752 Dl 3048 7176 3024 7151 Dl 3542 7252 3048 7176 Dl 3597 7159 3543 7253 Dl (45)3219 7020 w 3761 7254 3543 7254 Dl 3543 7253 1 1 De 4944 7254 4917 7254 Dl 4944 7253 4926 7214 Dl 4924 7213 4886 7169 Dl 5040 7055 5040 5716 Dl 4857 7099 5040 7056 Dl (54)4671 6413 w 3543 7254 3114 7254 Dl 3113 7253 3048 7176 Dl 5 R f (62)3212 7238 w 10 R f 0.1 setlinewidth 4954 7201 4926 7214 Dl 4954 7200 4893 7143 Dl 5040 7247 5040 7056 Dl 5035 7250 5040 7248 Dl 5034 7249 4955 7201 Dl 5 R f (74)4950 7150 w 10 R f 0.1 setlinewidth 5034 7254 4944 7254 Dl 5034 7251 5034 7254 Dl 3114 7254 3024 7254 Dl 3024 7253 3024 7151 Dl 5035 7254 5040 7254 Dl 5040 7253 5040 7248 Dl 20 R f 16 setlinewidth 5040 7254 3024 7254 Dl 5040 5238 5040 7254 Dl 3024 5238 5040 5238 Dl 3024 7254 3024 5238 Dl 4176 6765 4032 6246 Dl 4175 6765 4139 6701 Dl 4175 6765 4173 6691 Dl 10 B f (Fig. 110:)1 372 1 1030 7452 t 10 R f (pr. proj. it. 10,)3 575 1 1427 7452 t 10 I f (v)2027 7452 w 10 R f (=)2096 7452 w 10 I f (center)2177 7452 w 10 B f (Fig. 111:)1 372 1 3161 7452 t 10 R f (pr. proj. it. 10,)3 575 1 3558 7452 t 10 I f (v)4158 7452 w 10 R f (=)4227 7452 w 10 I f (center)4308 7452 w 10 S f (+)4557 7452 w 10 R f (\(.1,0,0\))4612 7452 w (January 30, 1987)2 685 1 2537 7680 t 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4471 4247 4456 4254 Dl 4477 4184 4471 4246 Dl 4455 4254 4343 4256 Dl 4591 4128 4590 4136 Dl 4591 4127 4588 4123 Dl 4574 4030 4541 4017 Dl 4564 4046 4574 4031 Dl 4540 4015 4494 4003 Dl 3733 4360 3689 4342 Dl 3843 4383 3733 4361 Dl 3696 4332 3689 4342 Dl 3867 4332 3843 4383 Dl 3959 4381 3844 4399 Dl 3843 4398 3843 4383 Dl 3973 4316 3960 4380 Dl 4026 4458 3969 4402 Dl 4079 4379 4026 4458 Dl 3968 4400 3960 4380 Dl 4078 4337 4080 4379 Dl 4221 4390 4170 4395 Dl 4169 4395 4080 4379 Dl 4221 4389 4196 4318 Dl 4361 4339 4239 4403 Dl 4239 4402 4222 4389 Dl 4354 4314 4361 4339 Dl 4353 4314 4334 4289 Dl 4470 4303 4467 4313 Dl 4456 4254 4471 4302 Dl 4466 4314 4353 4314 Dl 4601 4291 4592 4293 Dl 4551 4204 4602 4290 Dl 4550 4203 4542 4196 Dl 4592 4292 4471 4246 Dl 4541 4196 4498 4172 Dl 4650 4184 4589 4146 Dl 4650 4184 4542 4196 Dl 4649 4125 4592 4127 Dl 4649 4124 4566 4084 Dl 3217 4302 3133 4188 Dl 3535 4317 3217 4302 Dl 3600 4272 3536 4318 Dl (45)3336 4241 w 3600 4420 3585 4421 Dl 3584 4420 3536 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1859 1404 Dl 1849 1394 1837 1384 Dl 1810 1842 1776 1827 Dl 1776 1827 1737 1745 Dl 1811 1842 1801 1778 Dl 1835 1893 1812 1842 Dl 1863 1869 1835 1894 Dl 1862 1868 1839 1789 Dl 1910 1856 1888 1888 Dl 1888 1887 1863 1869 Dl 1910 1855 1872 1771 Dl 1960 1804 1956 1863 Dl 1955 1862 1914 1859 Dl 1913 1859 1911 1856 Dl 1959 1802 1933 1766 Dl 1983 1714 1958 1673 Dl 1982 1714 1976 1807 Dl 1975 1807 1960 1803 Dl 1957 1673 1948 1666 Dl 1964 1603 1958 1585 Dl 1958 1584 1905 1519 Dl 1957 1673 1964 1604 Dl 1850 1394 1841 1385 Dl 1840 1384 1837 1384 Dl 1743 1311 1738 1322 Dl 1767 1335 1744 1310 Dl 1738 1343 1738 1322 Dl 1856 1924 1836 1905 Dl 1905 1948 1857 1923 Dl 1837 1904 1835 1894 Dl 1905 1949 1888 1888 Dl 1944 1939 1914 1969 Dl 1914 1968 1906 1949 Dl 1944 1938 1914 1859 Dl 2024 2046 1961 1965 Dl 2025 2046 1985 1917 Dl 1960 1965 1945 1938 Dl 1984 1917 1956 1863 Dl 2039 1895 2026 1917 Dl 2026 1917 1985 1917 Dl 2039 1894 1976 1807 Dl 2058 1908 2031 1761 Dl 2058 1909 2040 1895 Dl 2030 1761 2007 1734 Dl 2005 1733 1982 1714 Dl 2019 1661 2009 1646 Dl 2007 1646 1964 1604 Dl 2019 1662 2007 1734 Dl 2003 1541 2000 1530 Dl 2000 1530 1917 1485 Dl 1917 1485 1912 1485 Dl 2004 1542 1958 1585 Dl 1911 1486 1895 1496 Dl 1882 1386 1859 1404 Dl 1911 1485 1883 1385 Dl 1841 1384 1823 1334 Dl 1822 1335 1805 1368 Dl 1670 1814 1629 1730 Dl 1772 1864 1671 1815 Dl 1777 1827 1772 1865 Dl 1835 1983 1830 1983 Dl 1830 1983 1772 1865 Dl 1837 1905 1837 1984 Dl 1928 2020 1857 1923 Dl 1928 2022 1914 1969 Dl 1960 1965 1929 2025 Dl 1929 2025 1928 2022 Dl 2026 1918 2039 2075 Dl 2039 2074 2024 2046 Dl 2173 1843 2149 1774 Dl 2148 1773 2018 1661 Dl 2174 1842 2031 1761 Dl 2022 1574 2004 1542 Dl 2010 1645 2023 1573 Dl 1926 1398 1898 1357 Dl 1898 1358 1883 1385 Dl 1918 1484 1928 1398 Dl 1809 1323 1779 1323 Dl 1822 1331 1811 1324 Dl 1779 1341 1779 1323 Dl 1823 1334 1823 1332 Dl 1183 765 1203 882 Dl 1737 1322 1182 765 Dl (54)1426 1145 w 1884 2058 1837 1984 Dl 1933 2043 1884 2059 Dl 1933 2042 1929 2025 Dl 2080 2166 2050 2202 Dl 2049 2201 1933 2042 Dl 2080 2166 2039 2075 Dl 2141 2201 2080 2166 Dl 2110 1980 2142 2201 Dl 2109 1978 2058 1909 Dl 5 R f (57)2055 2059 w 10 R f 0.1 setlinewidth 2230 1947 2174 1843 Dl 2229 1949 2109 1980 Dl 5 R f (58)2096 1894 w 10 R f 0.1 setlinewidth 2149 1773 2143 1745 Dl 2143 1743 2023 1573 Dl 2000 1480 1928 1398 Dl 2000 1529 2000 1480 Dl 1880 1308 1823 1332 Dl 1898 1356 1880 1307 Dl 1719 1938 1671 1815 Dl 1791 2022 1719 1938 Dl 1831 1984 1791 2023 Dl 2050 2202 2050 2214 Dl 2050 2214 1928 2214 Dl 1927 2213 1884 2059 Dl 2321 2066 2230 1948 Dl 2321 2066 2239 2338 Dl 2239 2337 2142 2201 Dl 5 R f (64)2187 2123 w 10 R f 0.1 setlinewidth 2218 1496 2171 1479 Dl 2170 1480 2000 1480 Dl 2144 1744 2219 1496 Dl 5 R f (65)2087 1582 w 10 R f 0.1 setlinewidth 1778 1323 1730 1272 Dl 1743 1310 1730 1272 Dl 1928 2280 1838 2180 Dl 1837 2179 1791 2023 Dl 1928 2214 1928 2280 Dl 5 R f (67)1838 2131 w 10 R f 0.1 setlinewidth 2118 2502 2082 2502 Dl 2081 2501 1989 2453 Dl 1989 2453 1928 2280 Dl 2051 2215 2117 2502 Dl 5 R f (68)1995 2357 w 10 R f 0.1 setlinewidth 2316 2502 2117 2502 Dl 2317 2501 2239 2338 Dl 5 R f (69)2140 2373 w 10 R f 0.1 setlinewidth 2735 2502 2317 2502 Dl 2736 2461 2736 2502 Dl 2736 2460 2322 2065 Dl (70)2393 2367 w 2736 2461 2736 1959 Dl 2450 1486 2219 1496 Dl 2735 1959 2450 1486 Dl (71)2413 1923 w 2171 1479 1877 1280 Dl 1880 1307 1877 1280 Dl 5 R f (72)1977 1417 w 10 R f 0.1 setlinewidth 1876 1279 1864 1254 Dl 1864 1255 1811 1324 Dl 1179 744 1182 765 Dl 1672 1189 1179 743 Dl 1730 1272 1671 1190 Dl 5 R f (74)1481 1076 w 10 R f 0.1 setlinewidth 1789 2297 1730 2131 Dl 1729 2130 1719 1938 Dl 1836 2180 1788 2298 Dl 5 R f (75)1749 2129 w 10 R f 0.1 setlinewidth 2736 1958 2736 1570 Dl 2451 1486 2736 1570 Dl 5 R f (77)2615 1681 w 10 R f 0.1 setlinewidth 1855 1234 1671 1190 Dl 1863 1254 1856 1234 Dl 1979 2502 1821 2502 Dl 1821 2501 1788 2298 Dl 1989 2454 1980 2502 Dl 5 R f (79)1855 2381 w 10 R f 0.1 setlinewidth 2082 2502 1980 2502 Dl 1856 1234 1822 1061 Dl 2449 1485 1822 1061 Dl (82)2039 1343 w 1634 2041 1614 1717 Dl 1729 2131 1634 2041 Dl 5 R f (83)1644 1951 w 10 R f 0.1 setlinewidth 1821 2502 1688 2502 Dl 1624 2443 1588 2168 Dl 1634 2042 1588 2168 Dl 1688 2501 1625 2443 Dl (84)1645 2322 w 1687 2502 1603 2502 Dl 1623 2444 1603 2502 Dl 2735 486 1254 486 Dl 2736 1570 2736 486 Dl 1821 1061 1254 486 Dl (87)2157 909 w 1254 486 1126 486 Dl 1127 486 1179 743 Dl (88)1425 878 w 1587 2168 1256 1106 Dl (89)1446 1705 w 1603 2502 1356 2502 Dl 1355 2501 1227 1044 Dl (90)1364 2005 w 720 486 1126 486 Dl 720 2502 1356 2502 Dl 720 2502 720 486 Dl (91)943 1578 w 20 R f 16 setlinewidth 2736 2502 720 2502 Dl 2736 486 2736 2502 Dl 720 486 2736 486 Dl 720 2502 720 486 Dl 10 R f 0.1 setlinewidth 3986 1456 3986 1454 Dl 3987 1459 3987 1456 Dl 3987 1460 3987 1463 Dl 3987 1463 3985 1473 Dl 3986 1454 3981 1459 Dl 3985 1472 3981 1459 Dl 3933 1684 3693 1265 Dl 3946 1697 3934 1686 Dl 3987 1659 3947 1697 Dl 3986 1658 3985 1473 Dl 3980 1458 3693 1265 Dl 5 R f (4)3871 1499 w 10 R f 0.1 setlinewidth 3602 1108 3582 969 Dl 3628 1161 3603 1109 Dl 3693 1265 3628 1162 Dl 3972 1421 3582 969 Dl 3984 1445 3973 1422 Dl 3986 1449 3985 1445 Dl 3985 1452 3985 1449 Dl 3986 1453 3986 1452 Dl 5 R f (5)3739 1236 w 10 R f 0.1 setlinewidth 4005 1671 3987 1659 Dl 4062 1663 4005 1672 Dl 4061 1662 3987 1463 Dl 4077 1659 4070 1671 Dl 4070 1670 4062 1663 Dl 4077 1658 3987 1460 Dl 4094 1648 4086 1658 Dl 4085 1658 4078 1658 Dl 4094 1647 3987 1456 Dl 4107 1649 4106 1624 Dl 4107 1650 4094 1648 Dl 4106 1623 3986 1452 Dl 4119 1603 4113 1573 Dl 4118 1604 4106 1624 Dl 4111 1572 3985 1449 Dl 4123 1559 4111 1501 Dl 4125 1560 4113 1573 Dl 4111 1501 3985 1445 Dl 4027 1392 3973 1422 Dl 4126 1485 4088 1391 Dl 4125 1486 4123 1493 Dl 4082 1385 4027 1391 Dl 4088 1390 4083 1383 Dl 4122 1494 4111 1501 Dl 4040 1709 4005 1672 Dl 4086 1725 4040 1710 Dl 4085 1725 4070 1671 Dl 4111 1733 4095 1738 Dl 4094 1737 4086 1725 Dl 4111 1726 4111 1733 Dl 4111 1725 4086 1658 Dl 4129 1691 4111 1725 Dl 4130 1690 4108 1649 Dl 4155 1706 4147 1710 Dl 4154 1705 4134 1622 Dl 4145 1709 4130 1691 Dl 4134 1621 4119 1603 Dl 4160 1607 4150 1577 Dl 4159 1609 4134 1622 Dl 4149 1576 4124 1558 Dl 4163 1562 4150 1577 Dl 4163 1562 4123 1493 Dl 4085 1384 4083 1382 Dl 4086 1390 4086 1385 Dl 4084 1382 4083 1383 Dl 4075 1363 4066 1358 Dl 4040 1366 4027 1391 Dl 4082 1381 4075 1363 Dl 4066 1360 4041 1365 Dl 4155 1731 4155 1728 Dl 4155 1733 4127 1748 Dl 4126 1747 4111 1733 Dl 4155 1728 4147 1710 Dl 4207 1725 4196 1647 Dl 4206 1725 4160 1712 Dl 4195 1646 4160 1608 Dl 4159 1711 4155 1705 Dl 4173 1495 4165 1486 Dl 4181 1515 4174 1495 Dl 4181 1516 4173 1566 Dl 4165 1485 4126 1485 Dl 4174 1566 4164 1563 Dl 4159 1712 4155 1728 Dl 4217 1639 4173 1566 Dl 4219 1640 4196 1647 Dl 4142 1416 4135 1409 Dl 4097 1387 4086 1385 Dl 4124 1400 4098 1386 Dl 4165 1485 4143 1417 Dl 4134 1409 4124 1401 Dl 4103 1791 4074 1779 Dl 4073 1779 4040 1710 Dl 4103 1792 4095 1738 Dl 4123 1834 4104 1792 Dl 4147 1815 4123 1835 Dl 4146 1814 4127 1748 Dl 4187 1802 4168 1829 Dl 4167 1829 4147 1814 Dl 4186 1801 4155 1732 Dl 4227 1756 4224 1805 Dl 4224 1805 4190 1804 Dl 4190 1804 4188 1802 Dl 4227 1755 4206 1725 Dl 4246 1678 4226 1645 Dl 4246 1679 4241 1758 Dl 4240 1758 4228 1756 Dl 4225 1644 4218 1639 Dl 4231 1586 4226 1571 Dl 4225 1570 4182 1515 Dl 4226 1645 4231 1586 Dl 4134 1408 4127 1401 Dl 4126 1401 4124 1401 Dl 4045 1338 4041 1347 Dl 4065 1358 4045 1337 Dl 4041 1365 4041 1347 Dl 4141 1858 4124 1843 Dl 4182 1878 4142 1859 Dl 4124 1843 4123 1835 Dl 4181 1878 4168 1829 Dl 4213 1869 4188 1894 Dl 4188 1894 4182 1879 Dl 4215 1868 4190 1804 Dl 4276 1950 4227 1889 Dl 4277 1950 4247 1848 Dl 4227 1889 4215 1868 Dl 4246 1848 4224 1805 Dl 4290 1827 4280 1846 Dl 4280 1846 4247 1848 Dl 4290 1826 4241 1758 Dl 4304 1837 4284 1717 Dl 4304 1837 4291 1827 Dl 4284 1715 4266 1694 Dl 4264 1694 4246 1679 Dl 4273 1633 4266 1621 Dl 4266 1620 4231 1586 Dl 4274 1633 4266 1694 Dl 4260 1533 4258 1524 Dl 4257 1523 4191 1486 Dl 4191 1486 4187 1486 Dl 4260 1534 4226 1571 Dl 4186 1487 4174 1495 Dl 4161 1402 4143 1417 Dl 4187 1486 4162 1402 Dl 4127 1401 4112 1359 Dl 4111 1359 4098 1386 Dl 3983 1768 3947 1697 Dl 4069 1811 3983 1769 Dl 4074 1780 4070 1811 Dl 4124 1907 4119 1907 Dl 4118 1907 4070 1811 Dl 4124 1844 4124 1908 Dl 4200 1936 4142 1859 Dl 4198 1936 4188 1894 Dl 4227 1889 4201 1938 Dl 4200 1938 4200 1936 Dl 4281 1847 4289 1973 Dl 4288 1972 4277 1951 Dl 4389 1774 4371 1719 Dl 4370 1719 4273 1633 Dl 4390 1774 4284 1717 Dl 4274 1559 4260 1533 Dl 4266 1621 4275 1560 Dl 4197 1414 4174 1380 Dl 4173 1380 4162 1402 Dl 4192 1486 4198 1414 Dl 4101 1349 4076 1348 Dl 4111 1356 4102 1350 Dl 4076 1363 4076 1348 Dl 4111 1359 4111 1357 Dl 3571 877 3582 969 Dl 4041 1346 3571 877 Dl 5 R f (54)3793 1190 w 10 R f 0.1 setlinewidth 4162 1966 4124 1908 Dl 4204 1953 4163 1967 Dl 4204 1951 4201 1938 Dl 4318 2042 4294 2071 Dl 4294 2070 4204 1952 Dl 4319 2042 4289 1973 Dl 4364 2062 4319 2041 Dl 4345 1891 4365 2063 Dl 4343 1891 4305 1838 Dl 4429 1853 4390 1774 Dl 4429 1854 4343 1891 Dl 4371 1719 4366 1696 Dl 4366 1696 4275 1560 Dl 4256 1482 4198 1414 Dl 4257 1524 4256 1483 Dl 4157 1339 4111 1357 Dl 4173 1380 4158 1339 Dl 4024 1869 3983 1769 Dl 4084 1937 4024 1869 Dl 4118 1908 4085 1938 Dl 4294 2071 4294 2080 Dl 4294 2081 4196 2084 Dl 4196 2084 4163 1967 Dl 4489 1935 4430 1854 Dl 4490 1936 4431 2154 Dl 4431 2153 4365 2063 Dl 5 R f (64)4389 1993 w 10 R f 0.1 setlinewidth 4404 1495 4374 1483 Dl 4374 1483 4256 1483 Dl 4367 1696 4405 1496 Dl 5 R f (65)4311 1567 w 10 R f 0.1 setlinewidth 4075 1347 4034 1304 Dl 4045 1336 4034 1304 Dl 4194 2131 4122 2057 Dl 4122 2057 4085 1938 Dl 4195 2084 4194 2132 Dl 4338 2293 4238 2252 Dl 4237 2252 4194 2132 Dl 4295 2081 4339 2294 Dl 5 R f (68)4240 2185 w 10 R f 0.1 setlinewidth 4573 2502 4492 2502 Dl 4576 2472 4574 2502 Dl 4492 2501 4339 2294 Dl 4575 2471 4431 2154 Dl 5 R f (69)4399 2293 w 10 R f 0.1 setlinewidth 4961 2384 4576 2471 Dl 4959 2383 4489 1935 Dl (70)4592 2268 w 4532 1489 4405 1496 Dl 4961 2384 4994 2401 Dl 4994 2400 4533 1488 Dl (71)4565 1893 w 4374 1481 4155 1316 Dl 4158 1337 4155 1316 Dl 4154 1316 4144 1296 Dl 4144 1296 4102 1350 Dl 3569 861 3571 877 Dl 3984 1236 3569 861 Dl 4033 1304 3984 1236 Dl 5 R f (74)3820 1142 w 10 R f 0.1 setlinewidth 4079 2138 4033 2016 Dl 4033 2015 4024 1869 Dl 4121 2059 4080 2139 Dl 4299 2502 4186 2502 Dl 4185 2501 4155 2424 Dl 4299 2501 4206 2356 Dl 4206 2357 4155 2424 Dl 5040 2448 5040 1717 Dl 4534 1489 5040 1717 Dl 4995 2401 5040 2448 Dl (77)4820 1915 w 4137 1280 3984 1236 Dl 4143 1295 4137 1280 Dl 4155 2422 4120 2365 Dl 4119 2366 4080 2139 Dl 4237 2253 4206 2356 Dl 5 R f (79)4131 2247 w 10 R f 0.1 setlinewidth 4491 2502 4300 2502 Dl 5 R f (80)4303 2406 w 10 R f 0.1 setlinewidth 5039 2502 4574 2502 Dl 5040 2449 5040 2502 Dl 5 R f (81)4819 2469 w 10 R f 0.1 setlinewidth 4136 1280 4106 1149 Dl 4532 1487 4106 1149 Dl 5 R f (82)4269 1365 w 10 R f 0.1 setlinewidth 3955 1941 3934 1686 Dl 4032 2015 3955 1941 Dl 3954 2207 3922 2025 Dl 3955 1942 3922 2025 Dl 4120 2365 3954 2208 Dl 5 R f (84)3989 2152 w 10 R f 0.1 setlinewidth 4186 2502 3852 2502 Dl 3851 2501 3837 2431 Dl 3953 2208 3837 2431 Dl 5 R f (85)3971 2407 w 10 R f 0.1 setlinewidth 5039 1446 4098 486 Dl 4097 486 3548 486 Dl 5040 1716 5040 1446 Dl 3547 486 3539 584 Dl 4106 1149 3539 584 Dl (87)4267 1047 w 3540 585 3569 861 Dl (88)3765 986 w 3921 2025 3628 1162 Dl 5 R f (89)3811 1650 w 10 R f 0.1 setlinewidth 3837 2430 3603 1109 Dl (90)3750 1907 w 20 R f 16 setlinewidth 5040 2502 3024 2502 Dl 5040 486 5040 2502 Dl 3024 486 5040 486 Dl 3024 2502 3024 486 Dl 4523 1176 4032 1494 Dl 4523 1175 4473 1229 Dl 4523 1176 4453 1199 Dl 10 B f (Fig. 118:)1 372 1 1030 2700 t 10 R f (pr. proj. it. 14,)3 575 1 1427 2700 t 10 I f (v)2027 2700 w 10 R f (=)2096 2700 w 10 I f (center)2177 2700 w 10 B f (Fig. 119:)1 372 1 3161 2700 t 10 R f (pr. proj. it. 14,)3 575 1 3558 2700 t 10 I f (v)4158 2700 w 10 R f (=)4227 2700 w 10 I f (center)4308 2700 w 10 S f (+)4557 2700 w 10 R f (\(.1,0,0\))4612 2700 w 0.1 setlinewidth 1609 3779 1604 3774 Dl 1616 3788 1609 3779 Dl 1624 3798 1617 3789 Dl 1642 3821 1625 3798 Dl 1609 3787 1604 3774 Dl 1642 3821 1609 3787 Dl 720 3223 720 3170 Dl 1922 4219 720 3224 Dl 1945 4233 1922 4219 Dl 1945 4235 1930 4176 Dl 1929 4174 1642 3822 Dl 1609 3787 720 3170 Dl (4)1352 3726 w 720 3170 720 3001 Dl 1516 3684 720 3001 Dl 1582 3748 1516 3684 Dl 1592 3759 1582 3749 Dl 1600 3770 1592 3760 Dl 1604 3772 1602 3770 Dl (5)1023 3360 w 1958 4194 1930 4176 Dl 1988 4179 1958 4194 Dl 1989 4177 1625 3798 Dl 2003 4187 1995 4169 Dl 2003 4187 1989 4177 Dl 1994 4169 1617 3789 Dl 2000 4169 1995 4154 Dl 2000 4169 1995 4169 Dl 1995 4154 1609 3779 Dl 2007 4157 1978 4119 Dl 2007 4156 1995 4154 Dl 1978 4118 1602 3770 Dl 1963 4088 1920 4037 Dl 1977 4119 1964 4088 Dl 1920 4035 1592 3760 Dl 1913 4013 1818 3901 Dl 1920 4036 1913 4014 Dl 1818 3900 1582 3749 Dl 1508 3608 1516 3684 Dl 1807 3871 1583 3625 Dl 1816 3887 1807 3872 Dl 1559 3603 1507 3608 Dl 1583 3625 1560 3603 Dl 1817 3901 1817 3887 Dl 5 R f (13)1608 3743 w 10 R f 0.1 setlinewidth 2022 4243 1958 4194 Dl 2068 4259 2023 4243 Dl 2068 4260 2003 4188 Dl 2090 4269 2085 4275 Dl 2086 4275 2069 4260 Dl 2092 4269 2085 4259 Dl 2084 4259 2000 4169 Dl 2083 4258 2064 4214 Dl 2065 4214 2008 4157 Dl 2094 4234 2093 4239 Dl 2095 4233 1997 4117 Dl 2092 4238 2064 4214 Dl 1996 4117 1964 4088 Dl 2001 4098 1958 4049 Dl 2002 4099 1997 4117 Dl 1957 4049 1913 4014 Dl 1957 4049 1951 4026 Dl 1951 4025 1817 3887 Dl 1567 3607 1558 3599 Dl 1582 3625 1567 3607 Dl 1560 3603 1558 3599 Dl 1499 3537 1474 3517 Dl 1507 3607 1457 3529 Dl 1557 3598 1500 3537 Dl 1473 3517 1457 3529 Dl 2118 4267 2116 4263 Dl 2119 4267 2115 4286 Dl 2115 4285 2092 4268 Dl 2115 4262 2093 4239 Dl 2146 4262 2069 4160 Dl 2147 4261 2104 4242 Dl 2068 4160 2001 4099 Dl 2103 4242 2095 4234 Dl 1869 3902 1847 3882 Dl 1905 3944 1869 3903 Dl 1962 4033 1905 3944 Dl 1846 3882 1807 3872 Dl 1963 4033 1951 4026 Dl 2115 4262 2104 4242 Dl 2079 4152 1964 4033 Dl 2078 4153 2069 4160 Dl 1704 3715 1679 3692 Dl 1585 3616 1567 3607 Dl 1649 3664 1586 3616 Dl 1847 3881 1705 3716 Dl 1679 3692 1649 3665 Dl 2137 4337 2109 4326 Dl 2108 4325 2023 4243 Dl 2136 4337 2085 4275 Dl 2180 4382 2137 4338 Dl 2180 4382 2179 4359 Dl 2179 4359 2115 4286 Dl 2201 4373 2193 4345 Dl 2202 4374 2179 4359 Dl 2192 4345 2118 4266 Dl 2217 4351 2184 4298 Dl 2217 4350 2196 4348 Dl 2196 4347 2193 4345 Dl 2184 4298 2147 4262 Dl 2135 4209 2090 4161 Dl 2194 4301 2135 4209 Dl 2194 4302 2184 4298 Dl 2090 4161 2079 4152 Dl 2034 4075 2013 4050 Dl 2012 4050 1905 3944 Dl 2090 4160 2035 4076 Dl 1679 3691 1654 3668 Dl 1654 3668 1649 3665 Dl 1406 3467 1384 3434 Dl 1474 3516 1384 3434 Dl 1456 3529 1406 3468 Dl 2208 4405 2188 4391 Dl 2242 4422 2208 4405 Dl 2187 4390 2180 4382 Dl 2243 4422 2202 4374 Dl 2255 4436 2253 4412 Dl 2255 4436 2243 4422 Dl 2252 4411 2196 4348 Dl 2332 4483 2273 4431 Dl 2333 4484 2259 4394 Dl 2272 4431 2253 4412 Dl 2259 4394 2218 4351 Dl 2276 4394 2271 4376 Dl 2276 4394 2259 4394 Dl 2270 4376 2194 4302 Dl 2285 4387 2192 4260 Dl 2285 4387 2271 4376 Dl 2192 4260 2162 4232 Dl 2160 4231 2135 4209 Dl 2115 4153 2098 4135 Dl 2098 4135 2035 4076 Dl 2161 4231 2115 4154 Dl 2000 3996 1986 3978 Dl 1986 3978 1873 3888 Dl 1872 3888 1869 3888 Dl 2012 4050 2000 3996 Dl 1869 3902 1869 3888 Dl 1704 3716 1696 3682 Dl 1868 3888 1696 3682 Dl 1655 3668 1537 3535 Dl 1586 3615 1537 3535 Dl 2044 4323 1945 4234 Dl 2132 4361 2044 4323 Dl 2132 4362 2109 4326 Dl 2231 4452 2229 4452 Dl 2228 4451 2133 4361 Dl 2231 4452 2188 4391 Dl 2286 4472 2208 4405 Dl 2286 4472 2256 4436 Dl 2288 4474 2273 4431 Dl 2289 4475 2287 4473 Dl 2348 4501 2276 4394 Dl 2349 4501 2333 4484 Dl 2300 4338 2254 4278 Dl 2253 4278 2115 4154 Dl 2300 4338 2192 4260 Dl 2043 4044 2000 3996 Dl 2098 4135 2044 4045 Dl 1760 3726 1663 3623 Dl 1696 3682 1663 3623 Dl 1873 3888 1761 3726 Dl 1499 3501 1460 3486 Dl 1530 3527 1500 3502 Dl 1499 3536 1460 3486 Dl 1535 3535 1530 3528 Dl 731 2862 720 2862 Dl 720 2862 720 3001 Dl 1405 3468 731 2862 Dl 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3748 Dl 4253 3961 4205 3895 Dl 3877 3546 3864 3579 Dl 3977 3660 3878 3546 Dl 4402 4355 4307 4263 Dl 4470 4404 4402 4356 Dl 4469 4378 4471 4405 Dl 4618 4487 4615 4482 Dl 4618 4487 4584 4494 Dl 4583 4494 4519 4420 Dl 4642 4406 4583 4343 Dl 4689 4527 4642 4406 Dl 4690 4527 4638 4477 Dl 4336 3962 4299 3932 Dl 4300 3931 4205 3895 Dl 4467 4198 4337 3962 Dl 3804 3543 3637 3389 Dl 3739 3499 3637 3389 Dl 4602 4523 4546 4485 Dl 4545 4485 4471 4405 Dl 4602 4522 4584 4494 Dl 4699 4596 4657 4583 Dl 4657 4582 4602 4523 Dl 4699 4595 4618 4487 Dl 4822 4704 4804 4661 Dl 4823 4704 4700 4597 Dl 4803 4661 4690 4528 Dl 4805 4660 4898 4648 Dl 4896 4647 4642 4406 Dl 5 R f (70)4741 4572 w 10 R f 0.1 setlinewidth 4426 3993 4337 3962 Dl 4908 4655 4898 4648 Dl 4909 4655 4426 3994 Dl 5 R f (71)4552 4272 w 10 R f 0.1 setlinewidth 4299 3932 3824 3480 Dl 3877 3546 3824 3480 Dl 3824 3480 3760 3409 Dl 3838 3558 3760 3409 Dl 3077 2862 3024 2862 Dl 3024 2862 3024 2872 Dl 3316 3078 3077 2862 Dl 3636 3389 3317 3078 Dl 5 R 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4231 6797 4218 6750 Dl 4359 6689 4358 6626 Dl 4359 6689 4255 6804 Dl 4254 6804 4231 6797 Dl 4357 6625 4347 6613 Dl 4456 6485 4446 6518 Dl 4456 6483 4427 6344 Dl 4446 6518 4358 6626 Dl 5 R f (33)4367 6497 w 10 R f 0.1 setlinewidth 4450 6024 4438 5995 Dl 4437 5994 4430 5991 Dl 4239 5719 4209 5760 Dl 4289 5813 4240 5718 Dl 4209 5760 4187 5833 Dl 3948 6912 3925 6892 Dl 4015 6940 3949 6912 Dl 3928 6882 3925 6892 Dl 4031 6881 4015 6940 Dl 4089 6934 4015 6958 Dl 4015 6940 4015 6958 Dl 4100 6855 4090 6935 Dl 4130 7032 4094 6960 Dl 4171 6919 4131 7032 Dl 4094 6960 4090 6935 Dl 4170 6919 4170 6863 Dl 4276 6904 4235 6924 Dl 4235 6924 4171 6919 Dl 4277 6903 4255 6804 Dl 4389 6758 4291 6920 Dl 4291 6919 4277 6904 Dl 4389 6757 4379 6719 Dl 4379 6719 4359 6689 Dl 4476 6597 4476 6621 Dl 4475 6596 4446 6518 Dl 4475 6622 4379 6719 Dl 4603 6394 4595 6417 Dl 4602 6393 4494 6274 Dl 4495 6273 4483 6273 Dl 4594 6418 4456 6484 Dl 4482 6274 4435 6292 Dl 5 R f (42)4475 6387 w 10 R f 0.1 setlinewidth 4547 6012 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7054 4124 7118 Dl 4176 7143 4124 7118 Dl 4303 6988 4176 7145 Dl 4303 6986 4291 6920 Dl 5 R f (57)4189 7035 w 10 R f 0.1 setlinewidth 4519 6870 4490 6973 Dl 4490 6974 4304 6987 Dl 5 R f (58)4379 6904 w 10 R f 0.1 setlinewidth 4576 6757 4556 6791 Dl 4586 6481 4577 6756 Dl 5 R f (59)4517 6643 w 10 R f 0.1 setlinewidth 4667 6292 4632 6067 Dl 4667 6293 4603 6394 Dl 5 R f (60)4570 6257 w 10 R f 0.1 setlinewidth 4654 5765 4457 5822 Dl 4654 5764 4626 5935 Dl 5 R f (61)4513 5911 w 10 R f 0.1 setlinewidth 3681 6914 3648 6783 Dl 3768 6991 3681 6914 Dl 3863 6964 3768 6993 Dl 5 R f (62)3731 6903 w 10 R f 0.1 setlinewidth 4058 7138 4050 7145 Dl 4050 7145 3879 7135 Dl 3905 7029 3879 7135 Dl 4489 6974 4487 7072 Dl 4486 7073 4194 7224 Dl 4194 7224 4176 7145 Dl 5 R f (64)4309 7090 w 10 R f 0.1 setlinewidth 4983 6405 4941 6356 Dl 4940 6356 4667 6292 Dl 4983 6407 4577 6756 Dl (65)4683 6498 w 4341 5774 4237 5564 Dl 4239 5718 4237 5564 Dl 3843 7171 3761 7107 Dl 3768 6994 3761 7107 Dl 3879 7135 3843 7171 Dl 5 R f (67)3807 7071 w 10 R f 0.1 setlinewidth 3982 7254 3836 7254 Dl 3843 7172 3836 7254 Dl 4050 7146 3983 7254 Dl 5 R f (68)3906 7204 w 10 R f 0.1 setlinewidth 4186 7254 3983 7254 Dl 4193 7225 4185 7254 Dl 5 R f (69)4076 7207 w 10 R f 0.1 setlinewidth 4534 7254 4185 7254 Dl 4534 7253 4487 7072 Dl 5 R f (70)4365 7202 w 10 R f 0.1 setlinewidth 4758 7254 4535 7254 Dl 5040 6420 5040 6816 Dl 5039 6418 4983 6406 Dl 5039 6817 4759 7254 Dl (71)4723 6888 w 4941 6356 4687 5664 Dl 4686 5664 4654 5764 Dl (72)4696 6098 w 4687 5664 4690 5559 Dl 4690 5559 4433 5791 Dl 5 R f (73)4562 5724 w 10 R f 0.1 setlinewidth 4129 5238 3892 5238 Dl 4236 5564 4129 5238 Dl (74)4054 5461 w 3631 7169 3607 7067 Dl 3681 6916 3607 7067 Dl 3760 7107 3631 7169 Dl 5 R f (75)3665 7059 w 10 R f 0.1 setlinewidth 5039 7254 4759 7254 Dl 5040 6817 5040 7254 Dl 5 R f (77)4921 7118 w 10 R f 0.1 setlinewidth 4257 5238 4129 5238 Dl 4698 5473 4258 5238 Dl 4691 5559 4698 5473 Dl (78)4354 5525 w 3834 7254 3603 7254 Dl 3631 7170 3603 7254 Dl 5 R f (79)3707 7206 w 10 R f 0.1 setlinewidth 5030 5238 4742 5238 Dl 5040 6419 5040 5289 Dl 4699 5473 4742 5238 Dl 5039 5289 5029 5238 Dl (82)4846 5743 w 3568 6653 3471 6995 Dl 3607 7066 3471 6995 Dl 5 R f (83)3557 6893 w 10 R f 0.1 setlinewidth 3604 7254 3425 7254 Dl 3347 7222 3353 7079 Dl 3471 6996 3353 7079 Dl 3424 7253 3346 7222 Dl 5 R f (84)3461 7151 w 10 R f 0.1 setlinewidth 3424 7254 3278 7254 Dl 3346 7223 3278 7254 Dl 4742 5238 4258 5238 Dl 5 R f (88)4541 5326 w 10 R f 0.1 setlinewidth 3024 6422 3024 5857 Dl 3353 7078 3024 6423 Dl (89)3218 6547 w 3278 7254 3024 7254 Dl 3024 7253 3024 6423 Dl (90)3100 6984 w 20 R f 16 setlinewidth 5040 7254 3024 7254 Dl 5040 5238 5040 7254 Dl 3024 5238 5040 5238 Dl 3024 7254 3024 5238 Dl 4639 7092 4032 6246 Dl 4638 7093 4582 7045 Dl 4639 7093 4612 7024 Dl 10 B f (Fig. 122:)1 372 1 1030 7452 t 10 R f (pr. proj. it. 16,)3 575 1 1427 7452 t 10 I f (v)2027 7452 w 10 R f (=)2096 7452 w 10 I f (center)2177 7452 w 10 B f (Fig. 123:)1 372 1 3161 7452 t 10 R f (pr. proj. it. 16,)3 575 1 3558 7452 t 10 I f (v)4158 7452 w 10 R f (=)4227 7452 w 10 I f (center)4308 7452 w 10 S f (+)4557 7452 w 10 R f (\(.1,0,0\))4612 7452 w (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 33 34 %%Page: 34 35 /saveobj save def mark 35 pagesetup 10 R f (- 34 -)2 216 1 2772 282 t 0.1 setlinewidth 1716 1479 1714 1479 Dl 1713 1480 1708 1481 Dl 1708 1481 1702 1482 Dl 1702 1483 1683 1486 Dl 1717 1479 1699 1481 Dl 1698 1481 1683 1486 Dl 1534 1408 1240 1567 Dl 1242 1571 1240 1567 Dl 1374 1557 1243 1571 Dl 1683 1486 1375 1557 Dl 1698 1480 1535 1407 Dl 5 R f (4)1471 1502 w 10 R f 0.1 setlinewidth 1827 1297 1637 1349 Dl 1637 1349 1594 1368 Dl 1594 1369 1535 1407 Dl 1826 1296 1747 1466 Dl 1747 1467 1729 1475 Dl 1729 1475 1724 1476 Dl 1724 1477 1719 1478 Dl 1719 1478 1717 1478 Dl 5 R f (5)1681 1403 w 10 R f 0.1 setlinewidth 1380 1562 1375 1557 Dl 1483 1560 1380 1562 Dl 1701 1482 1483 1559 Dl 1515 1557 1483 1562 Dl 1483 1561 1483 1559 Dl 1708 1481 1516 1557 Dl 1557 1554 1527 1557 Dl 1526 1557 1516 1557 Dl 1713 1479 1557 1553 Dl 1611 1544 1573 1554 Dl 1573 1553 1557 1553 Dl 1718 1479 1613 1545 Dl 1704 1525 1664 1537 Dl 1664 1538 1613 1545 Dl 1724 1476 1704 1524 Dl 1814 1497 1742 1519 Dl 1741 1519 1704 1524 Dl 1813 1497 1729 1475 Dl 1862 1455 1747 1466 Dl 1945 1455 1856 1491 Dl 1856 1492 1841 1494 Dl 1947 1453 1863 1455 Dl 1948 1453 1945 1455 Dl 1841 1495 1814 1497 Dl 1379 1562 1368 1577 Dl 1412 1583 1368 1577 Dl 1483 1563 1413 1584 Dl 1437 1588 1404 1589 Dl 1412 1584 1404 1589 Dl 1450 1585 1437 1587 Dl 1526 1558 1450 1584 Dl 1535 1572 1450 1584 Dl 1573 1555 1536 1571 Dl 1544 1577 1526 1578 Dl 1654 1544 1545 1577 Dl 1535 1571 1526 1578 Dl 1664 1537 1655 1544 Dl 1745 1528 1710 1540 Dl 1710 1539 1655 1544 Dl 1745 1526 1742 1519 Dl 1786 1522 1746 1527 Dl 1841 1495 1786 1522 Dl 1952 1451 1 1 De 1952 1453 1945 1455 Dl 1952 1452 1949 1452 Dl 1967 1444 1962 1442 Dl 1918 1445 1863 1455 Dl 1967 1444 1952 1451 Dl 1962 1443 1919 1445 Dl 1506 1586 1501 1587 Dl 1500 1588 1434 1593 Dl 1436 1588 1434 1593 Dl 1526 1579 1506 1586 Dl 1692 1556 1577 1586 Dl 1576 1587 1540 1580 Dl 1710 1540 1692 1555 Dl 1545 1578 1540 1580 Dl 1904 1493 1902 1496 Dl 1902 1497 1882 1504 Dl 1881 1504 1793 1523 Dl 1905 1491 1856 1491 Dl 1793 1523 1786 1522 Dl 1539 1580 1506 1586 Dl 1793 1524 1733 1553 Dl 1733 1553 1692 1555 Dl 1979 1463 1978 1465 Dl 1965 1452 1953 1452 Dl 1977 1457 1964 1452 Dl 1977 1465 1905 1492 Dl 1980 1459 1980 1462 Dl 1321 1609 1298 1604 Dl 1368 1577 1298 1604 Dl 1403 1589 1321 1610 Dl 1320 1610 1272 1627 Dl 1344 1620 1272 1627 Dl 1433 1594 1345 1620 Dl 1421 1617 1347 1627 Dl 1347 1626 1345 1620 Dl 1501 1588 1423 1616 Dl 1553 1599 1463 1619 Dl 1463 1619 1422 1617 Dl 1423 1616 1422 1617 Dl 1577 1587 1554 1599 Dl 1733 1556 1702 1570 Dl 1700 1571 1564 1601 Dl 1564 1600 1554 1599 Dl 1733 1555 1733 1553 Dl 1848 1526 1830 1532 Dl 1882 1505 1849 1527 Dl 1830 1532 1733 1555 Dl 1981 1460 1980 1462 Dl 1981 1458 1979 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3862 1562 3788 1573 Dl 3896 1547 3863 1561 Dl 3870 1567 3854 1568 Dl 3966 1539 3871 1567 Dl 3862 1562 3854 1568 Dl 3974 1532 3967 1538 Dl 4046 1524 4016 1534 Dl 4015 1534 3967 1538 Dl 4046 1523 4044 1517 Dl 4083 1518 4047 1523 Dl 4131 1495 4083 1519 Dl 4230 1456 1 1 De 4230 1457 4224 1459 Dl 4230 1457 4227 1457 Dl 4244 1448 4239 1447 Dl 4200 1451 4152 1459 Dl 4243 1450 4230 1456 Dl 4239 1448 4201 1450 Dl 3837 1575 3833 1576 Dl 3833 1576 3774 1581 Dl 3776 1576 3774 1581 Dl 3854 1569 3837 1575 Dl 3999 1548 3899 1575 Dl 3899 1574 3867 1569 Dl 4015 1534 4000 1548 Dl 3871 1567 3867 1569 Dl 4188 1493 4186 1496 Dl 4186 1496 4168 1503 Dl 4167 1503 4089 1520 Dl 4188 1491 4145 1491 Dl 4089 1520 4083 1519 Dl 3866 1570 3837 1575 Dl 4089 1521 4036 1546 Dl 4036 1546 4000 1548 Dl 4253 1466 4253 1468 Dl 4241 1457 4231 1457 Dl 4253 1463 4241 1458 Dl 4252 1469 4188 1492 Dl 4254 1463 4254 1465 Dl 3676 1596 3656 1591 Dl 3716 1568 3656 1591 Dl 3748 1578 3677 1596 Dl 3676 1595 3635 1610 Dl 3697 1604 3635 1610 Dl 3773 1581 3697 1604 Dl 3765 1601 3700 1609 Dl 3699 1609 3697 1604 Dl 3832 1577 3765 1601 Dl 3879 1586 3800 1603 Dl 3800 1603 3764 1602 Dl 3765 1602 3764 1602 Dl 3899 1576 3879 1586 Dl 4035 1548 4008 1560 Dl 4009 1561 3889 1588 Dl 3888 1587 3879 1586 Dl 4036 1548 4036 1546 Dl 4137 1523 4122 1528 Dl 4168 1502 4139 1522 Dl 4122 1528 4037 1548 Dl 4255 1463 4254 1465 Dl 4255 1463 4253 1463 Dl 4240 1441 4223 1444 Dl 4240 1440 4239 1447 Dl 4223 1444 4201 1450 Dl 3623 1614 3621 1619 Dl 3639 1626 3621 1619 Dl 3634 1611 3623 1613 Dl 3699 1610 3639 1627 Dl 3694 1625 3623 1632 Dl 3639 1627 3623 1632 Dl 3763 1602 3694 1625 Dl 3676 1633 3635 1656 Dl 3760 1620 3635 1656 Dl 3693 1625 3675 1632 Dl 3800 1604 3759 1619 Dl 3838 1614 3797 1620 Dl 3796 1619 3759 1619 Dl 3889 1588 3839 1613 Dl 3992 1574 3836 1617 Dl 3838 1613 3836 1617 Dl 4005 1567 3993 1575 Dl 4008 1561 4006 1566 Dl 4108 1541 4099 1545 Dl 4122 1529 4109 1541 Dl 4100 1546 4006 1566 Dl 4233 1507 4223 1510 Dl 4233 1507 4216 1493 Dl 4216 1493 4211 1493 Dl 4223 1510 4139 1522 Dl 4211 1494 4186 1496 Dl 4292 1463 4253 1468 Dl 4293 1464 4211 1493 Dl 4291 1448 4255 1463 Dl 4291 1449 4241 1458 Dl 3608 1562 3548 1586 Dl 3601 1601 3548 1586 Dl 3655 1592 3601 1602 Dl 3521 1635 3516 1635 Dl 3601 1602 3516 1635 Dl 3623 1613 3521 1635 Dl 3620 1620 3569 1648 Dl 3622 1633 3569 1648 Dl 3674 1632 3566 1648 Dl 3568 1648 3566 1648 Dl 3796 1620 3612 1664 Dl 3633 1657 3612 1664 Dl 4073 1580 4012 1600 Dl 4098 1546 4073 1579 Dl 4012 1600 3993 1575 Dl 4222 1511 4201 1520 Dl 4201 1521 4109 1541 Dl 4333 1456 4314 1468 Dl 4334 1456 4293 1463 Dl 4314 1468 4216 1493 Dl 4290 1445 4263 1445 Dl 4293 1447 4291 1445 Dl 4264 1445 4245 1450 Dl 4293 1448 4291 1448 Dl 4214 1288 4119 1320 Dl 4222 1443 4215 1288 Dl 5 R f (54)4127 1399 w 10 R f 0.1 setlinewidth 3521 1636 3476 1657 Dl 3548 1654 3476 1657 Dl 3566 1648 3549 1653 Dl 3537 1690 3463 1699 Dl 3549 1654 3463 1699 Dl 3613 1664 3538 1689 Dl 3549 1699 3538 1689 Dl 3794 1639 3548 1700 Dl 3836 1618 3795 1638 Dl 4011 1600 3932 1630 Dl 3932 1631 3795 1638 Dl 4100 1571 4073 1579 Dl 4201 1520 4101 1571 Dl 4314 1468 4285 1492 Dl 4284 1492 4233 1506 Dl 4368 1441 4294 1447 Dl 4368 1441 4334 1455 Dl 3547 1587 3444 1621 Dl 3444 1621 3419 1645 Dl 3516 1635 3419 1645 Dl 3462 1699 3447 1702 Dl 3445 1701 3322 1699 Dl 3475 1657 3322 1699 Dl 3931 1631 3859 1664 Dl 3859 1664 3463 1738 Dl 3548 1701 3463 1738 Dl 4405 1499 4394 1494 Dl 4394 1494 4285 1492 Dl 4406 1501 4101 1571 Dl 4265 1430 4263 1445 Dl 4266 1429 4241 1440 Dl 3268 1689 3239 1717 Dl 3418 1646 3268 1688 Dl 3323 1700 3239 1717 Dl 3126 1782 3083 1762 Dl 3239 1717 3083 1762 Dl 3446 1703 3126 1783 Dl 3024 1876 3024 1826 Dl 3044 1873 3024 1877 Dl 3126 1783 3024 1826 Dl 3463 1738 3044 1872 Dl 5 R f (69)3227 1789 w 10 R f 0.1 setlinewidth 3464 1908 3044 1872 Dl 3858 1664 3464 1908 Dl (70)3406 1825 w 4532 1500 4406 1500 Dl 3453 1923 3464 1908 Dl 4533 1501 3453 1923 Dl (71)3950 1688 w 4392 1433 4394 1494 Dl 4391 1433 4368 1440 Dl 4404 1425 4392 1432 Dl 4404 1426 4291 1445 Dl 4232 1283 4215 1288 Dl 4288 1405 4232 1282 Dl 4288 1406 4266 1429 Dl 3206 1673 3064 1716 Dl 3443 1621 3206 1672 Dl 3268 1688 3064 1716 Dl 3024 2479 3024 2126 Dl 4533 1501 4289 2072 Dl 4289 2072 3024 2480 Dl 3453 1923 3024 2126 Dl (77)3701 2041 w 4416 1420 4289 1406 Dl 4415 1420 4404 1425 Dl 3024 1771 3024 1726 Dl 3064 1717 3024 1726 Dl 3083 1762 3024 1771 Dl 3024 1825 3024 1771 Dl 3024 2126 3024 1877 Dl 5 R f (81)3151 1979 w 10 R f 0.1 setlinewidth 4531 1371 4416 1419 Dl 4531 1372 4533 1501 Dl 3606 1558 3205 1646 Dl 3205 1647 3206 1672 Dl 3024 1672 3024 1726 Dl 3205 1646 3024 1671 Dl 3431 486 3024 632 Dl 4498 1175 4148 486 Dl 4531 1370 4499 1175 Dl 4498 1176 4232 1282 Dl 5 R f (88)4372 1322 w 10 R f 0.1 setlinewidth 3024 1666 3024 1671 Dl 3915 1385 3024 1666 Dl 5 R f (89)3466 1555 w 10 R f 0.1 setlinewidth 3024 1580 3024 1666 Dl 3952 1367 3024 1579 Dl 5 R f (90)3325 1544 w 10 R f 0.1 setlinewidth 4148 486 3431 486 Dl 3024 633 3024 1579 Dl (91)3606 1004 w 20 R f 16 setlinewidth 5040 2502 3024 2502 Dl 5040 486 5040 2502 Dl 3024 486 5040 486 Dl 3024 2502 3024 486 Dl 4181 1788 4032 1494 Dl 4180 1788 4132 1732 Dl 4180 1787 4164 1715 Dl 10 B f (Fig. 124:)1 372 1 1030 2700 t 10 R f (pr. proj. it. 17,)3 575 1 1427 2700 t 10 I f (v)2027 2700 w 10 R f (=)2096 2700 w 10 I f (center)2177 2700 w 10 B f (Fig. 125:)1 372 1 3161 2700 t 10 R f (pr. proj. it. 17,)3 575 1 3558 2700 t 10 I f (v)4158 2700 w 10 R f (=)4227 2700 w 10 I f (center)4308 2700 w 10 S f (+)4557 2700 w 10 R f (\(.1,0,0\))4612 2700 w 0.1 setlinewidth 1699 3845 1692 3846 Dl 1691 3847 1676 3849 Dl 1675 3849 1659 3851 Dl 1659 3851 1608 3857 Dl 1698 3845 1650 3848 Dl 1650 3849 1608 3857 Dl 720 3923 720 3971 Dl 1241 3736 720 3923 Dl 863 3963 720 3971 Dl 1608 3857 863 3962 Dl 1650 3848 1241 3735 Dl (4)1134 3879 w 2027 3530 1499 3636 Dl 1498 3636 1388 3670 Dl 1388 3671 1241 3735 Dl 2027 3530 1783 3824 Dl 1783 3824 1733 3839 Dl 1732 3839 1720 3841 Dl 1718 3842 1704 3844 Dl 1704 3844 1699 3844 Dl (5)1633 3721 w 873 3969 863 3962 Dl 1107 3968 874 3970 Dl 1659 3851 1107 3968 Dl 5 R f (7)1188 3939 w 10 R f 0.1 setlinewidth 1184 3966 1107 3972 Dl 1107 3968 1107 3972 Dl 1676 3848 1184 3965 Dl 1281 3961 1209 3966 Dl 1209 3965 1184 3965 Dl 1692 3846 1282 3960 Dl 1420 3948 1323 3962 Dl 1323 3961 1282 3960 Dl 1705 3844 1421 3947 Dl 1659 3918 1552 3936 Dl 1552 3936 1421 3947 Dl 1719 3842 1659 3917 Dl 1965 3871 1761 3908 Dl 1760 3909 1659 3917 Dl 1965 3871 1733 3839 Dl 2114 3799 1783 3824 Dl 2363 3794 2088 3860 Dl 2087 3860 2044 3865 Dl 2373 3788 2114 3798 Dl 2373 3788 2363 3793 Dl 2044 3866 1965 3871 Dl 5 R f (13)2011 3839 w 10 R f 0.1 setlinewidth 873 3971 848 3991 Dl 945 4001 848 3991 Dl 1106 3973 944 4002 Dl 997 4007 924 4008 Dl 944 4001 924 4008 Dl 1027 4003 997 4007 Dl 1209 3966 1028 4003 Dl 1228 3986 1028 4003 Dl 1322 3962 1229 3985 Dl 1250 3995 1205 3997 Dl 1526 3947 1250 3995 Dl 1228 3987 1205 3997 Dl 1552 3937 1527 3947 Dl 1768 3921 1671 3939 Dl 1671 3940 1527 3947 Dl 1768 3919 1761 3908 Dl 1882 3912 1769 3921 Dl 2044 3866 1882 3911 Dl 2387 3788 2386 3787 Dl 2387 3789 2363 3793 Dl 2386 3787 2374 3788 Dl 2436 3772 2418 3770 Dl 2282 3778 2114 3798 Dl 2436 3774 2386 3787 Dl 2417 3770 2283 3777 Dl 1155 4008 1145 4009 Dl 1145 4010 991 4016 Dl 997 4008 991 4016 Dl 1205 3997 1157 4007 Dl 1620 3964 1325 4009 Dl 1325 4008 1238 3998 Dl 1671 3939 1622 3963 Dl 1250 3995 1238 3998 Dl 2234 3858 2224 3864 Dl 2225 3865 2162 3878 Dl 2160 3879 1901 3913 Dl 2234 3859 2088 3860 Dl 1902 3913 1882 3911 Dl 1238 3999 1157 4007 Dl 1901 3914 1730 3960 Dl 1730 3960 1622 3963 Dl 2469 3804 2465 3809 Dl 2424 3789 2387 3789 Dl 2467 3796 2424 3789 Dl 2464 3810 2234 3859 Dl 2468 3798 2469 3803 Dl 720 4031 720 4021 Dl 743 4036 720 4032 Dl 848 3991 720 4021 Dl 923 4009 743 4036 Dl 720 4053 720 4041 Dl 743 4036 720 4041 Dl 793 4051 720 4054 Dl 991 4016 793 4050 Dl 961 4048 797 4059 Dl 797 4059 793 4050 Dl 1144 4009 962 4047 Dl 1266 4027 1051 4052 Dl 1051 4052 959 4049 Dl 961 4048 959 4049 Dl 1326 4008 1267 4026 Dl 1729 3964 1643 3985 Dl 1643 3985 1292 4029 Dl 1292 4028 1267 4026 Dl 1730 3960 1730 3963 Dl 2059 3916 2005 3926 Dl 2160 3879 2059 3915 Dl 2005 3926 1730 3963 Dl 2474 3798 2469 3803 Dl 2475 3798 2468 3798 Dl 2425 3757 2362 3764 Dl 2425 3755 2418 3770 Dl 2362 3764 2283 3777 Dl 720 4072 720 4054 Dl 797 4060 720 4072 Dl 720 4085 720 4072 Dl 778 4084 720 4086 Dl 958 4049 778 4082 Dl 720 4112 720 4097 Dl 730 4094 720 4097 Dl 941 4076 720 4112 Dl 778 4082 730 4093 Dl 1051 4053 941 4076 Dl 1146 4070 1036 4078 Dl 1036 4078 941 4076 Dl 1292 4030 1147 4070 Dl 1590 4008 1139 4076 Dl 1146 4069 1139 4076 Dl 1632 3995 1591 4008 Dl 1643 3985 1632 3995 Dl 1958 3950 1928 3957 Dl 2005 3926 1959 3949 Dl 1927 3957 1632 3995 Dl 2388 3881 2352 3888 Dl 2387 3880 2328 3857 Dl 2327 3857 2311 3857 Dl 2351 3888 2059 3915 Dl 2311 3857 2224 3864 Dl 2614 3795 2465 3809 Dl 2613 3794 2311 3857 Dl 2611 3766 2476 3798 Dl 2609 3766 2424 3789 Dl 720 3971 720 4021 Dl 720 4041 720 4032 Dl 720 4094 720 4086 Dl 730 4094 720 4094 Dl 720 4119 720 4112 Dl 1036 4078 720 4119 Dl 1835 4015 1641 4050 Dl 1928 3957 1836 4015 Dl 1640 4049 1591 4008 Dl 2352 3888 2275 3906 Dl 2274 3908 1959 3949 Dl 2736 3780 2736 3787 Dl 2735 3788 2697 3800 Dl 2735 3780 2614 3795 Dl 2696 3801 2328 3857 Dl 2609 3759 2507 3761 Dl 2620 3763 2610 3759 Dl 2507 3761 2437 3773 Dl 2620 3763 2610 3765 Dl 2362 3446 2027 3529 Dl 2363 3763 2363 3446 Dl (54)2085 3677 w 720 4096 720 4094 Dl 720 4147 720 4119 Dl 1022 4108 720 4148 Dl 1139 4078 1022 4108 Dl 1641 4051 1395 4099 Dl 1394 4100 1022 4108 Dl 5 R f (58)1352 4076 w 10 R f 0.1 setlinewidth 1925 4000 1836 4015 Dl 2274 3907 1925 4000 Dl 2696 3801 2582 3849 Dl 2582 3850 2388 3881 Dl 2736 3755 2736 3779 Dl 2735 3755 2620 3763 Dl 720 4191 720 4148 Dl 1394 4100 1175 4151 Dl 1175 4151 720 4192 Dl 5 R f (64)981 4150 w 10 R f 0.1 setlinewidth 2736 3845 2736 3891 Dl 2735 3845 2582 3849 Dl 2735 3892 1925 4000 Dl 5 R f (65)2397 3918 w 10 R f 0.1 setlinewidth 2520 3731 2507 3761 Dl 2520 3730 2425 3755 Dl 720 4288 720 4192 Dl 1175 4152 720 4289 Dl 5 R f (70)846 4221 w 10 R f 0.1 setlinewidth 2736 3892 2736 4003 Dl 720 4386 720 4289 Dl 2736 4003 720 4386 Dl (71)1677 4143 w 2736 3787 2736 3844 Dl 2736 3744 2736 3754 Dl 2735 3744 2610 3759 Dl 2426 3431 2363 3446 Dl 2610 3678 2427 3430 Dl 2609 3679 2521 3730 Dl 5 R f (74)2426 3625 w 10 R f 0.1 setlinewidth 2736 4878 720 4878 Dl 2736 4004 2736 4878 Dl 720 4877 720 4386 Dl (77)1772 4547 w 2736 3744 2736 3682 Dl 2736 3681 2610 3679 Dl 2736 3680 2736 3337 Dl 2735 3338 2427 3430 Dl (88)2573 3529 w 720 3813 720 3923 Dl 1388 3671 720 3813 Dl 5 R f (89)931 3810 w 10 R f 0.1 setlinewidth 720 3757 720 3813 Dl 1499 3636 720 3756 Dl 5 R f (90)986 3741 w 10 R f 0.1 setlinewidth 2736 2862 720 2862 Dl 2736 3337 2736 2862 Dl 720 2862 720 3756 Dl (91)1582 3248 w 20 R f 16 setlinewidth 2736 4878 720 4878 Dl 2736 2862 2736 4878 Dl 720 2862 2736 2862 Dl 720 4878 720 2862 Dl 10 R f 0.1 setlinewidth 4008 3848 4001 3849 Dl 4000 3850 3987 3852 Dl 3986 3851 3972 3853 Dl 3972 3854 3929 3859 Dl 4007 3849 3965 3851 Dl 3965 3852 3929 3859 Dl 3621 3757 3060 3957 Dl 3061 3958 3063 3963 Dl 3293 3950 3063 3963 Dl 3929 3859 3294 3949 Dl 3965 3851 3622 3756 Dl (4)3509 3884 w 4283 3584 3840 3674 Dl 3838 3674 3746 3702 Dl 3747 3702 3622 3756 Dl 4283 3584 4080 3830 Dl 4079 3831 4036 3843 Dl 4035 3843 4024 3845 Dl 4024 3845 4012 3847 Dl 4012 3848 4008 3848 Dl (5)3947 3748 w 3303 3955 3294 3949 Dl 3499 3954 3303 3955 Dl 3972 3854 3499 3954 Dl 3564 3952 3499 3957 Dl 3499 3954 3499 3957 Dl 3986 3852 3565 3952 Dl 3648 3948 3587 3952 Dl 3586 3952 3565 3952 Dl 4000 3850 3648 3948 Dl 3768 3937 3684 3949 Dl 3683 3949 3648 3948 Dl 4011 3847 3767 3936 Dl 3972 3911 3880 3926 Dl 3879 3926 3767 3936 Dl 4023 3846 3972 3911 Dl 4236 3871 4060 3903 Dl 4059 3904 3972 3911 Dl 4236 3871 4036 3843 Dl 4365 3809 4080 3830 Dl 4578 3805 4342 3862 Dl 4341 3862 4304 3866 Dl 4587 3800 4365 3808 Dl 4587 3800 4578 3804 Dl 4303 3866 4236 3871 Dl 5 R f (13)4272 3845 w 10 R f 0.1 setlinewidth 3303 3955 3281 3973 Dl 3362 3982 3281 3973 Dl 3500 3958 3363 3983 Dl 3406 3987 3345 3988 Dl 3362 3983 3345 3988 Dl 3432 3984 3407 3987 Dl 3586 3953 3433 3984 Dl 3603 3970 3433 3984 Dl 3683 3949 3604 3969 Dl 3622 3977 3584 3978 Dl 3859 3936 3623 3977 Dl 3604 3969 3584 3978 Dl 3880 3927 3859 3936 Dl 4066 3914 3983 3929 Dl 3983 3930 3859 3936 Dl 4067 3913 4060 3903 Dl 4164 3906 4067 3913 Dl 4304 3867 4164 3905 Dl 4598 3800 4597 3799 Dl 4598 3801 4578 3804 Dl 4597 3799 4587 3800 Dl 4641 3786 4625 3784 Dl 4509 3790 4365 3808 Dl 4640 3787 4597 3799 Dl 4625 3784 4510 3790 Dl 3542 3988 3533 3989 Dl 3533 3989 3402 3994 Dl 3407 3987 3402 3994 Dl 3584 3980 3543 3988 Dl 3940 3950 3688 3988 Dl 3687 3988 3612 3980 Dl 3983 3930 3941 3950 Dl 3622 3978 3612 3980 Dl 4466 3860 4458 3865 Dl 4458 3866 4404 3877 Dl 4404 3878 4181 3907 Dl 4467 3861 4342 3862 Dl 4181 3906 4164 3905 Dl 3612 3981 3543 3988 Dl 4181 3908 4034 3947 Dl 4033 3947 3941 3950 Dl 4667 3813 4664 3818 Dl 4630 3800 4599 3800 Dl 4667 3807 4631 3800 Dl 4663 3818 4467 3860 Dl 4667 3808 4667 3813 Dl 3194 4010 3154 4003 Dl 3280 3973 3154 4003 Dl 3345 3989 3194 4011 Dl 3193 4011 3109 4029 Dl 3236 4023 3109 4029 Dl 3402 3995 3237 4023 Dl 3379 4022 3241 4031 Dl 3241 4030 3237 4023 Dl 3533 3990 3380 4021 Dl 3639 4004 3457 4025 Dl 3456 4024 3377 4022 Dl 3379 4021 3377 4022 Dl 3687 3989 3639 4003 Dl 4033 3949 3960 3967 Dl 3959 3969 3661 4006 Dl 3661 4005 3639 4003 Dl 4034 3947 4034 3949 Dl 4315 3910 4269 3918 Dl 4403 3877 4315 3908 Dl 4269 3917 4034 3949 Dl 4672 3808 4667 3813 Dl 4672 3808 4667 3808 Dl 4631 3771 4577 3778 Dl 4630 3772 4625 3784 Dl 4576 3778 4510 3790 Dl 3086 4033 3081 4040 Dl 3116 4050 3081 4040 Dl 3109 4030 3086 4033 Dl 3240 4031 3116 4051 Dl 3228 4050 3084 4057 Dl 3116 4051 3084 4057 Dl 3377 4023 3228 4050 Dl 3188 4058 3105 4086 Dl 3366 4044 3105 4086 Dl 3226 4050 3188 4059 Dl 3456 4025 3366 4044 Dl 3540 4039 3448 4046 Dl 3448 4045 3366 4044 Dl 3661 4006 3541 4039 Dl 3915 3988 3535 4044 Dl 3540 4039 3535 4044 Dl 3950 3977 3916 3988 Dl 3959 3969 3950 3976 Dl 4227 3938 4201 3944 Dl 4268 3917 4228 3936 Dl 4201 3944 3950 3976 Dl 4591 3880 4561 3885 Dl 4592 3879 4546 3859 Dl 4544 3859 4531 3859 Dl 4560 3885 4315 3908 Dl 4531 3859 4458 3865 Dl 4788 3806 4664 3818 Dl 4788 3805 4531 3859 Dl 4787 3780 4673 3808 Dl 4787 3780 4631 3800 Dl 3024 3973 3024 4011 Dl 3063 3963 3024 3973 Dl 3044 4016 3024 4011 Dl 3153 4004 3044 4016 Dl 3024 4040 3024 4021 Dl 3044 4016 3024 4021 Dl 3086 4033 3024 4040 Dl 3024 4066 3024 4059 Dl 3081 4041 3024 4059 Dl 3084 4058 3024 4067 Dl 3024 4071 3024 4067 Dl 3188 4059 3024 4071 Dl 3447 4047 3061 4096 Dl 3104 4087 3061 4096 Dl 4122 3991 3960 4019 Dl 4201 3943 4122 3990 Dl 3959 4020 3916 3988 Dl 4560 3885 4494 3900 Dl 4493 3900 4228 3936 Dl 4920 3788 4854 3810 Dl 4921 3789 4788 3805 Dl 4854 3811 4546 3859 Dl 4786 3776 4700 3777 Dl 4795 3778 4787 3775 Dl 4700 3777 4641 3787 Dl 4794 3779 4787 3780 Dl 4560 3518 4283 3584 Dl 4576 3778 4561 3516 Dl (54)4326 3712 w 3024 4058 3024 4040 Dl 3024 4102 3024 4071 Dl 3061 4096 3024 4103 Dl 3024 4123 3024 4103 Dl 3440 4070 3024 4124 Dl 3535 4044 3440 4069 Dl 3959 4020 3756 4059 Dl 3756 4059 3440 4069 Dl 5 R f (58)3713 4044 w 10 R f 0.1 setlinewidth 4196 3978 4122 3990 Dl 4494 3901 4196 3978 Dl 4854 3811 4754 3852 Dl 4753 3853 4591 3879 Dl 5037 3761 4795 3779 Dl 5037 3760 4921 3788 Dl 3024 4011 3024 4021 Dl 3024 4149 3024 4124 Dl 3755 4060 3581 4099 Dl 3581 4100 3024 4150 Dl 5 R f (64)3337 4111 w 10 R f 0.1 setlinewidth 5040 3844 5040 3861 Dl 5039 3844 4754 3852 Dl 5039 3861 4196 3978 Dl 5 R f (65)4644 3904 w 10 R f 0.1 setlinewidth 4710 3752 4700 3777 Dl 4711 3751 4631 3772 Dl 3024 4259 3024 4150 Dl 3581 4100 3024 4259 Dl 5 R f (70)3184 4179 w 10 R f 0.1 setlinewidth 5040 3861 5040 3918 Dl 3024 4289 3024 4259 Dl 5040 3919 3024 4290 Dl (71)4012 4077 w 5040 3760 5040 3844 Dl 5039 3760 5038 3760 Dl 5040 3744 5040 3759 Dl 5039 3745 4787 3775 Dl 4613 3504 4561 3516 Dl 4782 3707 4613 3504 Dl 4782 3707 4710 3750 Dl 5 R f (74)4620 3666 w 10 R f 0.1 setlinewidth 5040 3919 5040 3931 Dl 3024 4317 3024 4290 Dl 5039 3932 4165 4116 Dl 4165 4116 3024 4317 Dl 5 R f (77)3934 4142 w 10 R f 0.1 setlinewidth 5040 3743 5040 3713 Dl 5039 3713 4783 3707 Dl 5 R f (78)4839 3749 w 10 R f 0.1 setlinewidth 3024 3963 3024 3973 Dl 3060 3957 3024 3962 Dl 5039 3031 4701 2862 Dl 5040 3713 5040 3382 Dl 5039 3383 4613 3504 Dl (88)4825 3582 w 3024 3860 3024 3962 Dl 3746 3703 3024 3860 Dl 5 R f (89)3253 3851 w 10 R f 0.1 setlinewidth 3024 3808 3024 3860 Dl 3840 3674 3024 3807 Dl 5 R f (90)3301 3786 w 10 R f 0.1 setlinewidth 4701 2862 3024 2862 Dl 5040 3381 5040 3031 Dl 3024 2862 3024 3807 Dl (91)3871 3277 w 20 R f 16 setlinewidth 5040 4878 3024 4878 Dl 5040 2862 5040 4878 Dl 3024 2862 5040 2862 Dl 3024 4878 3024 2862 Dl 4078 4065 4032 3870 Dl 4076 4064 4043 3998 Dl 4078 4064 4078 3990 Dl 10 B f (Fig. 126:)1 372 1 1030 5076 t 10 R f (pr. proj. it. 18,)3 575 1 1427 5076 t 10 I f (v)2027 5076 w 10 R f (=)2096 5076 w 10 I f (center)2177 5076 w 10 B f (Fig. 127:)1 372 1 3161 5076 t 10 R f (pr. proj. it. 18,)3 575 1 3558 5076 t 10 I f (v)4158 5076 w 10 R f (=)4227 5076 w 10 I f (center)4308 5076 w 10 S f (+)4557 5076 w 10 R f (\(.1,0,0\))4612 5076 w 0.1 setlinewidth 1662 6176 1655 6179 Dl 1654 6180 1640 6186 Dl 1640 6187 1624 6193 Dl 1623 6193 1573 6210 Dl 1661 6176 1610 6186 Dl 1609 6186 1573 6210 Dl 720 6317 720 6521 Dl 1015 5884 720 6318 Dl 871 6498 720 6521 Dl 1573 6210 871 6498 Dl 1611 6186 1015 5883 Dl (4)1058 6234 w 1623 5323 1175 5617 Dl 1175 5618 1097 5710 Dl 1097 5711 1015 5883 Dl 1731 6116 1624 5322 Dl 1730 6118 1692 6159 Dl 1692 6159 1681 6166 Dl 1680 6167 1667 6174 Dl 1667 6174 1662 6176 Dl (5)1410 5810 w 891 6518 871 6498 Dl 1145 6514 892 6519 Dl 1623 6193 1145 6514 Dl 5 R f (7)1192 6415 w 10 R f 0.1 setlinewidth 1228 6508 1151 6526 Dl 1150 6526 1145 6514 Dl 1639 6187 1228 6508 Dl 1331 6496 1257 6510 Dl 1256 6508 1228 6508 Dl 1655 6180 1332 6495 Dl 1473 6459 1380 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w 3537 1320 3502 1719 Dl 5 R f (89)3553 1570 w 10 R f 0.1 setlinewidth 3528 1293 3318 1722 Dl 5 R f (90)3426 1596 w 10 R f (91)3236 1343 w 20 R f 16 setlinewidth 5040 2502 3024 2502 Dl 5040 486 5040 2502 Dl 3024 486 5040 486 Dl 3024 2502 3024 486 Dl 3844 1334 4032 1494 Dl 3843 1333 3909 1366 Dl 3843 1333 3886 1393 Dl 10 B f (Fig. 130:)1 372 1 1030 2700 t 10 R f (pr. proj. it. 20,)3 575 1 1427 2700 t 10 I f (v)2027 2700 w 10 R f (=)2096 2700 w 10 I f (center)2177 2700 w 10 B f (Fig. 131:)1 372 1 3161 2700 t 10 R f (pr. proj. it. 20,)3 575 1 3558 2700 t 10 I f (v)4158 2700 w 10 R f (=)4227 2700 w 10 I f (center)4308 2700 w 10 S f (+)4557 2700 w 10 R f (\(.1,0,0\))4612 2700 w 0.1 setlinewidth 1719 3856 1717 3856 Dl 1717 3856 1713 3857 Dl 1713 3858 1709 3859 Dl 1709 3859 1697 3862 Dl 1719 3855 1707 3857 Dl 1707 3857 1697 3862 Dl 1615 3803 1532 3908 Dl 1532 3910 1532 3908 Dl 1565 3909 1532 3911 Dl 1696 3862 1566 3908 Dl 1706 3857 1616 3804 Dl 1811 3621 1663 3741 Dl 1661 3741 1640 3765 Dl 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3747 2050 3793 Dl 2155 3749 2016 3790 Dl 1533 3912 1519 3922 Dl 1532 3933 1519 3922 Dl 1546 3932 1532 3934 Dl 1514 3947 1513 3947 Dl 1532 3935 1513 3947 Dl 1538 3942 1514 3947 Dl 1537 3946 1525 3957 Dl 1537 3954 1525 3957 Dl 1552 3957 1524 3957 Dl 1524 3957 1 1 De 1594 3959 1536 3968 Dl 1541 3966 1536 3968 Dl 1760 3951 1709 3963 Dl 1789 3922 1761 3952 Dl 1709 3963 1697 3942 Dl 1972 3876 1931 3890 Dl 1931 3891 1800 3916 Dl 2323 3734 2236 3775 Dl 2323 3735 2158 3778 Dl 2235 3775 1959 3852 Dl 2155 3741 2073 3755 Dl 2165 3744 2156 3741 Dl 2072 3756 2024 3774 Dl 2164 3746 2156 3748 Dl 1968 3475 1811 3620 Dl 1977 3770 1969 3474 Dl 5 R f (54)1857 3695 w 10 R f 0.1 setlinewidth 1514 3947 1505 3954 Dl 1520 3957 1505 3954 Dl 1525 3956 1521 3957 Dl 1518 3974 1503 3972 Dl 1521 3958 1503 3972 Dl 1536 3968 1518 3974 Dl 1520 3979 1518 3974 Dl 1592 3970 1520 3980 Dl 1609 3962 1592 3970 Dl 1709 3965 1656 3978 Dl 1655 3977 1592 3970 Dl 1788 3947 1761 3952 Dl 1930 3891 1789 3945 Dl 2235 3776 2129 3835 Dl 2129 3836 1993 3870 Dl 2524 3658 2165 3744 Dl 2524 3658 2324 3734 Dl 1518 3922 1498 3934 Dl 1498 3935 1494 3945 Dl 1513 3946 1494 3945 Dl 1502 3972 1500 3972 Dl 1498 3972 1478 3962 Dl 1504 3955 1478 3962 Dl 1655 3978 1617 3990 Dl 1617 3989 1502 3988 Dl 1520 3980 1502 3988 Dl 2736 3787 2736 3769 Dl 2735 3769 2716 3769 Dl 2715 3769 2129 3835 Dl 2735 3787 1789 3945 Dl 5 R f (65)2237 3856 w 10 R f 0.1 setlinewidth 2083 3722 2073 3755 Dl 2082 3723 2016 3758 Dl 1469 3955 1466 3964 Dl 1493 3945 1470 3954 Dl 1478 3963 1466 3964 Dl 1453 3980 1448 3970 Dl 1466 3964 1448 3970 Dl 1498 3973 1452 3980 Dl 1443 4001 1422 3999 Dl 1453 3980 1422 3999 Dl 1502 3989 1443 4002 Dl 1490 4048 1443 4002 Dl 1617 3991 1491 4049 Dl 2736 3895 2736 3787 Dl 1490 4049 1487 4052 Dl 2735 3896 1487 4052 Dl (71)2163 3938 w 2715 3768 2710 3592 Dl 2709 3593 2524 3658 Dl 5 R f (72)2479 3741 w 10 R f 0.1 setlinewidth 2736 3581 2736 3566 Dl 2735 3581 2710 3592 Dl 2735 3567 2156 3741 Dl 2008 3438 1969 3474 Dl 2155 3652 2009 3438 Dl 2155 3652 2083 3722 Dl 5 R f (74)2013 3626 w 10 R f 0.1 setlinewidth 1460 3945 1445 3953 Dl 1497 3935 1461 3944 Dl 1470 3954 1445 3953 Dl 1314 4000 1314 3998 Dl 1410 3965 1314 3998 Dl 1372 4000 1315 4001 Dl 1425 3968 1373 3999 Dl 1425 3968 1411 3965 Dl 2736 4878 720 4878 Dl 2736 3896 2736 4878 Dl 720 4877 720 4847 Dl 720 4847 1324 4073 Dl 1487 4053 1324 4073 Dl (77)1847 4479 w 2736 3566 2736 3528 Dl 2735 3529 2155 3652 Dl 5 R f (78)2351 3651 w 10 R f 0.1 setlinewidth 1414 3962 1411 3965 Dl 1444 3953 1414 3961 Dl 1447 3970 1425 3968 Dl 1421 3999 1373 3999 Dl 1323 4072 1315 4001 Dl 2736 3769 2736 3582 Dl 1532 3910 1460 3933 Dl 1461 3944 1460 3933 Dl 1435 3934 1412 3943 Dl 1459 3933 1435 3934 Dl 1414 3961 1412 3943 Dl 1368 3937 1309 3958 Dl 1411 3942 1368 3936 Dl 1314 3998 1309 3958 Dl 720 2862 1168 2862 Dl 720 4847 720 2862 Dl 1168 2862 1309 3958 Dl (86)918 3740 w 2735 2862 2576 2862 Dl 2736 3528 2736 2862 Dl 2576 2862 2009 3438 Dl (88)2398 3319 w 1640 3766 1435 3934 Dl 1662 3741 1368 3936 Dl 2575 2862 1168 2862 Dl (91)1652 3271 w 20 R f 16 setlinewidth 2736 4878 720 4878 Dl 2736 2862 2736 4878 Dl 720 2862 2736 2862 Dl 720 4878 720 2862 Dl 10 R f 0.1 setlinewidth 4024 3857 4022 3857 Dl 4022 3857 4019 3858 Dl 4018 3858 4015 3859 Dl 4014 3860 4003 3863 Dl 4024 3857 4013 3859 Dl 4012 3859 4003 3863 Dl 3930 3811 3855 3905 Dl 3855 3907 3855 3905 Dl 3886 3905 3856 3907 Dl 4003 3863 3886 3904 Dl 4012 3858 3931 3810 Dl 4105 3648 3973 3754 Dl 3973 3755 3954 3776 Dl 3953 3776 3931 3810 Dl 4105 3648 4044 3844 Dl 4044 3845 4032 3853 Dl 4031 3853 4029 3854 Dl 4028 3855 4025 3856 Dl 4025 3856 4024 3856 Dl 3887 3906 3886 3904 Dl 3918 3909 3888 3907 Dl 4014 3860 3918 3909 Dl 3928 3910 3918 3911 Dl 3918 3910 3918 3909 Dl 4018 3859 3929 3910 Dl 3945 3909 3934 3910 Dl 3932 3910 3929 3910 Dl 4021 3858 3944 3909 Dl 3969 3905 3952 3910 Dl 3951 3910 3944 3909 Dl 4024 3857 3968 3905 Dl 4016 3894 3993 3901 Dl 3993 3902 3968 3905 Dl 4028 3855 4016 3893 Dl 4096 3869 4040 3889 Dl 4039 3890 4016 3893 Dl 4097 3868 4032 3853 Dl 4146 3821 4044 3844 Dl 4255 3806 4138 3861 Dl 4137 3861 4122 3864 Dl 4261 3801 4146 3820 Dl 4260 3801 4255 3805 Dl 4122 3865 4097 3869 Dl 3887 3908 3885 3915 Dl 3897 3920 3885 3915 Dl 3917 3912 3897 3920 Dl 3904 3922 3895 3922 Dl 3897 3920 3895 3922 Dl 3908 3923 3904 3923 Dl 3933 3911 3908 3922 Dl 3936 3919 3908 3922 Dl 3951 3910 3937 3918 Dl 3941 3923 3934 3923 Dl 3989 3907 3941 3923 Dl 3937 3919 3934 3923 Dl 3994 3901 3989 3906 Dl 4043 3896 4020 3904 Dl 4019 3904 3989 3906 Dl 4042 3894 4040 3889 Dl 4073 3891 4043 3895 Dl 4122 3865 4073 3891 Dl 4268 3800 4268 3799 Dl 4267 3800 4255 3805 Dl 4267 3800 4261 3801 Dl 4294 3784 4284 3783 Dl 4215 3798 4146 3820 Dl 4296 3784 4268 3799 Dl 4285 3784 4216 3798 Dl 3926 3926 3925 3926 Dl 3924 3926 3903 3926 Dl 3903 3924 3903 3926 Dl 3933 3923 3926 3926 Dl 4009 3916 3953 3930 Dl 3953 3929 3939 3924 Dl 4019 3905 4009 3915 Dl 3941 3923 3939 3924 Dl 4195 3858 4191 3862 Dl 4190 3862 4165 3872 Dl 4165 3872 4078 3892 Dl 4195 3858 4138 3861 Dl 4078 3892 4073 3891 Dl 3938 3924 3926 3926 Dl 4078 3893 4034 3915 Dl 4034 3915 4009 3915 Dl 4314 3807 4312 3812 Dl 4288 3798 4268 3800 Dl 4314 3801 4289 3798 Dl 4313 3812 4196 3857 Dl 4314 3807 4314 3802 Dl 3874 3928 3869 3925 Dl 3885 3915 3869 3925 Dl 3894 3923 3874 3929 Dl 3874 3929 3864 3934 Dl 3880 3934 3864 3934 Dl 3903 3926 3880 3934 Dl 3900 3938 3881 3938 Dl 3880 3936 3880 3934 Dl 3924 3927 3900 3937 Dl 3944 3936 3913 3941 Dl 3912 3940 3900 3937 Dl 3953 3931 3944 3936 Dl 4033 3917 4014 3925 Dl 4014 3925 3948 3937 Dl 3948 3937 3944 3936 Dl 4034 3917 4034 3915 Dl 4129 3895 4111 3900 Dl 4165 3872 4129 3894 Dl 4110 3900 4034 3916 Dl 4318 3802 4315 3807 Dl 4318 3802 4314 3802 Dl 4288 3771 4254 3782 Dl 4287 3771 4284 3783 Dl 4254 3783 4216 3798 Dl 3860 3935 3860 3937 Dl 3864 3942 3860 3937 Dl 3863 3935 3861 3935 Dl 3880 3938 3865 3943 Dl 3879 3944 3861 3944 Dl 3864 3943 3861 3944 Dl 3900 3938 3880 3945 Dl 3874 3948 3864 3956 Dl 3899 3947 3864 3956 Dl 3879 3945 3874 3947 Dl 3912 3942 3899 3947 Dl 3926 3949 3911 3949 Dl 3911 3949 3899 3947 Dl 3947 3937 3926 3949 Dl 4003 3936 3926 3952 Dl 3926 3950 3926 3952 Dl 4011 3930 4003 3935 Dl 4014 3925 4012 3929 Dl 4096 3913 4087 3916 Dl 4110 3900 4096 3912 Dl 4086 3916 4012 3929 Dl 4268 3870 4250 3875 Dl 4268 3869 4238 3854 Dl 4237 3854 4230 3854 Dl 4250 3876 4129 3894 Dl 4229 3855 4191 3862 Dl 4413 3789 4312 3812 Dl 4413 3788 4230 3854 Dl 4411 3762 4319 3802 Dl 4411 3762 4289 3798 Dl 3855 3907 3843 3917 Dl 3855 3927 3843 3917 Dl 3867 3925 3855 3927 Dl 3839 3939 3838 3939 Dl 3855 3928 3838 3939 Dl 3860 3935 3839 3939 Dl 3860 3938 3849 3948 Dl 3861 3945 3849 3948 Dl 3874 3948 3849 3948 Dl 3911 3950 3859 3958 Dl 3864 3956 3859 3958 Dl 4061 3944 4015 3954 Dl 4087 3916 4062 3943 Dl 4014 3954 4003 3935 Dl 4249 3876 4213 3888 Dl 4212 3889 4096 3912 Dl 4558 3750 4482 3786 Dl 4558 3750 4414 3788 Dl 4481 3786 4238 3854 Dl 4410 3756 4338 3768 Dl 4418 3758 4411 3756 Dl 4339 3769 4296 3785 Dl 4419 3760 4412 3762 Dl 4244 3521 4106 3648 Dl 4254 3781 4245 3520 Dl 5 R f (54)4143 3716 w 10 R f 0.1 setlinewidth 3839 3940 3831 3946 Dl 3845 3948 3831 3946 Dl 3848 3949 3845 3949 Dl 3841 3963 3828 3962 Dl 3844 3950 3828 3962 Dl 3857 3959 3842 3964 Dl 3844 3969 3842 3964 Dl 3909 3960 3844 3969 Dl 3925 3953 3910 3960 Dl 4015 3955 3967 3967 Dl 3966 3967 3910 3960 Dl 4087 3938 4062 3943 Dl 4212 3889 4086 3938 Dl 4482 3786 4389 3839 Dl 4388 3840 4268 3870 Dl 4731 3685 4419 3759 Dl 4731 3684 4559 3750 Dl 3842 3918 3824 3929 Dl 3824 3928 3821 3937 Dl 3838 3938 3821 3937 Dl 3828 3962 3826 3962 Dl 3826 3962 3807 3953 Dl 3830 3946 3807 3953 Dl 3966 3967 3932 3978 Dl 3932 3978 3828 3977 Dl 3844 3970 3828 3977 Dl 5000 3782 4898 3781 Dl 4898 3782 4389 3839 Dl 5000 3784 4086 3938 Dl 5 R f (65)4487 3858 w 10 R f 0.1 setlinewidth 4346 3739 4338 3768 Dl 4347 3739 4289 3770 Dl 3799 3946 3796 3954 Dl 3820 3938 3799 3946 Dl 3806 3953 3796 3954 Dl 3783 3968 3779 3960 Dl 3796 3955 3779 3960 Dl 3825 3964 3783 3970 Dl 3773 3989 3754 3987 Dl 3782 3970 3754 3987 Dl 3827 3977 3774 3989 Dl 3817 4031 3774 3989 Dl 3932 3979 3818 4032 Dl 5040 3876 5040 3778 Dl 5039 3777 5001 3782 Dl 3816 4031 3814 4034 Dl 5039 3876 3814 4034 Dl (71)4475 3923 w 4897 3781 4890 3628 Dl 4889 3628 4731 3684 Dl 5 R f (72)4688 3758 w 10 R f 0.1 setlinewidth 5003 3578 4890 3628 Dl 5004 3578 4411 3756 Dl 4279 3488 4245 3520 Dl 4410 3677 4280 3489 Dl 4409 3677 4347 3738 Dl 5 R f (74)4282 3656 w 10 R f 0.1 setlinewidth 3790 3937 3776 3944 Dl 3824 3928 3791 3936 Dl 3799 3945 3776 3944 Dl 3657 3988 3657 3986 Dl 3744 3956 3657 3986 Dl 3709 3988 3657 3989 Dl 3758 3959 3710 3987 Dl 3758 3957 3745 3955 Dl 5040 3876 5040 3934 Dl 5039 3935 3875 4089 Dl 3875 4089 3665 4054 Dl 3814 4035 3665 4054 Dl (77)4346 4009 w 5040 3563 5040 3545 Dl 5040 3545 4410 3677 Dl 5039 3562 5004 3577 Dl 5 R f (78)4612 3669 w 10 R f 0.1 setlinewidth 3748 3953 3745 3955 Dl 3777 3945 3749 3952 Dl 3779 3960 3759 3959 Dl 3754 3987 3710 3987 Dl 3664 4053 3657 3989 Dl 5040 3777 5040 3562 Dl 5 R f (82)4946 3696 w 10 R f 0.1 setlinewidth 3855 3905 3790 3926 Dl 3791 3936 3790 3926 Dl 3766 3928 3746 3936 Dl 3789 3927 3767 3928 Dl 3748 3952 3746 3936 Dl 3707 3931 3653 3950 Dl 3746 3935 3707 3930 Dl 3657 3986 3653 3950 Dl 3528 2862 3653 3950 Dl 5039 2862 4901 2862 Dl 5040 3545 5040 2862 Dl 4901 2862 4280 3489 Dl (88)4692 3342 w 3953 3777 3767 3928 Dl 3973 3755 3707 3930 Dl 4901 2862 3528 2862 Dl (91)3992 3268 w 20 R f 16 setlinewidth 5040 4878 3024 4878 Dl 5040 2862 5040 4878 Dl 3024 2862 5040 2862 Dl 3024 4878 3024 2862 Dl 3968 4073 4032 3870 Dl 3966 4073 3971 3999 Dl 3968 4073 4006 4010 Dl 10 B f (Fig. 132:)1 372 1 1030 5076 t 10 R f (pr. proj. it. 21,)3 575 1 1427 5076 t 10 I f (v)2027 5076 w 10 R f (=)2096 5076 w 10 I f (center)2177 5076 w 10 B f (Fig. 133:)1 372 1 3161 5076 t 10 R f (pr. proj. it. 21,)3 575 1 3558 5076 t 10 I f (v)4158 5076 w 10 R f (=)4227 5076 w 10 I f (center)4308 5076 w 10 S f (+)4557 5076 w 10 R f (\(.1,0,0\))4612 5076 w 0.1 setlinewidth 1699 6232 1 1 De 1701 6234 1700 6233 Dl 1703 6235 1702 6234 Dl 1704 6238 1702 6235 Dl 1699 6234 1699 6232 Dl 1704 6238 1699 6234 Dl 1738 6289 1621 6202 Dl 1743 6292 1738 6289 Dl 1750 6291 1744 6293 Dl 1750 6289 1705 6238 Dl 1699 6234 1621 6202 Dl 1586 6176 1553 6146 Dl 1597 6184 1587 6176 Dl 1621 6201 1598 6185 Dl 1685 6220 1553 6146 Dl 1695 6228 1685 6221 Dl 1697 6229 1696 6228 Dl 1698 6231 1697 6230 Dl 1758 6295 1750 6290 Dl 1778 6300 1758 6295 Dl 1779 6300 1702 6235 Dl 1785 6303 1785 6305 Dl 1784 6304 1779 6301 Dl 1786 6302 1702 6234 Dl 1791 6302 1789 6303 Dl 1789 6303 1786 6302 Dl 1791 6302 1700 6233 Dl 1799 6304 1792 6296 Dl 1799 6304 1792 6302 Dl 1792 6295 1699 6231 Dl 1792 6289 1780 6277 Dl 1792 6291 1792 6296 Dl 1779 6277 1697 6230 Dl 1781 6272 1751 6244 Dl 1780 6272 1780 6277 Dl 1750 6243 1696 6228 Dl 1684 6221 1677 6201 Dl 1748 6234 1685 6187 Dl 1750 6239 1748 6235 Dl 1679 6186 1677 6201 Dl 1685 6186 1680 6184 Dl 1751 6239 1751 6244 Dl 1778 6308 1758 6295 Dl 1803 6321 1779 6309 Dl 1802 6321 1785 6305 Dl 1818 6327 1810 6325 Dl 1808 6326 1802 6321 Dl 1817 6328 1816 6326 Dl 1815 6326 1789 6303 Dl 1821 6321 1816 6326 Dl 1821 6321 1800 6305 Dl 1841 6330 1836 6330 Dl 1840 6331 1807 6299 Dl 1834 6330 1821 6321 Dl 1806 6298 1793 6290 Dl 1817 6297 1801 6282 Dl 1817 6297 1807 6299 Dl 1801 6282 1781 6272 Dl 1803 6276 1801 6282 Dl 1802 6275 1751 6239 Dl 1681 6184 1679 6184 Dl 1684 6187 1681 6184 Dl 1679 6185 1679 6184 Dl 1666 6175 1663 6175 Dl 1677 6200 1665 6185 Dl 1679 6183 1667 6175 Dl 1664 6185 1663 6175 Dl 1844 6338 1 1 De 1844 6339 1829 6336 Dl 1829 6335 1818 6328 Dl 1844 6337 1836 6330 Dl 1881 6352 1854 6320 Dl 1881 6353 1844 6335 Dl 1854 6320 1818 6297 Dl 1844 6333 1840 6331 Dl 1774 6235 1765 6230 Dl 1789 6247 1774 6235 Dl 1810 6278 1790 6248 Dl 1763 6231 1748 6235 Dl 1810 6278 1803 6276 Dl 1844 6335 1844 6338 Dl 1871 6321 1810 6278 Dl 1871 6322 1854 6320 Dl 1711 6188 1704 6186 Dl 1683 6182 1681 6184 Dl 1696 6182 1684 6182 Dl 1765 6230 1712 6189 Dl 1704 6185 1697 6183 Dl 1820 6338 1803 6329 Dl 1804 6329 1779 6309 Dl 1821 6337 1810 6325 Dl 1835 6351 1820 6339 Dl 1848 6355 1836 6352 Dl 1848 6355 1829 6336 Dl 1876 6366 1864 6365 Dl 1863 6364 1848 6355 Dl 1875 6365 1845 6339 Dl 1906 6381 1906 6370 Dl 1907 6381 1879 6368 Dl 1879 6367 1877 6366 Dl 1905 6370 1882 6353 Dl 1908 6348 1880 6327 Dl 1918 6375 1910 6348 Dl 1918 6375 1906 6370 Dl 1880 6327 1872 6322 Dl 1860 6294 1848 6284 Dl 1847 6283 1790 6248 Dl 1880 6326 1860 6294 Dl 1703 6185 1697 6183 Dl 1697 6183 1 1 De 1655 6175 1650 6169 Dl 1663 6174 1650 6169 Dl 1665 6185 1655 6176 Dl 1849 6361 1838 6354 Dl 1876 6377 1848 6361 Dl 1837 6354 1836 6352 Dl 1876 6377 1864 6365 Dl 1901 6389 1882 6383 Dl 1882 6383 1877 6378 Dl 1901 6389 1879 6368 Dl 1956 6431 1912 6398 Dl 1957 6430 1929 6400 Dl 1911 6398 1901 6390 Dl 1929 6399 1907 6381 Dl 1975 6418 1962 6416 Dl 1962 6415 1929 6400 Dl 1975 6419 1918 6376 Dl 1994 6429 1959 6379 Dl 1993 6429 1976 6419 Dl 1958 6379 1933 6362 Dl 1933 6361 1910 6348 Dl 1920 6330 1907 6321 Dl 1906 6321 1860 6294 Dl 1932 6360 1920 6330 Dl 1851 6254 1841 6246 Dl 1841 6245 1775 6226 Dl 1775 6228 1774 6228 Dl 1850 6255 1848 6284 Dl 1774 6236 1774 6228 Dl 1711 6189 1703 6171 Dl 1773 6227 1703 6171 Dl 1697 6182 1666 6159 Dl 1684 6181 1666 6159 Dl 1764 6310 1744 6293 Dl 1804 6333 1764 6310 Dl 1804 6333 1803 6329 Dl 1840 6362 1838 6361 Dl 1838 6360 1805 6333 Dl 1841 6363 1838 6354 Dl 1889 6392 1848 6361 Dl 1890 6393 1882 6383 Dl 1911 6397 1891 6393 Dl 1890 6393 1 1 De 1966 6439 1962 6416 Dl 1966 6439 1956 6431 Dl 2154 6483 2107 6436 Dl 2107 6434 1920 6330 Dl 2155 6481 1959 6379 Dl 1881 6276 1851 6254 Dl 1907 6321 1882 6276 Dl 1718 6164 1685 6146 Dl 1703 6169 1685 6146 Dl 1775 6226 1719 6165 Dl 1659 6158 1658 6166 Dl 1663 6158 1658 6158 Dl 1667 6175 1658 6166 Dl 1664 6159 1663 6158 Dl 1552 6146 1529 6127 Dl 1655 6175 1529 6127 Dl 1865 6382 1841 6363 Dl 1894 6396 1866 6382 Dl 1893 6395 1891 6393 Dl 1991 6463 1962 6449 Dl 1962 6449 1893 6397 Dl 1992 6463 1967 6440 Dl 2039 6494 1992 6464 Dl 2041 6467 2039 6495 Dl 2041 6466 1993 6430 Dl 2236 6554 2154 6482 Dl 2237 6555 2042 6467 Dl 2107 6435 2089 6415 Dl 2090 6414 1882 6276 Dl 1803 6206 1719 6165 Dl 1841 6245 1803 6206 Dl 1663 6157 1648 6120 Dl 1685 6145 1648 6120 Dl 1789 6332 1764 6310 Dl 1820 6356 1789 6333 Dl 1838 6361 1821 6355 Dl 1963 6449 1961 6449 Dl 1961 6449 1884 6403 Dl 1884 6402 1866 6382 Dl 2361 6650 2237 6555 Dl 2362 6650 2096 6541 Dl 2095 6541 2039 6495 Dl 1968 6109 1888 6124 Dl 1887 6124 1803 6206 Dl 2089 6415 1969 6108 Dl 5 R f (65)1921 6249 w 10 R f 0.1 setlinewidth 1656 6166 1630 6156 Dl 1648 6169 1630 6156 Dl 1879 6404 1841 6376 Dl 1841 6375 1821 6355 Dl 1882 6404 1880 6405 Dl 1961 6467 1898 6424 Dl 1898 6423 1880 6405 Dl 1962 6467 1961 6449 Dl 2148 6608 2082 6570 Dl 2082 6570 1962 6468 Dl 2149 6607 2096 6541 Dl 2736 7012 2736 6912 Dl 2735 7011 2149 6608 Dl 2735 6912 2362 6650 Dl 5 R f (70)2433 6784 w 10 R f 0.1 setlinewidth 2735 5238 2682 5238 Dl 2736 6912 2736 5238 Dl 2682 5238 1969 6108 Dl (71)2408 6132 w 1887 6123 1627 6104 Dl 1647 6119 1627 6104 Dl 1627 6104 1610 6095 Dl 1658 6157 1610 6095 Dl 1528 6126 1524 6123 Dl 1595 6138 1524 6123 Dl 1630 6155 1596 6138 Dl 1820 6368 1799 6348 Dl 1798 6348 1789 6333 Dl 1840 6376 1820 6369 Dl 1962 6524 1944 6509 Dl 1943 6509 1845 6397 Dl 2017 6542 1962 6524 Dl 2017 6542 1871 6411 Dl 1870 6411 1845 6397 Dl 1596 6087 1596 6138 Dl 1608 6094 1596 6087 Dl 1845 6397 1833 6387 Dl 1832 6387 1820 6369 Dl 1898 6423 1871 6411 Dl 2082 6570 2018 6544 Dl 2736 7157 2736 7012 Dl 2735 7156 1962 6524 Dl (81)2386 6879 w 2681 5238 2129 5238 Dl 1596 6086 1494 6020 Dl 2129 5238 1494 6020 Dl (82)2011 5686 w 1765 6324 1738 6289 Dl 1799 6348 1766 6325 Dl 1772 6341 1758 6325 Dl 1765 6325 1758 6325 Dl 1832 6386 1772 6342 Dl 1766 6363 1738 6325 Dl 1773 6341 1738 6325 Dl 1943 6509 1766 6364 Dl 2736 7254 720 7254 Dl 2736 7159 2736 7254 Dl 720 7253 720 6163 Dl 1766 6363 1435 6092 Dl 720 6163 1435 6092 Dl (86)1444 6798 w 2129 5238 720 5238 Dl 720 5238 720 6163 Dl 1454 6069 1435 6092 Dl 1493 6021 1454 6069 Dl (87)1211 5652 w 1524 6123 1454 6069 Dl 1757 6325 1598 6185 Dl 1737 6325 1587 6176 Dl 20 R f 16 setlinewidth 2736 7254 720 7254 Dl 2736 5238 2736 7254 Dl 720 5238 2736 5238 Dl 720 7254 720 5238 Dl 10 R f 0.1 setlinewidth 4006 6233 1 1 De 4008 6235 4007 6234 Dl 4008 6236 4008 6235 Dl 4011 6238 4009 6236 Dl 4006 6235 4006 6233 Dl 4011 6239 4006 6235 Dl 4040 6285 3935 6206 Dl 4046 6288 4041 6285 Dl 4051 6287 4046 6289 Dl 4051 6285 4011 6239 Dl 4006 6235 3935 6206 Dl 3904 6183 3874 6156 Dl 3914 6190 3904 6183 Dl 3934 6206 3914 6191 Dl 3993 6223 3874 6156 Dl 4002 6230 3993 6223 Dl 4004 6231 4003 6230 Dl 4005 6233 4004 6232 Dl 4059 6290 4052 6286 Dl 4078 6295 4060 6290 Dl 4078 6295 4009 6236 Dl 4083 6297 4083 6299 Dl 4083 6297 4078 6295 Dl 4084 6296 4008 6235 Dl 4090 6296 4088 6297 Dl 4087 6298 4084 6297 Dl 4089 6295 4007 6234 Dl 4096 6298 4090 6291 Dl 4096 6298 4089 6296 Dl 4090 6291 4006 6233 Dl 4090 6285 4079 6274 Dl 4090 6286 4090 6291 Dl 4078 6274 4004 6232 Dl 4079 6269 4052 6244 Dl 4079 6269 4079 6274 Dl 4052 6244 4003 6230 Dl 3993 6223 3986 6205 Dl 4049 6236 3993 6193 Dl 4052 6240 4050 6236 Dl 3988 6191 3986 6205 Dl 3993 6193 3989 6191 Dl 4052 6240 4052 6244 Dl 4078 6302 4060 6290 Dl 4098 6312 4077 6302 Dl 4098 6314 4083 6299 Dl 4112 6320 4105 6318 Dl 4104 6317 4099 6313 Dl 4112 6319 4111 6318 Dl 4111 6317 4088 6297 Dl 4115 6314 4111 6318 Dl 4115 6314 4096 6299 Dl 4132 6322 4128 6322 Dl 4132 6323 4103 6294 Dl 4128 6322 4116 6314 Dl 4103 6293 4091 6286 Dl 4113 6291 4098 6279 Dl 4113 6293 4103 6294 Dl 4098 6278 4080 6269 Dl 4099 6274 4098 6279 Dl 4099 6272 4053 6240 Dl 3989 6189 3988 6189 Dl 3993 6192 3990 6190 Dl 3988 6190 3988 6189 Dl 3976 6181 3973 6181 Dl 3986 6205 3975 6191 Dl 3988 6188 3977 6181 Dl 3974 6190 3973 6181 Dl 4136 6329 1 1 De 4137 6329 4123 6326 Dl 4122 6326 4112 6320 Dl 4135 6328 4128 6322 Dl 4169 6341 4145 6312 Dl 4169 6340 4136 6325 Dl 4146 6312 4113 6292 Dl 4135 6325 4132 6323 Dl 4073 6236 4065 6232 Dl 4086 6247 4073 6237 Dl 4106 6274 4088 6248 Dl 4064 6233 4050 6236 Dl 4105 6275 4099 6273 Dl 4136 6326 4136 6329 Dl 4160 6314 4106 6275 Dl 4160 6313 4145 6312 Dl 4017 6194 4011 6192 Dl 3992 6188 3990 6190 Dl 4003 6188 3992 6188 Dl 4065 6232 4017 6194 Dl 4010 6191 4003 6189 Dl 4115 6328 4100 6320 Dl 4099 6320 4077 6302 Dl 4115 6329 4105 6318 Dl 4128 6341 4115 6330 Dl 4140 6343 4129 6341 Dl 4141 6343 4123 6326 Dl 4164 6354 4154 6353 Dl 4153 6352 4140 6344 Dl 4165 6354 4137 6330 Dl 4191 6367 4191 6357 Dl 4192 6367 4167 6355 Dl 4167 6355 4165 6354 Dl 4190 6356 4170 6341 Dl 4193 6337 4168 6318 Dl 4201 6362 4194 6338 Dl 4202 6362 4191 6357 Dl 4167 6318 4160 6314 Dl 4150 6288 4140 6279 Dl 4139 6279 4088 6248 Dl 4168 6318 4150 6289 Dl 4010 6191 4004 6189 Dl 4003 6189 1 1 De 3966 6181 3961 6176 Dl 3973 6181 3961 6176 Dl 3975 6190 3966 6182 Dl 4140 6349 4130 6343 Dl 4165 6364 4140 6349 Dl 4130 6342 4129 6341 Dl 4164 6364 4154 6353 Dl 4187 6374 4170 6369 Dl 4170 6368 4165 6364 Dl 4187 6374 4167 6355 Dl 4236 6411 4196 6382 Dl 4236 6412 4212 6384 Dl 4196 6381 4187 6374 Dl 4212 6383 4192 6367 Dl 4254 6400 4242 6398 Dl 4241 6398 4212 6384 Dl 4253 6400 4202 6362 Dl 4268 6409 4238 6365 Dl 4269 6409 4254 6400 Dl 4238 6365 4215 6350 Dl 4214 6350 4194 6338 Dl 4204 6321 4192 6313 Dl 4191 6313 4150 6289 Dl 4215 6350 4204 6322 Dl 4141 6253 4133 6246 Dl 4133 6245 4074 6228 Dl 4074 6229 4073 6229 Dl 4142 6253 4140 6279 Dl 4073 6236 4073 6229 Dl 4016 6194 4009 6178 Dl 4072 6229 4009 6178 Dl 4003 6188 3975 6168 Dl 3991 6188 3975 6168 Dl 4064 6304 4046 6289 Dl 4101 6324 4065 6304 Dl 4101 6324 4100 6320 Dl 4133 6350 4131 6349 Dl 4131 6349 4101 6325 Dl 4133 6351 4130 6343 Dl 4177 6377 4140 6349 Dl 4177 6377 4170 6369 Dl 4196 6382 4178 6378 Dl 4178 6377 1 1 De 4245 6418 4242 6398 Dl 4245 6419 4237 6412 Dl 4410 6456 4369 6415 Dl 4369 6414 4204 6322 Dl 4411 6456 4238 6365 Dl 4169 6272 4142 6253 Dl 4192 6313 4170 6273 Dl 4023 6172 3993 6156 Dl 4008 6177 3993 6156 Dl 4074 6227 4024 6173 Dl 3969 6167 3968 6174 Dl 3974 6166 3970 6166 Dl 3976 6181 3968 6174 Dl 3975 6167 3974 6166 Dl 3873 6156 3852 6138 Dl 3966 6182 3852 6138 Dl 4155 6368 4134 6351 Dl 4180 6380 4155 6368 Dl 4180 6380 4178 6378 Dl 4267 6440 4242 6428 Dl 4242 6427 4181 6381 Dl 4267 6439 4245 6419 Dl 4310 6468 4268 6441 Dl 4312 6443 4310 6468 Dl 4312 6442 4269 6410 Dl 4484 6519 4412 6456 Dl 4484 6520 4312 6443 Dl 4369 6415 4354 6397 Dl 4354 6396 4170 6273 Dl 4100 6209 4024 6173 Dl 4132 6245 4099 6210 Dl 3974 6165 3960 6132 Dl 3993 6155 3960 6132 Dl 4087 6323 4065 6304 Dl 4115 6343 4087 6323 Dl 4131 6349 4116 6344 Dl 4241 6428 4240 6428 Dl 4239 6428 4171 6387 Dl 4171 6386 4155 6368 Dl 4592 6603 4484 6520 Dl 4592 6603 4360 6509 Dl 4359 6509 4310 6468 Dl 4248 6123 4176 6136 Dl 4174 6137 4099 6210 Dl 4353 6396 4247 6122 Dl 5 R f (65)4202 6249 w 10 R f 0.1 setlinewidth 3968 6173 3944 6164 Dl 3961 6176 3944 6164 Dl 4169 6388 4134 6363 Dl 4134 6362 4116 6344 Dl 4171 6387 4169 6388 Dl 4241 6443 4185 6405 Dl 4184 6405 4169 6388 Dl 4240 6444 4240 6428 Dl 4407 6567 4348 6534 Dl 4348 6534 4241 6444 Dl 4407 6568 4360 6509 Dl 5040 7002 5040 6917 Dl 5039 7002 4407 6568 Dl 5039 6916 4592 6603 Dl 5 R f (70)4711 6762 w 10 R f 0.1 setlinewidth 5039 5238 4969 5238 Dl 5040 6917 5040 5238 Dl 4969 5238 4247 6122 Dl (71)4703 6130 w 4175 6136 3941 6118 Dl 3959 6132 3941 6118 Dl 3940 6117 3925 6109 Dl 3969 6165 3925 6109 Dl 3852 6138 3848 6135 Dl 3912 6149 3848 6135 Dl 3943 6163 3913 6148 Dl 4115 6356 4096 6338 Dl 4095 6337 4087 6323 Dl 4133 6362 4115 6356 Dl 4241 6495 4225 6482 Dl 4224 6482 4137 6382 Dl 4290 6511 4242 6495 Dl 4290 6511 4160 6394 Dl 4160 6394 4137 6382 Dl 4961 7253 3757 6284 Dl 3913 6102 3913 6148 Dl 3925 6109 3913 6102 Dl 4137 6381 4127 6372 Dl 4126 6372 4115 6356 Dl 4184 6405 4160 6394 Dl 4347 6534 4291 6511 Dl 5040 7146 5040 7003 Dl 5039 7146 4242 6495 Dl (81)4681 6863 w 4970 5238 4484 5238 Dl 3912 6103 3819 6042 Dl 4482 5238 3819 6042 Dl (82)4321 5695 w 4065 6316 4041 6285 Dl 4095 6337 4065 6317 Dl 4071 6333 4059 6318 Dl 4066 6318 4059 6318 Dl 4126 6372 4072 6332 Dl 4065 6352 4040 6318 Dl 4071 6332 4040 6318 Dl 4225 6481 4067 6352 Dl 5039 7254 4962 7254 Dl 5040 7147 5040 7254 Dl 4066 6352 3766 6107 Dl 3759 6284 3766 6107 Dl (86)4335 6720 w 3783 6086 3766 6107 Dl 3819 6042 3783 6085 Dl 3847 6134 3783 6085 Dl 4058 6317 3914 6191 Dl 4040 6317 3904 6183 Dl 20 R f 16 setlinewidth 5040 7254 3024 7254 Dl 5040 5238 5040 7254 Dl 3024 5238 5040 5238 Dl 3024 7254 3024 5238 Dl 3888 6378 4032 6246 Dl 3888 6377 3929 6316 Dl 3889 6378 3953 6343 Dl 10 B f (Fig. 134:)1 372 1 1030 7452 t 10 R f (pr. proj. it. 22,)3 575 1 1427 7452 t 10 I f (v)2027 7452 w 10 R f (=)2096 7452 w 10 I f (center)2177 7452 w 10 B f (Fig. 135:)1 372 1 3161 7452 t 10 R f (pr. proj. it. 22,)3 575 1 3558 7452 t 10 I f (v)4158 7452 w 10 R f (=)4227 7452 w 10 I f (center)4308 7452 w 10 S f (+)4557 7452 w 10 R f (\(.1,0,0\))4612 7452 w (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 35 36 %%Page: 36 37 /saveobj save def mark 37 pagesetup 10 R f (- 36 -)2 216 1 2772 480 t 10 B f (Views from ``Natural Variables'' \320 the)5 1699 1 720 840 t 10 BI f (Record)2444 840 w 10 B f (Pictures)2763 840 w 10 R f (In making the pictures on pages 6 and 7 of the)10 1847 1 970 996 t 10 I f (Record)2842 996 w 10 R f ( I used what I thought to be a ``natu-)9 1470(article [9],)1 415 2 3155 996 t (ral'')720 1116 w 10 I f (F)917 1116 w 10 R f ( invariance prop-)2 681(in \(16\) \320 rather than one with orthonormal columns; I hadn't yet thought about the)14 3355 2 1004 1116 t (erties that come with the latter)5 1222 1 720 1236 t 10 I f (F)1969 1236 w 10 R f (. \(The)1 265 1 2030 1236 t 10 I f (Record)2322 1236 w 10 R f ( two different linear program-)4 1203(pictures correspond to at least)4 1200 2 2637 1236 t (ming problems; I had asked that only one be used and had been told my request would be honored, but for-)20 4320 1 720 1356 t (got to double check this point when the proofs came around.\))10 2449 1 720 1476 t ( run of the primal projective algorithm as do figures 74\261135,)10 2502(The remaining figures depict the same)5 1568 2 970 1632 t ( the perspective of the variables in which I originally conceived the problem \(i.e., using the same)16 3884(but from)1 349 2 720 1752 t 10 I f (F)4979 1752 w 10 R f (as for the)2 393 1 720 1872 t 10 I f (Record)1149 1872 w 10 R f ( In)1 144( idea was to massage the constraints \(18\) and \(7\) into the form \(16\).)13 2849(pictures\). My)1 574 3 1473 1872 t (more detail, \(7a\) with)3 865 1 720 1997 t 10 I f (A)1610 1997 w 10 R f (as in \(18\) is of the form)6 943 1 1696 1997 t 10 I f (Bx)2664 1997 w 11 R f (\303)2731 1992 w 10 S f (=)2818 1997 w 10 I f (e)2922 1997 w 7 I f (m)2977 2017 w 7 S f (+)3043 2017 w 7 R f (1)3093 2017 w 10 R f (, where)1 293 1 3136 1997 t (\(19\))720 2362 w 10 I f (B)2138 2362 w 10 S f (=)2248 2362 w (\351)2360 2175 w (\357)2360 2275 w (\357)2360 2375 w (\357)2360 2475 w (\353)2360 2575 w 10 I f (e)2502 2562 w 7 R f (T)2557 2522 w 10 B f (0)2521 2432 w 10 I f (D)2492 2312 w 7 R f (1)2575 2332 w 10 I f (A)2410 2192 w 10 S f (\260)2471 2192 w 7 R f (T)2516 2152 w 10 I f (D)2575 2192 w 7 R f (1)2658 2212 w 10 I f (e)2785 2562 w 7 R f (T)2840 2522 w 10 I f (D)2775 2432 w 7 R f (2)2858 2452 w 10 B f (0)2803 2312 w 10 I f (D)2778 2192 w 7 R f (2)2855 2211 w 10 I f (e)2985 2562 w 7 R f (T)3040 2522 w 10 B f (0)3003 2432 w 10 I f (D)2975 2312 w 7 R f (3)3058 2332 w 10 B f (0)3006 2192 w 10 I f (e)3185 2562 w 7 R f (T)3240 2522 w 10 I f (D)3175 2432 w 7 R f (4)3258 2452 w 10 B f (0)3203 2312 w (0)3206 2192 w 10 R f (1)3431 2562 w 10 S f (-)3375 2432 w 10 I f (u)3446 2432 w 7 R f (2)3507 2452 w 10 S f (-)3375 2312 w 10 I f (u)3446 2312 w 7 R f (1)3507 2332 w 10 S f (-)3395 2192 w 10 I f (b)3466 2192 w 10 S f (\371)3550 2175 w (\357)3550 2275 w (\357)3550 2375 w (\357)3550 2475 w (\373)3550 2575 w 10 I f (.)3596 2362 w 10 R f (Here)720 2747 w 10 I f (D)939 2747 w 10 R f (is the diagonal matrix)3 872 1 1037 2747 t 10 I f (D)1936 2747 w 10 S f (=)2057 2747 w 10 R f (diag \()1 213 1 2161 2747 t 10 I f (D)2382 2747 w 7 R f (1)2465 2767 w 10 R f (,)2516 2747 w 10 I f (D)2582 2747 w 7 R f (2)2665 2767 w 10 R f (,)2716 2747 w 10 I f (D)2782 2747 w 7 R f (3)2865 2767 w 10 R f (,)2916 2747 w 10 I f (D)2982 2747 w 7 R f (4)3065 2767 w 10 R f (\), with)1 263 1 3116 2747 t 10 I f (D)3406 2747 w 7 R f (1)3489 2767 w 10 R f (,)3540 2747 w 10 I f (D)3606 2747 w 7 R f (3)3689 2767 w 10 S f (\316)3773 2747 w 10 I f (I R)1 78 1 3885 2747 t 7 R f (3)3968 2707 w 7 S f (\264)4008 2707 w 7 R f (3)4052 2707 w 10 R f (and)4122 2747 w 10 I f (D)4293 2747 w 7 R f (2)4376 2767 w 10 R f (,)4427 2747 w 10 I f (D)4493 2747 w 7 R f (4)4576 2767 w 10 S f (\316)4660 2747 w 10 I f (I R)1 78 1 4772 2747 t 7 I f (m)4855 2707 w 7 S f (\264)4910 2707 w 7 I f (m)4954 2707 w 10 R f (;)5012 2747 w 10 I f (u)720 2867 w 7 R f (1)781 2887 w 10 S f (\316)865 2867 w 10 I f (I R)1 78 1 977 2867 t 7 R f (3)1060 2827 w 10 R f (and)1137 2867 w 10 I f (u)1315 2867 w 7 R f (2)1376 2887 w 10 S f (\316)1460 2867 w 10 I f (I R)1 78 1 1572 2867 t 7 I f (m)1655 2827 w 10 R f ( row operations on)3 770( doing)1 262( By)1 176(are upper bound vectors.)3 1013 4 1747 2867 t 10 I f (B)4001 2867 w 10 R f (, we may first eliminate)4 978 1 4062 2867 t ( \(4,4\) blocks, and finally the \(1,5\), \(2,5\), and \(3,5\) blocks to)11 2407(the \(3,2\) block of \(19\), then the \(4,2\), \(4,3\), and)9 1913 2 720 2987 t (obtain)720 3107 w 10 I f (F)1005 3107 w 10 R f (in \(16\); the)2 464 1 1101 3107 t 10 I f (f)1600 3107 w 10 R f ( from doing the corresponding row operations to the right-hand side)10 2803(of \(16\) comes)2 574 2 1663 3107 t 10 I f (e)720 3227 w 7 I f (m)775 3247 w 7 S f (+)841 3247 w 7 R f (1)891 3247 w 10 R f ( this)1 177(. With)1 282 2 934 3227 t 10 I f (F)1426 3227 w 10 R f (and)1520 3227 w 10 I f (f)1697 3227 w 10 R f (, we get interesting views by looking forwards and backwards in the direction of)13 3315 1 1725 3227 t ( \(When)1 322(the current step.)2 642 2 720 3347 t 10 I f (F)1710 3347 w 10 R f ( it)1 81(is orthogonal, such forward and backward view directions swing so wildly that)11 3162 2 1797 3347 t ( phase-2)1 342( 136\261177 show these views for all 21)7 1532( Figures)1 356(is hard to make sense out of the resulting pictures.\))9 2090 4 720 3467 t ( forward views, and the odd-numbered ones are corresponding)8 2616(iterations; the even-numbered figures are)4 1704 2 720 3587 t ( the first three iterations)4 994( In)1 143(backward views, all from the center of the projectively transformed polytope.)10 3183 3 720 3707 t ( binding at the solution \320 are)6 1272( the unimportant constraints \320 those not)6 1717( Then)1 269(the view changes rapidly.)3 1062 4 720 3827 t (pushed further and further behind, until they are no longer visible in the final two iterations.)15 3670 1 720 3947 t 0.1 setlinewidth 720 4109 2062 4109 Dl 720 6125 1766 6125 Dl 2736 4286 2736 5133 Dl 720 4109 720 6125 Dl 1767 6124 2736 5133 Dl 2063 4109 2736 4286 Dl (4)1596 5060 w 2735 4109 2062 4109 Dl 2736 4109 2736 4286 Dl 5 R f (5)2499 4178 w 10 R f 0.1 setlinewidth 2735 6125 1766 6125 Dl 2736 6124 2736 5133 Dl (7)2387 5814 w 20 R f 16 setlinewidth 2736 6125 720 6125 Dl 2736 4109 2736 6125 Dl 720 4109 2736 4109 Dl 720 6125 720 4109 Dl 10 R f 0.1 setlinewidth 3877 6125 3178 6125 Dl 3864 6059 3877 6125 Dl 3864 6059 3178 6125 Dl 5 R f (7)3628 6112 w 10 R f 0.1 setlinewidth 3178 6125 3024 6125 Dl 3024 5531 3024 6125 Dl 3835 5652 3881 5898 Dl 3880 5899 3864 6058 Dl 3835 5651 3024 5531 Dl (8)3391 5865 w 3024 5133 3024 5531 Dl 3846 5389 3848 5540 Dl 3847 5540 3835 5651 Dl 3846 5387 3024 5132 Dl (9)3382 5440 w 3024 4830 3024 5132 Dl 3866 5196 3877 5291 Dl 3878 5291 3846 5388 Dl 3866 5195 3024 4830 Dl (10)3366 5147 w 3024 4498 3024 4830 Dl 3911 5002 3911 5073 Dl 3910 5073 3866 5195 Dl 3910 5001 3024 4497 Dl (11)3378 4886 w 3024 4498 3024 4167 Dl 3995 4849 3960 4949 Dl 3960 4950 3910 5001 Dl 3996 4850 3024 4167 Dl (12)3406 4626 w 3489 4109 3024 4109 Dl 3024 4167 3024 4109 Dl 4095 4652 3489 4109 Dl 4045 4831 4124 4727 Dl 4044 4832 4029 4840 Dl 4128 4718 4096 4652 Dl 4124 4727 4128 4718 Dl 4029 4840 3996 4850 Dl (13)3560 4442 w 4180 6125 3877 6125 Dl 4092 5867 4182 6125 Dl 4091 5867 3881 5898 Dl 5 R f (14)3983 6021 w 10 R f 0.1 setlinewidth 4052 5558 4106 5775 Dl 4106 5776 4091 5866 Dl 4033 5533 4052 5558 Dl 4032 5532 3848 5540 Dl (15)3916 5731 w 3966 5294 4032 5532 Dl 3965 5293 3877 5291 Dl 5 R f (16)3901 5437 w 10 R f 0.1 setlinewidth 4016 5210 4006 5261 Dl 3954 5077 4016 5210 Dl 4005 5262 3967 5293 Dl 3952 5076 3911 5073 Dl 5 R f (17)3911 5206 w 10 R f 0.1 setlinewidth 4008 4957 4016 4995 Dl 4015 4995 3952 5077 Dl 4007 4955 3960 4949 Dl 4045 4922 4008 4956 Dl 4044 4920 4029 4840 Dl 4131 4722 4131 4718 Dl 4129 4723 4124 4727 Dl 4130 4718 4128 4718 Dl 4149 4664 4096 4652 Dl 4153 4703 4158 4691 Dl 4130 4718 4152 4703 Dl 4157 4690 4149 4664 Dl 4035 5265 4039 5268 Dl 4039 5269 4075 5454 Dl 4075 5456 4052 5558 Dl 4034 5264 4006 5261 Dl 5 R f (22)4002 5399 w 10 R f 0.1 setlinewidth 4070 5004 4093 5093 Dl 4091 5093 4026 5207 Dl 4068 5003 4016 4995 Dl 4026 5207 4016 5210 Dl 5 R f (23)4001 5101 w 10 R f 0.1 setlinewidth 4108 4844 4104 4837 Dl 4107 4861 4109 4845 Dl 4106 4863 4060 4919 Dl 4104 4836 4044 4831 Dl 4060 4919 4045 4921 Dl 4027 5207 4034 5265 Dl 4098 4969 4060 4919 Dl 4097 4969 4068 5003 Dl 4148 4783 4148 4775 Dl 4139 4735 4130 4723 Dl 4148 4764 4140 4736 Dl 4104 4837 4147 4783 Dl 4148 4774 4148 4764 Dl 4182 6125 4485 6125 Dl 4278 5737 4472 6046 Dl 4473 6047 4485 6125 Dl 4277 5737 4106 5775 Dl (28)4220 5974 w 4313 5605 4277 5736 Dl 4198 5431 4314 5605 Dl 4196 5431 4075 5454 Dl 5 R f (29)4150 5615 w 10 R f 0.1 setlinewidth 4138 5252 4194 5349 Dl 4194 5349 4197 5431 Dl 4137 5252 4039 5268 Dl 5 R f (30)4094 5364 w 10 R f 0.1 setlinewidth 4123 5089 4151 5149 Dl 4150 5149 4140 5246 Dl 4140 5247 4137 5252 Dl 4122 5089 4093 5093 Dl 4108 4968 4128 4982 Dl 4128 4982 4134 5068 Dl 4134 5068 4122 5088 Dl 4106 4968 4098 4969 Dl 4135 4897 4135 4907 Dl 4135 4896 4106 4862 Dl 4135 4907 4107 4967 Dl 4149 4774 4150 4766 Dl 4149 4766 4148 4764 Dl 4185 4661 4149 4664 Dl 4186 4661 1 1 De 4159 4690 4187 4661 Dl 4308 5487 4330 5597 Dl 4256 5334 4308 5487 Dl 4330 5596 4314 5605 Dl 4256 5334 4194 5349 Dl 5 R f (36)4234 5463 w 10 R f 0.1 setlinewidth 4211 5229 4268 5321 Dl 4268 5321 4256 5333 Dl 4210 5229 4140 5246 Dl 4255 5159 4227 5213 Dl 4190 5140 4255 5158 Dl 4226 5214 4211 5229 Dl 4189 5140 4151 5149 Dl 4190 5055 4196 5082 Dl 4196 5083 4189 5140 Dl 4190 5055 4134 5068 Dl 4166 4977 4199 5045 Dl 4199 5046 4190 5055 Dl 4149 4977 4167 4977 Dl 4148 4977 4128 4982 Dl 4165 4916 4170 4921 Dl 4136 4908 4166 4916 Dl 4170 4922 4149 4977 Dl 4189 4863 4190 4858 Dl 4190 4857 4144 4838 Dl 4143 4838 4137 4838 Dl 4188 4863 4135 4896 Dl 4137 4838 4109 4845 Dl 4179 4784 4147 4783 Dl 4138 4838 4180 4784 Dl 4150 4766 4183 4739 Dl 4183 4738 4140 4736 Dl 4486 6125 4772 6125 Dl 4636 6001 4772 6125 Dl 4472 6046 4635 6000 Dl 5 R f (45)4578 6086 w 10 R f 0.1 setlinewidth 4475 5580 4497 5597 Dl 4498 5598 4635 6000 Dl 4330 5596 4474 5581 Dl (46)4403 5823 w 4308 5311 4308 5487 Dl 4269 5320 4308 5310 Dl 4228 5214 4310 5309 Dl 4310 5309 4308 5310 Dl 4198 5082 4266 5153 Dl 4265 5153 4255 5158 Dl 4225 4926 4230 4944 Dl 4171 4921 4225 4926 Dl 4230 4945 4167 4977 Dl 4190 4864 4194 4875 Dl 4193 4875 4166 4916 Dl 4202 4800 4204 4780 Dl 4181 4784 4204 4780 Dl 4145 4838 4201 4801 Dl 4186 4727 4174 4701 Dl 4185 4737 4187 4728 Dl 4173 4701 4152 4703 Dl 4183 4738 4185 4738 Dl 4430 5413 4474 5581 Dl 4322 5306 4430 5412 Dl 4310 5308 4321 5305 Dl 5 R f (55)4350 5484 w 10 R f 0.1 setlinewidth 4294 5145 4330 5183 Dl 4329 5183 4321 5305 Dl 4266 5152 4294 5145 Dl 4294 5099 4294 5145 Dl 4229 5038 4293 5099 Dl 4201 5045 4229 5037 Dl 4231 4945 4249 4960 Dl 4249 4960 4229 5037 Dl 4225 4917 4225 4926 Dl 4194 4875 4226 4917 Dl 4208 4837 4201 4801 Dl 4191 4858 4209 4838 Dl 4222 4761 4185 4738 Dl 4204 4780 4222 4761 Dl 4773 6125 5040 6125 Dl 5040 5858 5040 6125 Dl 4725 5628 5040 5857 Dl 4498 5598 4724 5628 Dl (62)4739 5900 w 4331 5183 4338 5184 Dl 4338 5184 4480 5307 Dl 4480 5307 4430 5412 Dl 5 R f (63)4367 5309 w 10 R f 0.1 setlinewidth 4248 4960 4276 4960 Dl 4277 4959 4322 5063 Dl 4321 5064 4293 5099 Dl 4279 4838 4286 4840 Dl 4209 4837 4278 4837 Dl 4227 4916 4286 4840 Dl 4174 4702 4227 4648 Dl 4186 4661 4227 4648 Dl 4521 5293 4647 5391 Dl 4647 5391 4724 5628 Dl 4479 5307 4520 5292 Dl 5 R f (67)4539 5485 w 10 R f 0.1 setlinewidth 4433 5147 4520 5217 Dl 4520 5218 4520 5292 Dl 4338 5184 4433 5147 Dl 4385 5038 4420 5052 Dl 4420 5053 4433 5147 Dl 4322 5063 4384 5038 Dl 4354 4928 4384 5038 Dl 4276 4959 4353 4927 Dl 4286 4839 4322 4837 Dl 4354 4926 4356 4924 Dl 4323 4838 4356 4924 Dl 4278 4837 4237 4754 Dl 4223 4760 4237 4754 Dl 4238 4754 4248 4746 Dl 4248 4745 4187 4728 Dl 4186 4661 4258 4628 Dl 4228 4648 4258 4628 Dl 5040 5661 5040 5857 Dl 4763 5297 4899 5394 Dl 4900 5395 5040 5661 Dl 4647 5389 4762 5297 Dl (75)4803 5579 w 4525 4992 4534 4992 Dl 4535 4992 4669 5165 Dl 4480 5023 4525 4991 Dl 4480 5024 4599 5182 Dl 4600 5181 4669 5165 Dl 4322 4837 4412 4847 Dl 4411 4848 4404 4906 Dl 4356 4924 4404 4906 Dl 4260 4627 4311 4597 Dl 4259 4741 4311 4597 Dl 4248 4746 4258 4741 Dl 4669 5166 4703 5181 Dl 4703 5181 4762 5297 Dl 4521 5217 4599 5182 Dl 5 R f (79)4612 5279 w 10 R f 0.1 setlinewidth 4420 5052 4479 5024 Dl 5 R f (80)4472 5135 w 10 R f 0.1 setlinewidth 4405 4906 4525 4991 Dl 4294 4732 4330 4742 Dl 4259 4739 4294 4732 Dl 4323 4837 4330 4742 Dl 5040 5332 5040 5661 Dl 4900 5395 5040 5332 Dl 5 R f (83)4968 5472 w 10 R f 0.1 setlinewidth 5040 5242 5040 5332 Dl 4843 5107 4969 5148 Dl 4970 5148 5040 5240 Dl 4704 5180 4843 5106 Dl 5 R f (84)4860 5255 w 10 R f 0.1 setlinewidth 4624 4939 4740 4960 Dl 4740 4959 4843 5106 Dl 4534 4992 4623 4938 Dl 5 R f (85)4665 5062 w 10 R f 0.1 setlinewidth 4461 4814 4552 4814 Dl 4552 4815 4623 4938 Dl 4412 4847 4460 4815 Dl 5 R f (86)4485 4906 w 10 R f 0.1 setlinewidth 4331 4740 4428 4715 Dl 4461 4814 4428 4715 Dl 4311 4597 4313 4595 Dl 4294 4732 4313 4595 Dl 5040 5107 5040 5240 Dl 4970 5147 5040 5106 Dl 5040 4746 5040 5106 Dl 4741 4959 5040 4746 Dl (90)4877 4992 w 5040 4746 5040 4413 Dl 4553 4814 5040 4413 Dl (91)4783 4748 w 5040 4412 5040 4160 Dl 4428 4715 5040 4160 Dl (92)4712 4544 w 4797 4109 5040 4109 Dl 5040 4160 5040 4109 Dl 4313 4595 4796 4109 Dl (93)4599 4416 w 4796 4109 3489 4109 Dl (94)4105 4329 w 20 R f 16 setlinewidth 5040 6125 3024 6125 Dl 5040 4109 5040 6125 Dl 3024 4109 5040 4109 Dl 3024 6125 3024 4109 Dl 10 B f (Fig. 136:)1 372 1 929 6323 t 10 R f (pr.p.it. 2,)1 364 1 1326 6323 t 10 I f (d)1715 6323 w 10 S f (=)1790 6323 w 10 I f (ahead)1870 6323 w 10 R f (, nat. vars.)2 413 1 2114 6323 t 10 B f (Fig. 137:)1 372 1 3219 6323 t 10 R f (pr.p.it. 2,)1 364 1 3616 6323 t 10 I f (d)4005 6323 w 10 S f (=)4080 6323 w 10 I f (behind)4160 6323 w 10 R f (, nat. vars.)2 413 1 4432 6323 t (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 36 37 %%Page: 37 38 /saveobj save def mark 38 pagesetup 10 R f (- 37 -)2 216 1 2772 282 t 0.1 setlinewidth 720 486 2736 486 Dl 720 2502 2736 2502 Dl 2736 486 2736 2502 Dl 720 486 720 2502 Dl (5)1703 1514 w 20 R f 16 setlinewidth 2736 2502 720 2502 Dl 2736 486 2736 2502 Dl 720 486 2736 486 Dl 720 2502 720 486 Dl 10 R f 0.1 setlinewidth 5040 2502 3024 2502 Dl 5040 1263 5040 2502 Dl 3024 1806 3024 2502 Dl 5040 1262 3024 1805 Dl (45)4076 2025 w 5040 1261 5040 876 Dl 3024 1805 3024 1355 Dl 5040 877 3024 1355 Dl (83)3955 1352 w 5040 486 3024 486 Dl 5040 876 5040 486 Dl 3024 1355 3024 486 Dl (89)3854 836 w 20 R f 16 setlinewidth 5040 2502 3024 2502 Dl 5040 486 5040 2502 Dl 3024 486 5040 486 Dl 3024 2502 3024 486 Dl 10 B f (Fig. 138:)1 372 1 929 2700 t 10 R f (pr.p.it. 3,)1 364 1 1326 2700 t 10 I f (d)1715 2700 w 10 S f (=)1790 2700 w 10 I f (ahead)1870 2700 w 10 R f (, nat. vars.)2 413 1 2114 2700 t 10 B f (Fig. 139:)1 372 1 3219 2700 t 10 R f (pr.p.it. 3,)1 364 1 3616 2700 t 10 I f (d)4005 2700 w 10 S f (=)4080 2700 w 10 I f (behind)4160 2700 w 10 R f (, nat. vars.)2 413 1 4432 2700 t 0.1 setlinewidth 720 2862 2736 2862 Dl 2736 2862 2736 3670 Dl 720 2862 720 3710 Dl 2736 3671 720 3710 Dl (5)1695 3296 w 2736 4878 720 4878 Dl 2736 4877 2736 3670 Dl 720 4877 720 3710 Dl (89)1683 4304 w 20 R f 16 setlinewidth 2736 4878 720 4878 Dl 2736 2862 2736 4878 Dl 720 2862 2736 2862 Dl 720 4878 720 2862 Dl 10 R f 0.1 setlinewidth 5040 4474 5040 3787 Dl 3024 4381 3024 3798 Dl 3024 4383 5040 4474 Dl 3024 3799 5040 3787 Dl (2)4034 4131 w 3024 2862 5040 2862 Dl 5040 3787 5040 2862 Dl 3024 3798 3024 2862 Dl (5)4004 3347 w 3024 4878 5040 4878 Dl 5040 4475 5040 4878 Dl 3024 4383 3024 4878 Dl (7)3972 4672 w 20 R f 16 setlinewidth 5040 4878 3024 4878 Dl 5040 2862 5040 4878 Dl 3024 2862 5040 2862 Dl 3024 4878 3024 2862 Dl 10 B f (Fig. 140:)1 372 1 929 5076 t 10 R f (pr.p.it. 4,)1 364 1 1326 5076 t 10 I f (d)1715 5076 w 10 S f (=)1790 5076 w 10 I f (ahead)1870 5076 w 10 R f (, nat. vars.)2 413 1 2114 5076 t 10 B f (Fig. 141:)1 372 1 3219 5076 t 10 R f (pr.p.it. 4,)1 364 1 3616 5076 t 10 I f (d)4005 5076 w 10 S f (=)4080 5076 w 10 I f (behind)4160 5076 w 10 R f (, nat. vars.)2 413 1 4432 5076 t 0.1 setlinewidth 720 5238 2736 5238 Dl 2736 5238 2736 5743 Dl 720 5238 720 5919 Dl 2736 5745 720 5919 Dl (5)1653 5556 w 2736 7254 720 7254 Dl 2736 7253 2736 5743 Dl 720 7253 720 5919 Dl (89)1698 6561 w 20 R f 16 setlinewidth 2736 7254 720 7254 Dl 2736 5238 2736 7254 Dl 720 5238 2736 5238 Dl 720 7254 720 5238 Dl 10 R f 0.1 setlinewidth 5040 6580 5040 6060 Dl 3024 6463 3024 6007 Dl 3024 6464 5040 6580 Dl 3024 6008 5040 6060 Dl (2)4029 6299 w 3024 5238 5040 5238 Dl 5040 6060 5040 5238 Dl 3024 6007 3024 5238 Dl (5)4017 5656 w 3024 7254 5040 7254 Dl 5040 6581 5040 7254 Dl 3024 6465 3024 7254 Dl (7)3980 6907 w 20 R f 16 setlinewidth 5040 7254 3024 7254 Dl 5040 5238 5040 7254 Dl 3024 5238 5040 5238 Dl 3024 7254 3024 5238 Dl 10 B f (Fig. 142:)1 372 1 929 7452 t 10 R f (pr.p.it. 5,)1 364 1 1326 7452 t 10 I f (d)1715 7452 w 10 S f (=)1790 7452 w 10 I f (ahead)1870 7452 w 10 R f (, nat. vars.)2 413 1 2114 7452 t 10 B f (Fig. 143:)1 372 1 3219 7452 t 10 R f (pr.p.it. 5,)1 364 1 3616 7452 t 10 I f (d)4005 7452 w 10 S f (=)4080 7452 w 10 I f (behind)4160 7452 w 10 R f (, nat. vars.)2 413 1 4432 7452 t (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 37 38 %%Page: 38 39 /saveobj save def mark 39 pagesetup 10 R f (- 38 -)2 216 1 2772 282 t 0.1 setlinewidth 720 486 2409 486 Dl 720 486 720 1851 Dl 720 1850 783 1827 Dl 801 1817 783 1827 Dl 820 1806 802 1817 Dl 850 1783 820 1805 Dl 905 1740 851 1782 Dl 2409 486 905 1740 Dl (5)1259 974 w 720 1934 720 1935 Dl 720 1935 1 1 De 720 1934 1 1 De 720 1935 720 1938 Dl 720 1936 1 1 De 720 1938 720 1937 Dl 720 1933 721 1933 Dl 720 1934 1 1 De 720 1944 1 1 De 720 1944 1 1 De 720 1942 720 1940 Dl 721 1940 720 1940 Dl 720 1943 722 1941 Dl 720 1939 720 1940 Dl 721 1937 722 1937 Dl 720 1939 722 1937 Dl 722 1935 721 1936 Dl 720 1935 722 1935 Dl 720 1946 720 1944 Dl 722 1944 1 1 De 722 1944 720 1944 Dl 720 1946 722 1945 Dl 720 1943 720 1942 Dl 721 1943 722 1941 Dl 722 1938 1 1 De 723 1936 1 1 De 720 1940 722 1938 Dl 722 1935 1 1 De 721 1934 1 1 De 720 1949 720 1946 Dl 722 1945 1 1 De 720 1950 722 1946 Dl 722 1943 722 1941 Dl 722 1939 722 1938 Dl 722 1940 722 1939 Dl 723 1936 724 1936 Dl 723 1936 1 1 De 720 1954 720 1950 Dl 722 1946 1 1 De 721 1952 722 1946 Dl 720 1953 721 1952 Dl 724 1939 722 1939 Dl 723 1943 725 1939 Dl 722 1932 721 1934 Dl 722 1933 721 1933 Dl 720 1963 720 1959 Dl 720 1963 720 1958 Dl 720 1959 1 1 De 720 1959 720 1954 Dl 723 1952 723 1951 Dl 721 1957 723 1952 Dl 723 1951 721 1952 Dl 723 1951 725 1944 Dl 724 1945 722 1946 Dl 725 1939 1 1 De 726 1944 726 1939 Dl 724 1938 724 1935 Dl 723 1935 725 1935 Dl 723 1932 721 1933 Dl 722 1932 1 1 De 724 1960 727 1949 Dl 726 1950 725 1951 Dl 723 1961 725 1951 Dl 723 1962 722 1962 Dl 727 1940 726 1939 Dl 727 1942 728 1940 Dl 726 1944 725 1944 Dl 725 1930 724 1931 Dl 725 1931 725 1935 Dl 720 1970 720 1963 Dl 723 1963 723 1962 Dl 720 1969 723 1962 Dl 722 1962 720 1963 Dl 724 1951 723 1952 Dl 727 1950 727 1944 Dl 726 1934 1 1 De 725 1935 1 1 De 726 1935 726 1939 Dl 720 1977 720 1975 Dl 720 1976 720 1974 Dl 720 1975 1 1 De 720 1974 720 1970 Dl 725 1964 725 1960 Dl 721 1974 725 1964 Dl 725 1960 723 1962 Dl 729 1950 729 1948 Dl 727 1960 729 1951 Dl 729 1948 727 1949 Dl 729 1940 729 1939 Dl 729 1947 730 1940 Dl 729 1939 728 1940 Dl 729 1935 727 1935 Dl 729 1939 729 1934 Dl 726 1930 726 1934 Dl 2735 486 2409 486 Dl 2736 2502 720 2502 Dl 2736 2502 2736 486 Dl 720 2501 720 1977 Dl 905 1740 725 1964 Dl (89)1865 1736 w 851 1783 729 1951 Dl 820 1805 730 1940 Dl 801 1817 729 1934 Dl 782 1828 725 1930 Dl 720 1850 720 1933 Dl 20 R f 16 setlinewidth 2736 2502 720 2502 Dl 2736 486 2736 2502 Dl 720 486 2736 486 Dl 720 2502 720 486 Dl 10 R f 0.1 setlinewidth 5039 2502 3386 2502 Dl 5040 2501 5040 1668 Dl 3024 1827 3024 803 Dl 3386 2501 3024 1828 Dl 5040 1667 3024 803 Dl (4)3931 1842 w 3024 486 5040 486 Dl 5040 1668 5040 486 Dl 3024 803 3024 486 Dl (5)4200 922 w 3386 2502 3024 2502 Dl 3024 1829 3024 2502 Dl (89)3094 2297 w 20 R f 16 setlinewidth 5040 2502 3024 2502 Dl 5040 486 5040 2502 Dl 3024 486 5040 486 Dl 3024 2502 3024 486 Dl 10 B f (Fig. 144:)1 372 1 929 2700 t 10 R f (pr.p.it. 6,)1 364 1 1326 2700 t 10 I f (d)1715 2700 w 10 S f (=)1790 2700 w 10 I f (ahead)1870 2700 w 10 R f (, nat. vars.)2 413 1 2114 2700 t 10 B f (Fig. 145:)1 372 1 3219 2700 t 10 R f (pr.p.it. 6,)1 364 1 3616 2700 t 10 I f (d)4005 2700 w 10 S f (=)4080 2700 w 10 I f (behind)4160 2700 w 10 R f (, nat. vars.)2 413 1 4432 2700 t 0.1 setlinewidth 720 2862 2391 2862 Dl 720 2862 720 4446 Dl 720 4445 1696 3889 Dl 1721 3871 1696 3889 Dl 1741 3853 1721 3871 Dl 1769 3824 1741 3854 Dl 1810 3769 1769 3823 Dl 2391 2862 1810 3769 Dl (5)1319 3475 w 720 4878 1126 4878 Dl 720 4877 720 4613 Dl 1126 4877 1308 4582 Dl 1309 4582 1575 4132 Dl 720 4612 1575 4132 Dl (7)1059 4611 w 720 4612 720 4575 Dl 1584 4120 1591 4105 Dl 1576 4132 1584 4121 Dl 720 4575 1591 4105 Dl 5 R f (8)1088 4394 w 10 R f 0.1 setlinewidth 720 4574 720 4543 Dl 1598 4095 1605 4083 Dl 1592 4105 1598 4096 Dl 720 4543 1605 4083 Dl 5 R f (9)1093 4366 w 10 R f 0.1 setlinewidth 720 4543 720 4518 Dl 1614 4072 1616 4066 Dl 1606 4083 1613 4073 Dl 720 4517 1616 4066 Dl 5 R f (10)1085 4341 w 10 R f 0.1 setlinewidth 720 4517 720 4489 Dl 1625 4053 1626 4048 Dl 1617 4065 1625 4053 Dl 720 4489 1626 4048 Dl 5 R f (11)1088 4319 w 10 R f 0.1 setlinewidth 720 4467 720 4489 Dl 1632 4040 1636 4033 Dl 1626 4049 1632 4042 Dl 720 4467 1636 4033 Dl 720 4447 720 4467 Dl 720 4447 1640 4023 Dl 1641 4028 1646 4021 Dl 1640 4030 1641 4029 Dl 1640 4022 1646 4021 Dl 1637 4033 1640 4031 Dl 1309 4582 1557 4188 Dl 1557 4187 1599 4111 Dl 1584 4120 1599 4111 Dl 1606 4103 1613 4088 Dl 1599 4111 1604 4104 Dl 1613 4088 1613 4087 Dl 1598 4095 1613 4087 Dl 1614 4086 1621 4068 Dl 1614 4072 1621 4068 Dl 1627 4064 1629 4059 Dl 1628 4058 1628 4051 Dl 1621 4068 1626 4064 Dl 1625 4053 1628 4051 Dl 1637 4041 1637 4039 Dl 1629 4051 1637 4041 Dl 1633 4041 1637 4039 Dl 1637 4038 1641 4034 Dl 1641 4031 1641 4034 Dl 1640 4022 1645 4020 Dl 1648 4020 1647 4021 Dl 1646 4019 1648 4019 Dl 1621 4078 1628 4063 Dl 1613 4088 1620 4079 Dl 1625 4062 1627 4062 Dl 1640 4045 1641 4039 Dl 1631 4058 1640 4046 Dl 1637 4041 1641 4039 Dl 1630 4058 1 1 De 1647 4027 1647 4026 Dl 1643 4033 1647 4028 Dl 1642 4028 1647 4026 Dl 1641 4034 1642 4034 Dl 1628 4063 1630 4058 Dl 1642 4033 1644 4035 Dl 1641 4039 1644 4035 Dl 1648 4021 1 1 De 1648 4021 1649 4021 Dl 1648 4026 1650 4022 Dl 1606 4118 1615 4098 Dl 1557 4187 1606 4118 Dl 1605 4104 1615 4098 Dl 1616 4097 1625 4086 Dl 1625 4085 1628 4073 Dl 1620 4078 1628 4073 Dl 1633 4065 1635 4058 Dl 1628 4073 1632 4066 Dl 1628 4062 1635 4058 Dl 1642 4048 1642 4044 Dl 1636 4058 1641 4049 Dl 1635 4058 1 1 De 1640 4045 1642 4044 Dl 1646 4035 1 1 De 1644 4042 1646 4035 Dl 1642 4044 1643 4042 Dl 1645 4035 1 1 De 1648 4029 1 1 De 1647 4028 1648 4029 Dl 1646 4034 1648 4029 Dl 1646 4020 1648 4018 Dl 1648 4018 1648 4019 Dl 1625 4085 1630 4077 Dl 1631 4076 1637 4064 Dl 1624 4086 1625 4086 Dl 1634 4066 1637 4064 Dl 1638 4062 1640 4055 Dl 1637 4063 1638 4062 Dl 1636 4057 1640 4055 Dl 1642 4052 1646 4047 Dl 1645 4047 1643 4047 Dl 1641 4054 1642 4053 Dl 1641 4048 1643 4047 Dl 1647 4041 1647 4039 Dl 1644 4047 1646 4042 Dl 1644 4041 1647 4039 Dl 1648 4039 1648 4034 Dl 1648 4039 1 1 De 1648 4034 1 1 De 1647 4034 1648 4034 Dl 1649 4029 1650 4029 Dl 1648 4034 1650 4029 Dl 1651 4024 1653 4024 Dl 1649 4028 1652 4025 Dl 1647 4026 1649 4025 Dl 1650 4022 1652 4021 Dl 1650 4025 1652 4021 Dl 1649 4021 1651 4019 Dl 1648 4020 1651 4019 Dl 1276 4878 1126 4878 Dl 1277 4877 1578 4217 Dl 1578 4215 1614 4113 Dl 1607 4118 1614 4113 Dl (45)1302 4616 w 1632 4084 1632 4083 Dl 1614 4112 1632 4083 Dl 1626 4085 1632 4083 Dl 1630 4075 1640 4060 Dl 1638 4061 1640 4060 Dl 1641 4060 1642 4053 Dl 1646 4047 1646 4042 Dl 1647 4047 1 1 De 1653 4030 1653 4029 Dl 1651 4029 1653 4029 Dl 1649 4033 1653 4029 Dl 1651 4029 1653 4026 Dl 1653 4020 1653 4021 Dl 1652 4020 1653 4020 Dl 1650 4024 1653 4021 Dl 1650 4019 1651 4019 Dl 1649 4019 1650 4019 Dl 1633 4081 1640 4068 Dl 1640 4068 1641 4060 Dl 1641 4060 1 1 De 1648 4048 1648 4046 Dl 1641 4060 1648 4049 Dl 1646 4047 1648 4046 Dl 1648 4046 1650 4042 Dl 1650 4041 1650 4037 Dl 1648 4038 1650 4037 Dl 1653 4029 1 1 De 1650 4037 1653 4031 Dl 1654 4028 1653 4026 Dl 1653 4021 1653 4023 Dl 1652 4024 1653 4023 Dl 1652 4019 1654 4019 Dl 1653 4019 1653 4020 Dl 1578 4216 1628 4109 Dl 1628 4109 1635 4086 Dl 1636 4084 1632 4083 Dl 1646 4059 1648 4049 Dl 1639 4068 1646 4059 Dl 1654 4031 1653 4031 Dl 1653 4037 1655 4030 Dl 1651 4040 1653 4038 Dl 1655 4022 1658 4021 Dl 1654 4027 1658 4021 Dl 1651 4017 1650 4019 Dl 1649 4018 1651 4016 Dl 1646 4066 1648 4058 Dl 1636 4085 1646 4067 Dl 1648 4058 1646 4059 Dl 1653 4051 1653 4045 Dl 1649 4058 1652 4052 Dl 1653 4046 1648 4049 Dl 1656 4037 1656 4036 Dl 1654 4044 1657 4037 Dl 1655 4036 1653 4038 Dl 1657 4035 1659 4027 Dl 1659 4028 1655 4030 Dl 1659 4021 1658 4021 Dl 1659 4026 1659 4021 Dl 1656 4018 1658 4021 Dl 1654 4019 1 1 De 1656 4018 1 1 De 1652 4018 1656 4017 Dl 1651 4016 1648 4018 Dl 1652 4015 1651 4016 Dl 1649 4069 1652 4060 Dl 1629 4109 1649 4069 Dl 1646 4066 1652 4060 Dl 1658 4048 1662 4033 Dl 1661 4033 1659 4035 Dl 1655 4048 1659 4035 Dl 1657 4049 1655 4049 Dl 1661 4021 1659 4021 Dl 1661 4025 1662 4021 Dl 1661 4025 1659 4026 Dl 1654 4013 1652 4015 Dl 1655 4013 1656 4017 Dl 1657 4049 1657 4048 Dl 1652 4060 1657 4050 Dl 1654 4050 1652 4052 Dl 1659 4035 1657 4037 Dl 1661 4032 1661 4025 Dl 1659 4016 1658 4016 Dl 1657 4017 1656 4017 Dl 1659 4016 1659 4021 Dl 1295 4878 1276 4878 Dl 1296 4877 1653 4065 Dl 1652 4066 1649 4069 Dl 1660 4051 1661 4046 Dl 1653 4065 1658 4052 Dl 1660 4047 1657 4050 Dl 1664 4033 1664 4030 Dl 1660 4046 1664 4034 Dl 1664 4031 1662 4033 Dl 1664 4020 1663 4020 Dl 1665 4030 1666 4021 Dl 1663 4020 1662 4021 Dl 1662 4015 1660 4016 Dl 1662 4015 1663 4020 Dl 1655 4013 1658 4016 Dl 2735 2862 2391 2862 Dl 2736 4878 1296 4878 Dl 2736 4878 2736 2862 Dl 1809 3770 1658 4052 Dl (89)2161 4085 w 1768 3824 1664 4034 Dl 1741 3854 1666 4021 Dl 1721 3872 1663 4015 Dl 1696 3890 1655 4013 Dl 720 4447 1 1 De 5 R f (94)1328 4129 w 20 R f 16 setlinewidth 2736 4878 720 4878 Dl 2736 2862 2736 4878 Dl 720 2862 2736 2862 Dl 720 4878 720 2862 Dl 10 R f 0.1 setlinewidth 5039 4878 4434 4878 Dl 5040 4877 5040 4191 Dl 4434 4877 3741 3389 Dl 5039 4191 3741 3389 Dl (4)4480 4288 w 3404 2862 5040 2862 Dl 5040 4191 5040 2862 Dl 3741 3389 3403 2862 Dl (5)4400 3353 w 3403 2862 3024 2862 Dl 4434 4878 3024 4878 Dl 3024 2862 3024 4878 Dl (89)3483 4070 w 20 R f 16 setlinewidth 5040 4878 3024 4878 Dl 5040 2862 5040 4878 Dl 3024 2862 5040 2862 Dl 3024 4878 3024 2862 Dl 10 B f (Fig. 146:)1 372 1 929 5076 t 10 R f (pr.p.it. 7,)1 364 1 1326 5076 t 10 I f (d)1715 5076 w 10 S f (=)1790 5076 w 10 I f (ahead)1870 5076 w 10 R f (, nat. vars.)2 413 1 2114 5076 t 10 B f (Fig. 147:)1 372 1 3219 5076 t 10 R f (pr.p.it. 7,)1 364 1 3616 5076 t 10 I f (d)4005 5076 w 10 S f (=)4080 5076 w 10 I f (behind)4160 5076 w 10 R f (, nat. vars.)2 413 1 4432 5076 t 0.1 setlinewidth 720 5238 2496 5238 Dl 720 5238 720 6631 Dl 720 6630 1604 6168 Dl 1713 6094 1604 6168 Dl 1809 6013 1713 6093 Dl 1992 5826 1810 6012 Dl 2496 5238 1992 5826 Dl (5)1343 5767 w 857 7254 987 7254 Dl 986 7254 1080 7110 Dl 856 7254 1080 7110 Dl 720 7254 856 7254 Dl 1125 7055 1167 6983 Dl 1081 7110 1124 7056 Dl 720 7253 1167 6983 Dl 5 R f (8)942 7157 w 10 R f 0.1 setlinewidth 720 7253 720 7182 Dl 1198 6940 1234 6886 Dl 1167 6982 1198 6940 Dl 720 7182 1234 6886 Dl 5 R f (9)941 7089 w 10 R f 0.1 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6685 Dl 1387 6671 1389 6685 Dl 1413 6635 1415 6634 Dl 1415 6634 1 1 De 1391 6642 1411 6631 Dl 1419 6629 1 1 De 1414 6633 1419 6629 Dl 1411 6631 1419 6629 Dl 1329 6800 1 1 De 1291 6868 1329 6801 Dl 1259 6909 1290 6868 Dl 1322 6803 1329 6800 Dl 1380 6729 1387 6704 Dl 1338 6779 1379 6730 Dl 1372 6711 1387 6704 Dl 1335 6782 1339 6780 Dl 1414 6655 1 1 De 1413 6659 1414 6655 Dl 1394 6681 1412 6660 Dl 1393 6665 1413 6654 Dl 1389 6684 1394 6681 Dl 1329 6799 1339 6780 Dl 1395 6681 1401 6688 Dl 1388 6703 1401 6688 Dl 1424 6638 1424 6639 Dl 1416 6634 1419 6634 Dl 1420 6635 1424 6636 Dl 1413 6654 1424 6639 Dl 1424 6636 1424 6637 Dl 1060 7254 1043 7254 Dl 1210 7049 1260 6954 Dl 1060 7253 1209 7050 Dl 1218 6980 1260 6954 Dl 1260 6953 1301 6904 Dl 1300 6903 1323 6847 Dl 1290 6867 1323 6847 Dl 1345 6816 1357 6783 Dl 1324 6847 1344 6816 Dl 1330 6800 1357 6783 Dl 1383 6743 1388 6724 Dl 1359 6780 1382 6744 Dl 1356 6782 1358 6780 Dl 1380 6729 1388 6724 Dl 1407 6688 1404 6687 Dl 1395 6716 1407 6689 Dl 1388 6723 1394 6716 Dl 1402 6688 1404 6687 Dl 1418 6666 1418 6664 Dl 1413 6660 1418 6664 Dl 1404 6687 1417 6667 Dl 1424 6636 1424 6637 Dl 1412 6630 1422 6624 Dl 1421 6624 1419 6629 Dl 1305 6900 1328 6862 Dl 1329 6861 1359 6806 Dl 1300 6904 1305 6900 Dl 1344 6816 1359 6806 Dl 1364 6800 1376 6769 Dl 1359 6806 1364 6801 Dl 1359 6780 1376 6769 Dl 1383 6762 1401 6740 Dl 1400 6739 1392 6737 Dl 1377 6768 1383 6762 Dl 1383 6743 1392 6737 Dl 1405 6716 1409 6707 Dl 1393 6736 1405 6716 Dl 1395 6716 1409 6707 Dl 1413 6703 1416 6684 Dl 1409 6706 1412 6703 Dl 1413 6685 1416 6684 Dl 1407 6688 1412 6685 Dl 1423 6666 1 1 De 1417 6666 1423 6666 Dl 1413 6685 1424 6667 Dl 1434 6650 1434 6649 Dl 1424 6649 1434 6649 Dl 1423 6649 1424 6649 Dl 1418 6663 1433 6649 Dl 1415 6655 1422 6650 Dl 1425 6638 1433 6634 Dl 1422 6649 1433 6634 Dl 1425 6635 1432 6628 Dl 1420 6634 1432 6628 Dl 1141 7254 1060 7254 Dl 1142 7253 1239 7030 Dl 1209 7048 1239 7030 Dl 1327 6895 1329 6890 Dl 1240 7030 1327 6896 Dl 1329 6890 1305 6900 Dl 1328 6861 1373 6795 Dl 1364 6800 1373 6795 Dl 1375 6793 1383 6762 Dl 1374 6794 1 1 De 1404 6736 1405 6716 Dl 1402 6739 1404 6737 Dl 1435 6669 1435 6664 Dl 1424 6667 1435 6664 Dl 1416 6683 1434 6668 Dl 1433 6651 1433 6649 Dl 1423 6665 1433 6652 Dl 1438 6631 1438 6635 Dl 1434 6634 1439 6631 Dl 1423 6649 1438 6635 Dl 1426 6626 1432 6626 Dl 1432 6627 1432 6628 Dl 1420 6629 1425 6626 Dl 1330 6889 1365 6830 Dl 1366 6830 1377 6793 Dl 1375 6794 1377 6793 Dl 1408 6745 1411 6733 Dl 1377 6792 1407 6746 Dl 1404 6737 1411 6733 Dl 1410 6732 1419 6716 Dl 1419 6716 1419 6698 Dl 1412 6703 1419 6698 Dl 1435 6671 1434 6668 Dl 1421 6698 1436 6672 Dl 1437 6663 1437 6661 Dl 1435 6660 1433 6652 Dl 1439 6635 1439 6642 Dl 1434 6648 1439 6642 Dl 1433 6628 1443 6626 Dl 1443 6626 1439 6631 Dl 1169 7254 1141 7254 Dl 1171 7253 1291 7022 Dl 1291 7022 1339 6908 Dl 1338 6908 1327 6896 Dl 1407 6746 1 1 De 1396 6793 1408 6747 Dl 1365 6830 1395 6792 Dl 1440 6672 1436 6672 Dl 1430 6704 1440 6671 Dl 1419 6716 1429 6704 Dl 1453 6638 1452 6638 Dl 1439 6642 1452 6638 Dl 1437 6661 1454 6638 Dl 1430 6618 1425 6626 Dl 1422 6624 1431 6618 Dl 1388 6826 1402 6788 Dl 1340 6908 1388 6827 Dl 1402 6787 1395 6792 Dl 1418 6760 1425 6734 Dl 1402 6787 1418 6761 Dl 1426 6735 1408 6747 Dl 1442 6701 1442 6696 Dl 1425 6734 1442 6701 Dl 1441 6696 1429 6704 Dl 1442 6696 1455 6660 Dl 1455 6660 1440 6671 Dl 1459 6636 1454 6638 Dl 1456 6659 1 1 De 1457 6659 1460 6636 Dl 1446 6624 1452 6638 Dl 1445 6624 1443 6626 Dl 1448 6622 1446 6624 Dl 1432 6626 1448 6621 Dl 1436 6614 1422 6624 Dl 1435 6614 1431 6618 Dl 1394 6842 1412 6801 Dl 1292 7022 1394 6842 Dl 1388 6826 1412 6801 Dl 1461 6685 1 1 De 1437 6749 1461 6685 Dl 1460 6685 1452 6693 Dl 1430 6752 1452 6693 Dl 1435 6750 1429 6752 Dl 1469 6639 1460 6636 Dl 1464 6654 1469 6639 Dl 1463 6655 1456 6659 Dl 1443 6606 1436 6613 Dl 1445 6606 1450 6620 Dl 1449 6620 1448 6621 Dl 1436 6757 1437 6750 Dl 1412 6800 1434 6757 Dl 1429 6753 1418 6761 Dl 1451 6694 1442 6701 Dl 1461 6684 1463 6654 Dl 1460 6617 1455 6617 Dl 1455 6618 1450 6620 Dl 1461 6618 1460 6636 Dl 1198 7254 1170 7254 Dl 1200 7253 1408 6832 Dl 1407 6832 1394 6842 Dl 1438 6772 1447 6747 Dl 1408 6832 1437 6773 Dl 1446 6747 1434 6757 Dl 1468 6695 1470 6678 Dl 1448 6747 1468 6695 Dl 1470 6677 1461 6685 Dl 1478 6639 1474 6634 Dl 1470 6677 1478 6640 Dl 1474 6634 1469 6639 Dl 1471 6616 1461 6618 Dl 1474 6634 1472 6615 Dl 1444 6606 1455 6617 Dl 2735 5238 2527 5238 Dl 2735 7254 1199 7254 Dl 2736 7254 2736 5238 Dl 2527 5238 1437 6773 Dl (89)2144 6518 w 2526 5238 2496 5238 Dl 1992 5826 1468 6695 Dl (90)1942 5955 w 1809 6013 1478 6640 Dl 5 R f (91)1705 6230 w 10 R f 0.1 setlinewidth 1713 6094 1472 6615 Dl 5 R f (92)1617 6304 w 10 R f 0.1 setlinewidth 1603 6168 1444 6606 Dl 5 R f (93)1548 6347 w 10 R f 0.1 setlinewidth 720 6631 720 6973 Dl (94)1076 6608 w 20 R f 16 setlinewidth 2736 7254 720 7254 Dl 2736 5238 2736 7254 Dl 720 5238 2736 5238 Dl 720 7254 720 5238 Dl 10 R f 0.1 setlinewidth 5039 7254 4437 7254 Dl 5040 7253 5040 6695 Dl 4437 7253 3744 5952 Dl 5039 6695 3744 5952 Dl (4)4478 6750 w 3161 5238 5040 5238 Dl 5040 6695 5040 5238 Dl 3744 5952 3160 5238 Dl (5)4322 5780 w 3160 5238 3024 5238 Dl 4437 7254 3024 7254 Dl 3024 5238 3024 7254 Dl (89)3471 6513 w 20 R f 16 setlinewidth 5040 7254 3024 7254 Dl 5040 5238 5040 7254 Dl 3024 5238 5040 5238 Dl 3024 7254 3024 5238 Dl 10 B f (Fig. 148:)1 372 1 929 7452 t 10 R f (pr.p.it. 8,)1 364 1 1326 7452 t 10 I f (d)1715 7452 w 10 S f (=)1790 7452 w 10 I f (ahead)1870 7452 w 10 R f (, nat. vars.)2 413 1 2114 7452 t 10 B f (Fig. 149:)1 372 1 3219 7452 t 10 R f (pr.p.it. 8,)1 364 1 3616 7452 t 10 I f (d)4005 7452 w 10 S f (=)4080 7452 w 10 I f (behind)4160 7452 w 10 R f (, nat. vars.)2 413 1 4432 7452 t (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 38 39 %%Page: 39 40 /saveobj save def mark 40 pagesetup 10 R f (- 39 -)2 216 1 2772 282 t 0.1 setlinewidth 720 486 2070 486 Dl 720 486 720 1420 Dl 720 1419 1452 1041 Dl 1907 677 1452 1041 Dl 2070 486 1908 677 Dl (5)1186 837 w 889 2502 900 2502 Dl 901 2501 907 2489 Dl 889 2501 907 2489 Dl 747 2502 889 2502 Dl 1032 2337 1053 2290 Dl 907 2488 1031 2337 Dl 747 2501 1053 2290 Dl 5 R f (11)881 2437 w 10 R f 0.1 setlinewidth 720 2502 746 2502 Dl 720 2442 720 2502 Dl 1132 2207 1181 2133 Dl 1053 2290 1131 2208 Dl 720 2441 1181 2133 Dl 5 R f (12)899 2350 w 10 R f 0.1 setlinewidth 720 2376 720 2441 Dl 720 2375 1213 2056 Dl 1239 2082 1293 2013 Dl 1224 2097 1239 2083 Dl 1214 2055 1294 2010 Dl 1293 2011 1293 2013 Dl 1182 2133 1223 2098 Dl 5 R f (13)955 2247 w 10 R f 0.1 setlinewidth 950 2502 964 2502 Dl 965 2501 976 2482 Dl 951 2501 976 2482 Dl 901 2502 950 2502 Dl 1041 2418 1082 2363 Dl 1083 2362 1081 2301 Dl 976 2483 1041 2419 Dl 1031 2337 1081 2301 Dl 1186 2186 1188 2168 Dl 1081 2301 1186 2187 Dl 1132 2208 1188 2168 Dl 1189 2167 1236 2119 Dl 1224 2098 1236 2119 Dl 1297 2009 1298 2009 Dl 1293 2014 1298 2009 Dl 1295 2010 1297 2008 Dl 1213 2055 1278 2011 Dl 1307 1996 1310 1996 Dl 1298 2008 1310 1996 Dl 1278 2011 1306 1996 Dl 964 2502 1005 2502 Dl 1068 2402 1067 2402 Dl 1006 2501 1069 2403 Dl 1042 2418 1067 2402 Dl 1218 2210 1236 2155 Dl 1096 2352 1218 2211 Dl 1186 2186 1236 2155 Dl 1084 2362 1096 2352 Dl 1303 2041 1306 2041 Dl 1303 2049 1306 2041 Dl 1253 2106 1303 2049 Dl 1239 2083 1302 2041 Dl 1237 2119 1252 2107 Dl 1068 2402 1096 2352 Dl 1253 2107 1276 2112 Dl 1237 2155 1276 2112 Dl 1331 2002 1332 2003 Dl 1299 2009 1311 2004 Dl 1312 2002 1327 2000 Dl 1303 2040 1332 2003 Dl 1328 2001 1330 2002 Dl 1061 2502 1005 2502 Dl 1121 2420 1157 2338 Dl 1062 2501 1120 2420 Dl 1070 2403 1157 2338 Dl 1230 2234 1244 2192 Dl 1162 2330 1230 2234 Dl 1157 2337 1162 2331 Dl 1218 2211 1244 2192 Dl 1285 2106 1296 2106 Dl 1265 2169 1296 2106 Dl 1245 2192 1263 2170 Dl 1277 2111 1284 2106 Dl 1319 2057 1321 2052 Dl 1302 2050 1321 2052 Dl 1284 2105 1320 2057 Dl 1330 2000 1330 2002 Dl 1327 2000 1329 2000 Dl 1278 2010 1311 1987 Dl 1312 1987 1313 1987 Dl 1312 1987 1306 1996 Dl 1095 2502 1062 2502 Dl 1095 2501 1167 2384 Dl 1120 2419 1167 2384 Dl 1183 2368 1216 2291 Dl 1168 2384 1183 2368 Dl 1162 2331 1216 2291 Dl 1237 2270 1288 2209 Dl 1260 2212 1288 2209 Dl 1217 2290 1236 2270 Dl 1232 2234 1260 2213 Dl 1296 2159 1306 2138 Dl 1260 2213 1296 2160 Dl 1263 2169 1306 2138 Dl 1318 2127 1324 2088 Dl 1306 2137 1316 2127 Dl 1313 2094 1324 2088 Dl 1295 2106 1311 2094 Dl 1340 2051 1342 2051 Dl 1320 2057 1339 2050 Dl 1312 2094 1342 2051 Dl 1365 2011 1366 2009 Dl 1333 2021 1366 2009 Dl 1328 2023 1333 2021 Dl 1322 2051 1365 2012 Dl 1307 2040 1329 2024 Dl 1332 2002 1357 1987 Dl 1328 2023 1357 1987 Dl 1329 2000 1349 1980 Dl 1311 2003 1349 1980 Dl 1098 2502 1095 2502 Dl 1098 2501 1211 2346 Dl 1183 2367 1211 2346 Dl 1214 2344 1236 2270 Dl 1212 2346 1213 2345 Dl 1296 2201 1296 2160 Dl 1288 2208 1296 2201 Dl 1375 2043 1376 2034 Dl 1342 2051 1376 2034 Dl 1324 2087 1375 2043 Dl 1365 2016 1365 2012 Dl 1340 2049 1366 2016 Dl 1375 1976 1374 1983 Dl 1357 1987 1375 1975 Dl 1333 2021 1374 1983 Dl 1329 1984 1349 1977 Dl 1348 1977 1350 1978 Dl 1310 1997 1327 1985 Dl 1349 1979 1350 1978 Dl 1142 2502 1099 2502 Dl 1142 2501 1188 2431 Dl 1188 2431 1221 2339 Dl 1214 2344 1221 2339 Dl 1309 2215 1316 2186 Dl 1221 2339 1308 2216 Dl 1296 2201 1316 2186 Dl 1317 2186 1341 2147 Dl 1340 2145 1337 2111 Dl 1317 2126 1337 2111 Dl 1380 2048 1375 2043 Dl 1338 2111 1380 2048 Dl 1376 2033 1378 2028 Dl 1366 2017 1378 2028 Dl 1375 1983 1380 1993 Dl 1367 2008 1380 1993 Dl 1351 1978 1386 1963 Dl 1376 1975 1386 1963 Dl 1310 2216 1308 2216 Dl 1277 2323 1311 2216 Dl 1188 2431 1276 2324 Dl 1381 2048 1393 2043 Dl 1370 2114 1393 2043 Dl 1340 2146 1368 2114 Dl 1420 1972 1423 1972 Dl 1380 1993 1419 1973 Dl 1379 2027 1423 1972 Dl 1339 1968 1327 1985 Dl 1313 1987 1339 1967 Dl 1195 2502 1142 2502 Dl 1256 2407 1297 2308 Dl 1195 2501 1255 2407 Dl 1277 2323 1297 2308 Dl 1343 2238 1361 2177 Dl 1297 2307 1342 2239 Dl 1311 2215 1361 2177 Dl 1406 2098 1403 2088 Dl 1361 2177 1406 2098 Dl 1370 2113 1403 2088 Dl 1403 2088 1435 2010 Dl 1393 2043 1435 2010 Dl 1424 1972 1441 1964 Dl 1436 2010 1437 2008 Dl 1438 2007 1441 1964 Dl 1394 1957 1419 1973 Dl 1387 1962 1394 1956 Dl 1399 1951 1394 1956 Dl 1349 1976 1398 1951 Dl 1312 1987 1352 1956 Dl 1351 1957 1339 1967 Dl 1237 2502 1195 2502 Dl 1272 2445 1326 2335 Dl 1238 2501 1272 2445 Dl 1256 2407 1326 2335 Dl 1455 2056 1455 2055 Dl 1394 2207 1456 2057 Dl 1432 2077 1455 2055 Dl 1375 2215 1432 2078 Dl 1393 2208 1375 2215 Dl 1469 1964 1441 1964 Dl 1456 1995 1468 1964 Dl 1455 1996 1437 2008 Dl 1373 1938 1352 1956 Dl 1374 1938 1403 1948 Dl 1399 1951 1403 1948 Dl 1389 2224 1393 2207 Dl 1326 2334 1388 2224 Dl 1373 2215 1342 2239 Dl 1431 2078 1406 2098 Dl 1456 2055 1456 1995 Dl 1420 1937 1438 1933 Dl 1404 1948 1420 1938 Dl 1439 1934 1441 1964 Dl 1264 2502 1238 2502 Dl 1265 2501 1306 2424 Dl 1306 2424 1272 2445 Dl 1391 2267 1419 2201 Dl 1307 2424 1391 2268 Dl 1418 2201 1388 2224 Dl 1472 2078 1478 2038 Dl 1420 2201 1473 2078 Dl 1478 2039 1456 2057 Dl 1493 1961 1481 1951 Dl 1479 2037 1494 1962 Dl 1480 1953 1468 1964 Dl 1466 1922 1438 1933 Dl 1466 1922 1481 1951 Dl 1373 1937 1 1 De 1375 1937 1420 1938 Dl 2735 2502 1265 2502 Dl 2736 2501 2736 2437 Dl 2735 2437 1391 2268 Dl (89)1845 2439 w 2735 486 2567 486 Dl 2736 2437 2736 486 Dl 2567 486 1473 2078 Dl (90)2219 1682 w 2566 486 2222 486 Dl 2222 486 1494 1962 Dl (91)2006 1080 w 2221 486 2070 486 Dl 1907 678 1466 1922 Dl (92)1806 1088 w 1452 1042 1374 1936 Dl (93)1528 1305 w 720 1420 720 2376 Dl (94)1010 1711 w 20 R f 16 setlinewidth 2736 2502 720 2502 Dl 2736 486 2736 2502 Dl 720 486 2736 486 Dl 720 2502 720 486 Dl 10 R f 0.1 setlinewidth 5039 2502 4600 2502 Dl 5040 2501 5040 2190 Dl 4599 2501 4067 1572 Dl 5039 2189 4067 1572 Dl (4)4606 2167 w 3255 486 5040 486 Dl 5040 2190 5040 486 Dl 3434 753 3254 486 Dl 4066 1573 3434 753 Dl (5)4364 1128 w 4600 2502 3024 2502 Dl 3024 805 3024 2502 Dl 3434 753 3024 804 Dl (89)3549 1816 w 3253 486 3024 486 Dl 3024 486 3024 804 Dl (90)3135 667 w 20 R f 16 setlinewidth 5040 2502 3024 2502 Dl 5040 486 5040 2502 Dl 3024 486 5040 486 Dl 3024 2502 3024 486 Dl 10 B f (Fig. 150:)1 372 1 929 2700 t 10 R f (pr.p.it. 9,)1 364 1 1326 2700 t 10 I f (d)1715 2700 w 10 S f (=)1790 2700 w 10 I f (ahead)1870 2700 w 10 R f (, nat. vars.)2 413 1 2114 2700 t 10 B f (Fig. 151:)1 372 1 3219 2700 t 10 R f (pr.p.it. 9,)1 364 1 3616 2700 t 10 I f (d)4005 2700 w 10 S f (=)4080 2700 w 10 I f (behind)4160 2700 w 10 R f (, nat. vars.)2 413 1 4432 2700 t 0.1 setlinewidth 720 4460 720 4572 Dl 869 4422 1023 4222 Dl 720 4571 868 4422 Dl 720 4460 1023 4222 Dl 5 R f (12)803 4426 w 10 R f 0.1 setlinewidth 720 4352 720 4460 Dl 720 4351 1098 4062 Dl 1201 4062 1352 3886 Dl 1152 4106 1200 4062 Dl 1099 4062 1354 3880 Dl 1354 3881 1352 3886 Dl 1023 4221 1152 4107 Dl 5 R f (13)957 4210 w 10 R f 0.1 setlinewidth 720 4651 720 4572 Dl 1043 4312 1050 4274 Dl 720 4651 1043 4313 Dl 868 4421 1050 4274 Dl 5 R f (18)837 4479 w 10 R f 0.1 setlinewidth 1050 4274 1195 4129 Dl 1152 4108 1195 4129 Dl 5 R f (19)1027 4245 w 10 R f 0.1 setlinewidth 1363 3872 1367 3872 Dl 1352 3885 1367 3872 Dl 1355 3880 1363 3873 Dl 1100 4062 1301 3906 Dl 1386 3844 1398 3839 Dl 1362 3872 1398 3839 Dl 1301 3905 1387 3845 Dl 720 4781 720 4651 Dl 1137 4325 1195 4196 Dl 745 4759 1138 4326 Dl 1042 4312 1195 4196 Dl 720 4781 743 4759 Dl 5 R f (23)904 4504 w 10 R f 0.1 setlinewidth 1387 3916 1398 3913 Dl 1389 3931 1398 3913 Dl 1244 4087 1389 3931 Dl 1200 4062 1386 3917 Dl 1196 4128 1244 4088 Dl 720 4793 720 4781 Dl 720 4793 743 4759 Dl 1244 4088 1314 4073 Dl 1196 4196 1314 4073 Dl 1463 3823 1468 3823 Dl 1368 3872 1406 3849 Dl 1406 3848 1454 3825 Dl 1387 3915 1468 3823 Dl 1454 3824 1463 3823 Dl 720 4878 805 4878 Dl 720 4877 720 4842 Dl 806 4877 932 4661 Dl 720 4843 932 4661 Dl 720 4841 720 4793 Dl 1169 4361 1217 4259 Dl 952 4639 1170 4362 Dl 932 4659 951 4639 Dl 1138 4325 1217 4259 Dl 5 R f (31)934 4577 w 10 R f 0.1 setlinewidth 1337 4053 1369 4042 Dl 1274 4196 1369 4042 Dl 1218 4258 1273 4197 Dl 1315 4072 1337 4054 Dl 1439 3928 1444 3916 Dl 1389 3931 1444 3916 Dl 1337 4054 1439 3929 Dl 1460 3822 1463 3823 Dl 1455 3824 1460 3821 Dl 1301 3905 1397 3829 Dl 1397 3829 1401 3826 Dl 1401 3826 1387 3845 Dl 864 4878 813 4878 Dl 866 4877 948 4761 Dl 814 4877 948 4761 Dl 812 4878 805 4878 Dl 1001 4706 1117 4498 Dl 949 4760 1000 4706 Dl 952 4639 1117 4498 Dl 5 R f (37)935 4702 w 10 R f 0.1 setlinewidth 1177 4436 1333 4258 Dl 1256 4289 1333 4258 Dl 1118 4497 1177 4436 Dl 1170 4362 1255 4290 Dl 5 R f (38)1132 4432 w 10 R f 0.1 setlinewidth 1363 4148 1396 4094 Dl 1255 4289 1363 4148 Dl 1273 4196 1396 4094 Dl 1425 4063 1447 3981 Dl 1397 4094 1425 4065 Dl 1415 4003 1447 3981 Dl 1369 4042 1415 4004 Dl 1494 3896 1499 3896 Dl 1439 3928 1493 3897 Dl 1415 4004 1499 3896 Dl 1564 3804 1567 3798 Dl 1476 3851 1567 3798 Dl 1462 3862 1475 3852 Dl 1445 3916 1563 3805 Dl 1399 3913 1462 3862 Dl 1468 3823 1540 3770 Dl 1462 3861 1540 3770 Dl 1459 3821 1513 3768 Dl 1405 3848 1513 3768 Dl 894 4878 866 4878 Dl 893 4877 1087 4631 Dl 1000 4706 1087 4631 Dl 1094 4625 1177 4436 Dl 1088 4631 1093 4626 Dl 1358 4233 1363 4148 Dl 1334 4257 1359 4234 Dl 1589 3853 1594 3834 Dl 1500 3896 1594 3834 Dl 1448 3981 1589 3853 Dl 1565 3812 1563 3805 Dl 1494 3896 1566 3812 Dl 1588 3733 1586 3747 Dl 1541 3771 1589 3733 Dl 1475 3852 1586 3747 Dl 1450 3800 1511 3765 Dl 1511 3764 1517 3764 Dl 1399 3839 1449 3801 Dl 1513 3767 1517 3764 Dl 978 4878 894 4878 Dl 978 4877 990 4861 Dl 990 4860 1117 4605 Dl 1094 4625 1117 4605 Dl 1389 4256 1416 4186 Dl 1117 4604 1388 4255 Dl 1359 4234 1416 4186 Dl 5 R f (56)1227 4405 w 10 R f 0.1 setlinewidth 1416 4185 1487 4084 Dl 1487 4083 1483 4016 Dl 1426 4063 1483 4016 Dl 1602 3858 1589 3853 Dl 1483 4016 1602 3859 Dl 1594 3834 1600 3822 Dl 1566 3812 1600 3822 Dl 1588 3747 1603 3759 Dl 1567 3797 1603 3759 Dl 1518 3763 1616 3702 Dl 1589 3731 1616 3702 Dl 1393 4255 1388 4255 Dl 1270 4530 1393 4255 Dl 990 4860 1270 4531 Dl 5 R f (63)1174 4565 w 10 R f 0.1 setlinewidth 1603 3859 1636 3839 Dl 1565 3998 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7147 3024 7254 Dl 3804 6055 3024 7146 Dl (90)3624 6858 w 3483 5238 3024 5238 Dl 3024 5238 3024 7146 Dl 3693 5633 3483 5238 Dl (91)3272 6029 w 3812 5238 3483 5238 Dl 3821 5370 3811 5238 Dl (92)3627 5395 w 3811 5238 4821 5238 Dl 4428 5538 4821 5238 Dl (93)4235 5367 w 4822 5238 5040 5238 Dl 5040 6211 5040 5238 Dl (94)4779 5650 w 20 R f 16 setlinewidth 5040 7254 3024 7254 Dl 5040 5238 5040 7254 Dl 3024 5238 5040 5238 Dl 3024 7254 3024 5238 Dl 10 B f (Fig. 154:)1 372 1 904 7452 t 10 R f (pr.p.it. 11,)1 414 1 1301 7452 t 10 I f (d)1740 7452 w 10 S f (=)1815 7452 w 10 I f (ahead)1895 7452 w 10 R f (, nat. vars.)2 413 1 2139 7452 t 10 B f (Fig. 155:)1 372 1 3194 7452 t 10 R f (pr.p.it. 11,)1 414 1 3591 7452 t 10 I f (d)4030 7452 w 10 S f (=)4105 7452 w 10 I f (behind)4185 7452 w 10 R f (, nat. vars.)2 413 1 4457 7452 t (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 39 40 %%Page: 40 41 /saveobj save def mark 41 pagesetup 10 R f (- 40 -)2 216 1 2772 282 t 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4447 4615 4449 Dl 5040 4557 5040 4569 Dl 4881 4601 5040 4569 Dl 4862 4574 4880 4602 Dl 5040 4029 5040 3993 Dl 5022 3998 5040 3993 Dl 4462 4366 4507 4421 Dl 4508 4422 4613 4458 Dl 4615 4450 4613 4458 Dl 4785 4634 4920 4682 Dl 4613 4459 4784 4633 Dl 4882 4602 4920 4682 Dl 5 R f (56)4747 4567 w 10 R f 0.1 setlinewidth 5040 4569 5040 4761 Dl 4921 4682 5040 4761 Dl 5 R f (57)4955 4661 w 10 R f 0.1 setlinewidth 4302 4239 4322 4299 Dl 4322 4300 4383 4356 Dl 4383 4356 4453 4363 Dl 4784 4634 4774 4636 Dl 4511 4500 4774 4636 Dl 4508 4423 4511 4500 Dl 5 R f (63)4593 4528 w 10 R f 0.1 setlinewidth 5040 3992 5040 3954 Dl 4951 3915 5040 3954 Dl 4912 3962 4950 3915 Dl 4394 4430 4484 4517 Dl 4383 4356 4393 4430 Dl 4511 4500 4484 4517 Dl 4512 4613 4738 4792 Dl 4484 4517 4512 4612 Dl 4774 4636 4738 4792 Dl 5 R f (68)4612 4646 w 10 R f 0.1 setlinewidth 4808 4878 5040 4878 Dl 5040 4762 5040 4878 Dl 4738 4793 4807 4878 Dl 5 R f (69)4860 4785 w 10 R f 0.1 setlinewidth 4907 3963 4919 3880 Dl 4949 3914 4919 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5040 3131 5040 2862 Dl 3024 3050 3024 2862 Dl 4051 3794 5040 3131 Dl (92)4004 3212 w 5040 3787 5040 3131 Dl 4108 3809 4868 3813 Dl (93)4652 3602 w (94)4519 3931 w 20 R f 16 setlinewidth 5040 4878 3024 4878 Dl 5040 2862 5040 4878 Dl 3024 2862 5040 2862 Dl 3024 4878 3024 2862 Dl 10 B f (Fig. 158:)1 372 1 904 5076 t 10 R f (pr.p.it. 13,)1 414 1 1301 5076 t 10 I f (d)1740 5076 w 10 S f (=)1815 5076 w 10 I f (ahead)1895 5076 w 10 R f (, nat. vars.)2 413 1 2139 5076 t 10 B f (Fig. 159:)1 372 1 3194 5076 t 10 R f (pr.p.it. 13,)1 414 1 3591 5076 t 10 I f (d)4030 5076 w 10 S f (=)4105 5076 w 10 I f (behind)4185 5076 w 10 R f (, nat. vars.)2 413 1 4457 5076 t 0.1 setlinewidth 720 7254 897 7254 Dl 720 7253 720 6649 Dl 720 6649 1575 6475 Dl 897 7253 1575 6475 Dl (77)967 6855 w 2735 7254 897 7254 Dl 2736 7253 2736 5844 Dl 2735 5844 1783 6264 Dl 1783 6265 1575 6475 Dl (86)2012 6744 w 720 6091 720 6649 Dl 720 6090 1783 6264 Dl (87)1079 6379 w 2736 5238 720 5238 Dl 2736 5238 2736 5844 Dl 720 5238 720 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6260 Dl 4751 6259 4767 6260 Dl 4771 6215 4774 6217 Dl 4746 6207 4752 6208 Dl 4753 6209 4766 6213 Dl 4771 6230 4774 6217 Dl 4765 6213 4770 6215 Dl 4661 6264 4672 6268 Dl 4657 6252 4661 6263 Dl 4677 6261 4672 6268 Dl 4673 6268 4674 6275 Dl 4675 6275 4690 6275 Dl 4692 6265 4690 6275 Dl 4698 6279 4713 6278 Dl 4691 6275 4698 6279 Dl 4711 6266 4713 6278 Dl 4734 6282 4746 6277 Dl 4715 6279 4733 6283 Dl 4713 6279 1 1 De 4740 6271 4746 6277 Dl 4770 6262 4775 6269 Dl 4753 6279 4775 6269 Dl 4746 6277 4753 6279 Dl 4767 6260 4770 6261 Dl 4790 6253 4790 6251 Dl 4775 6238 4790 6251 Dl 4771 6260 4789 6253 Dl 4768 6213 4770 6215 Dl 4766 6213 4767 6213 Dl 4727 6201 4731 6197 Dl 4732 6197 4739 6202 Dl 4675 6277 4680 6280 Dl 4679 6280 4695 6287 Dl 4674 6275 4674 6276 Dl 4697 6280 4695 6287 Dl 4697 6289 4715 6289 Dl 4696 6287 4696 6289 Dl 4715 6279 4715 6289 Dl 4717 6295 4732 6309 Dl 4736 6292 4732 6309 Dl 4715 6290 4717 6294 Dl 4733 6284 4736 6292 Dl 4757 6295 4768 6295 Dl 4737 6292 4757 6296 Dl 4753 6280 4768 6295 Dl 4775 6298 4791 6279 Dl 4769 6296 4775 6299 Dl 4784 6274 4791 6279 Dl 4776 6269 4784 6274 Dl 4805 6264 4807 6266 Dl 4790 6254 4805 6264 Dl 4784 6273 4807 6266 Dl 4829 6249 4829 6247 Dl 4790 6234 4829 6247 Dl 4787 6233 4789 6233 Dl 4790 6250 4828 6249 Dl 4775 6233 4786 6233 Dl 4774 6217 4792 6216 Dl 4786 6232 4792 6216 Dl 4769 6212 4769 6204 Dl 4753 6208 4769 6204 Dl 4619 6243 4623 6254 Dl 4624 6254 4654 6266 Dl 4661 6263 4654 6266 Dl 4660 6284 4662 6284 Dl 4654 6267 4660 6283 Dl 4672 6277 4662 6284 Dl 4680 6280 4694 6296 Dl 4696 6290 4694 6296 Dl 4694 6296 4717 6294 Dl 4756 6297 4734 6313 Dl 4732 6309 4734 6313 Dl 4859 6295 4857 6306 Dl 4808 6267 4860 6295 Dl 4791 6280 4857 6306 Dl 4828 6249 4831 6255 Dl 4805 6262 4831 6255 Dl 4809 6213 4816 6221 Dl 4793 6214 4808 6212 Dl 4789 6233 4816 6221 Dl 4748 6200 4764 6202 Dl 4764 6202 4769 6204 Dl 4743 6202 4747 6200 Dl 4664 6284 4671 6295 Dl 4671 6296 4693 6299 Dl 4693 6297 4693 6299 Dl 4718 6326 4737 6326 Dl 4694 6299 4718 6325 Dl 4735 6314 4737 6326 Dl 4737 6326 4759 6336 Dl 4786 6312 4759 6336 Dl 4775 6300 4787 6312 Dl 4858 6307 4865 6325 Dl 4787 6313 4865 6325 Dl 4860 6295 4863 6291 Dl 4831 6256 4863 6291 Dl 4817 6222 4842 6240 Dl 4830 6247 4842 6240 Dl 4769 6204 4809 6204 Dl 4809 6213 4809 6204 Dl 4623 6254 4625 6269 Dl 4626 6270 4641 6283 Dl 4661 6283 4641 6283 Dl 4718 6326 4716 6326 Dl 4668 6313 4716 6326 Dl 4671 6294 4667 6312 Dl 4866 6326 4893 6351 Dl 4782 6360 4893 6351 Dl 4760 6337 4781 6361 Dl 4970 6258 5005 6266 Dl 4842 6240 4970 6257 Dl 4864 6291 5005 6266 Dl 4732 6190 4747 6200 Dl 4731 6195 4731 6189 Dl 4638 6301 4658 6318 Dl 4640 6283 4638 6301 Dl 4666 6313 4658 6318 Dl 4658 6338 4698 6358 Dl 4658 6319 4658 6338 Dl 4715 6327 4698 6358 Dl 4802 6434 4764 6443 Dl 4698 6359 4764 6443 Dl 4781 6361 4802 6433 Dl 5040 6445 5040 6533 Dl 4803 6433 5040 6533 Dl 4894 6352 5040 6445 Dl 5 R f (70)4893 6441 w 10 R f 0.1 setlinewidth 5040 6271 5040 6445 Dl 5006 6266 5040 6270 Dl 5 R f (71)4945 6347 w 10 R f 0.1 setlinewidth 4814 6199 4970 6257 Dl 4809 6204 4814 6199 Dl 4814 6199 4813 6194 Dl 4765 6201 4813 6194 Dl 4729 6196 4726 6184 Dl 4731 6189 4726 6184 Dl 4607 6288 4608 6306 Dl 4625 6269 4607 6287 Dl 4637 6301 4608 6306 Dl 4610 6907 4649 6952 Dl 4597 6346 4609 6906 Dl 4731 6540 4649 6952 Dl 4628 6345 4732 6539 Dl 4627 6346 4597 6346 Dl 5 R f (76)4625 6636 w 10 R f 0.1 setlinewidth 4725 6184 4718 6174 Dl 4719 6175 4813 6190 Dl 4813 6193 4813 6190 Dl 4592 6336 4597 6346 Dl 4608 6307 4591 6335 Dl 4658 6338 4628 6345 Dl 4763 6443 4732 6539 Dl 4905 7254 5040 7254 Dl 5040 6534 5040 7254 Dl 4650 6953 4904 7254 Dl (81)4825 6860 w 5040 6269 5040 6222 Dl 4822 6177 4860 6164 Dl 4812 6189 4821 6177 Dl 4861 6163 5040 6222 Dl 4615 6240 4587 6272 Dl 4587 6272 4607 6287 Dl 4561 6279 4549 6302 Dl 4585 6272 4561 6279 Dl 4549 6303 4591 6335 Dl 4467 6323 4312 6579 Dl 4549 6303 4468 6322 Dl 4312 6579 4609 6906 Dl (85)4448 6589 w 4904 7254 3024 7254 Dl 3024 5891 3024 7254 Dl 4312 6578 3024 5890 Dl (86)3668 6785 w 5040 6222 5040 6070 Dl 4859 6163 4800 6109 Dl 4801 6108 5040 6070 Dl 5 R f (87)4926 6149 w 10 R f 0.1 setlinewidth 4718 6174 1 1 De 4718 6174 4821 6177 Dl 4559 6151 4561 6279 Dl 4556 6142 4468 6322 Dl 3024 5890 3024 5613 Dl 4559 6135 3024 5613 Dl (91)3761 6105 w 5040 5238 3024 5238 Dl 5040 6070 5040 5238 Dl 3024 5613 3024 5238 Dl 4567 6133 4800 6109 Dl (92)4115 5623 w 4586 6142 4718 6174 Dl 20 R f 16 setlinewidth 5040 7254 3024 7254 Dl 5040 5238 5040 7254 Dl 3024 5238 5040 5238 Dl 3024 7254 3024 5238 Dl 10 B f (Fig. 160:)1 372 1 904 7452 t 10 R f (pr.p.it. 14,)1 414 1 1301 7452 t 10 I f (d)1740 7452 w 10 S f (=)1815 7452 w 10 I f (ahead)1895 7452 w 10 R f (, nat. vars.)2 413 1 2139 7452 t 10 B f (Fig. 161:)1 372 1 3194 7452 t 10 R f (pr.p.it. 14,)1 414 1 3591 7452 t 10 I f (d)4030 7452 w 10 S f (=)4105 7452 w 10 I f (behind)4185 7452 w 10 R f (, nat. vars.)2 413 1 4457 7452 t (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 40 41 %%Page: 41 42 /saveobj save def mark 42 pagesetup 10 R f (- 41 -)2 216 1 2772 282 t 0.1 setlinewidth 2736 2502 720 2502 Dl 2736 2501 2736 1545 Dl 720 2501 720 1788 Dl 2735 1545 1872 1497 Dl 720 1787 1872 1497 Dl (86)1726 2061 w 720 1104 720 1788 Dl 720 1104 1872 1497 Dl (87)1054 1483 w 2736 486 720 486 Dl 2736 486 2736 1545 Dl 720 486 720 1103 Dl (92)1763 971 w 20 R f 16 setlinewidth 2736 2502 720 2502 Dl 2736 486 2736 2502 Dl 720 486 2736 486 Dl 720 2502 720 486 Dl 10 R f 0.1 setlinewidth 4425 1500 4426 1500 Dl 4426 1499 4427 1499 Dl 4425 1501 4425 1500 Dl 4404 1512 4363 1473 Dl 4405 1513 4404 1513 Dl 4414 1514 4406 1514 Dl 4424 1501 4414 1512 Dl 4425 1499 4363 1473 Dl 4426 1497 4350 1438 Dl 4350 1438 4327 1427 Dl 4320 1428 4327 1427 Dl 4327 1440 4321 1428 Dl 4339 1452 4327 1440 Dl 4362 1472 4340 1453 Dl 4415 1514 4417 1514 Dl 4417 1514 4427 1514 Dl 4427 1501 4427 1514 Dl 4428 1514 4430 1514 Dl 4428 1514 1 1 De 4428 1500 4430 1514 Dl 4431 1514 4433 1514 Dl 4430 1514 4431 1514 Dl 4428 1500 4433 1514 Dl 4436 1514 4437 1513 Dl 4433 1514 4435 1514 Dl 4428 1500 4437 1513 Dl 4441 1513 4442 1511 Dl 4437 1512 4440 1512 Dl 4428 1500 4442 1511 Dl 4446 1510 4448 1506 Dl 4442 1510 4445 1510 Dl 4428 1499 4448 1506 Dl 4428 1497 4443 1495 Dl 4452 1504 4453 1496 Dl 4451 1505 4452 1505 Dl 4443 1496 4453 1496 Dl 4453 1496 1 1 De 4449 1506 4451 1506 Dl 4417 1514 4420 1516 Dl 4421 1516 4427 1517 Dl 4427 1515 4427 1517 Dl 4428 1518 4430 1518 Dl 4427 1518 1 1 De 4430 1515 4430 1518 Dl 4431 1517 4436 1517 Dl 4436 1515 4436 1517 Dl 4437 1518 4438 1518 Dl 4440 1518 4442 1514 Dl 4436 1517 4437 1518 Dl 4441 1513 4442 1514 Dl 4448 1514 4448 1512 Dl 4442 1514 4447 1514 Dl 4446 1511 4448 1512 Dl 4449 1512 4452 1512 Dl 4452 1507 4452 1512 Dl 4454 1496 1 1 De 4443 1495 4447 1493 Dl 4453 1494 4454 1494 Dl 4454 1496 4454 1494 Dl 4447 1493 4452 1493 Dl 4432 1519 4437 1519 Dl 4431 1519 4432 1519 Dl 4437 1519 1 1 De 4446 1520 4450 1517 Dl 4440 1519 4445 1520 Dl 4448 1515 4450 1517 Dl 4461 1507 1 1 De 4461 1508 4461 1507 Dl 4454 1511 4460 1509 Dl 4453 1505 4460 1506 Dl 4452 1512 4453 1512 Dl 4437 1519 4439 1519 Dl 4454 1512 4454 1517 Dl 4450 1517 4454 1517 Dl 4463 1501 1 1 De 4454 1496 4456 1496 Dl 4457 1497 4461 1499 Dl 4461 1506 4463 1501 Dl 4461 1498 4462 1499 Dl 4422 1520 4425 1520 Dl 4421 1516 4422 1519 Dl 4427 1518 4425 1520 Dl 4425 1520 4425 1522 Dl 4425 1522 4430 1522 Dl 4431 1520 4430 1522 Dl 4433 1522 4437 1522 Dl 4430 1523 4432 1523 Dl 4437 1519 4437 1522 Dl 4442 1523 4446 1522 Dl 4437 1523 4441 1523 Dl 4446 1521 4446 1522 Dl 4455 1517 4455 1519 Dl 4448 1521 4455 1519 Dl 4447 1522 4448 1522 Dl 4455 1517 1 1 De 4462 1514 1 1 De 4460 1510 4462 1514 Dl 4455 1516 4461 1514 Dl 4462 1499 1 1 De 4447 1492 4449 1490 Dl 4451 1492 4449 1490 Dl 4426 1523 4427 1523 Dl 4427 1523 4431 1524 Dl 4432 1522 4431 1524 Dl 4431 1525 4436 1525 Dl 4436 1523 4436 1525 Dl 4436 1527 4438 1529 Dl 4440 1526 4438 1529 Dl 4436 1526 1 1 De 4441 1523 4441 1525 Dl 4447 1526 4449 1526 Dl 4442 1526 4446 1526 Dl 4448 1523 4449 1526 Dl 4450 1526 4457 1522 Dl 4450 1527 1 1 De 4457 1521 4457 1522 Dl 4455 1519 4456 1520 Dl 4464 1518 1 1 De 4462 1515 4464 1517 Dl 4457 1520 4464 1518 Dl 4473 1512 1 1 De 4466 1508 4473 1512 Dl 4465 1507 1 1 De 4462 1512 4472 1512 Dl 4461 1507 4464 1507 Dl 4464 1500 4469 1500 Dl 4464 1507 4469 1500 Dl 4462 1498 4463 1494 Dl 4457 1496 4463 1494 Dl 4406 1514 4408 1517 Dl 4409 1518 4419 1520 Dl 4421 1519 4419 1520 Dl 4419 1520 4421 1524 Dl 4425 1522 4422 1524 Dl 4428 1524 4430 1527 Dl 4430 1526 4430 1527 Dl 4430 1526 4436 1526 Dl 4439 1529 4446 1526 Dl 4439 1530 1 1 De 4467 1526 4469 1524 Dl 4463 1518 4469 1524 Dl 4457 1522 4467 1527 Dl 4471 1512 4471 1514 Dl 4464 1516 4471 1514 Dl 4474 1501 4474 1498 Dl 4469 1499 4474 1498 Dl 4465 1507 4475 1502 Dl 4456 1493 4461 1493 Dl 4462 1494 4463 1494 Dl 4455 1493 4456 1492 Dl 4421 1525 4423 1527 Dl 4425 1527 4430 1527 Dl 4434 1532 4438 1532 Dl 4429 1528 4433 1532 Dl 4438 1530 4438 1532 Dl 4439 1532 4442 1533 Dl 4442 1533 4451 1529 Dl 4451 1527 4451 1529 Dl 4467 1527 4465 1530 Dl 4452 1529 4465 1530 Dl 4470 1523 4471 1523 Dl 4471 1514 4471 1523 Dl 4475 1502 4477 1509 Dl 4472 1511 4477 1509 Dl 4464 1493 4477 1493 Dl 4475 1498 4477 1493 Dl 4409 1518 4410 1522 Dl 4410 1522 4415 1524 Dl 4421 1524 4415 1524 Dl 4422 1531 4433 1532 Dl 4424 1527 4422 1530 Dl 4465 1531 4465 1534 Dl 4444 1536 4465 1534 Dl 4442 1535 4443 1537 Dl 4501 1513 4505 1515 Dl 4478 1509 4501 1513 Dl 4472 1522 4505 1515 Dl 4455 1492 4450 1486 Dl 4450 1490 4450 1486 Dl 4414 1530 4419 1532 Dl 4414 1526 4414 1529 Dl 4421 1532 4419 1532 Dl 4420 1535 4427 1537 Dl 4418 1533 4418 1535 Dl 4433 1532 4427 1537 Dl 4432 1543 4439 1543 Dl 4428 1538 4433 1545 Dl 4442 1536 4439 1543 Dl 4440 1544 4478 1552 Dl 4466 1534 4478 1552 Dl 4506 1516 4535 1521 Dl 4478 1553 4479 1553 Dl 4480 1553 4535 1521 Dl 4480 1490 4501 1513 Dl 4477 1493 4479 1491 Dl 4480 1489 4480 1487 Dl 4462 1492 4480 1487 Dl 4449 1489 4448 1482 Dl 4450 1485 4448 1482 Dl 4405 1527 4405 1530 Dl 4409 1522 4404 1526 Dl 4413 1529 4405 1530 Dl 4404 1560 4406 1560 Dl 4403 1537 4403 1560 Dl 4421 1550 4406 1560 Dl 4412 1536 4422 1550 Dl 4410 1536 4403 1536 Dl 4535 1522 4625 1604 Dl 4481 1576 4625 1604 Dl 4480 1553 4482 1574 Dl 4447 1481 4444 1474 Dl 4444 1475 4481 1485 Dl 4481 1487 4481 1485 Dl 4402 1535 4403 1536 Dl 4405 1530 4401 1535 Dl 4417 1535 4410 1536 Dl 4432 1545 4422 1550 Dl 4407 1561 4482 1574 Dl 4488 1475 4504 1465 Dl 4482 1484 4487 1476 Dl 4505 1466 4535 1521 Dl 4403 1513 4396 1523 Dl 4403 1526 4396 1523 Dl 4387 1525 4386 1530 Dl 4395 1523 4388 1525 Dl 4401 1535 4386 1530 Dl 4361 1535 4359 1553 Dl 4386 1531 4363 1534 Dl 4402 1560 4359 1553 Dl 5040 2502 3024 2502 Dl 5040 1709 5040 2502 Dl 3024 1555 3024 2502 Dl 4001 1500 3024 1554 Dl 4359 1552 4001 1500 Dl 4626 1604 5040 1708 Dl (86)3957 2049 w 5040 1707 5040 1195 Dl 4502 1465 4477 1387 Dl 4478 1387 5040 1195 Dl (87)4768 1479 w 4444 1474 4487 1476 Dl 4341 1453 4388 1525 Dl 4329 1441 4363 1534 Dl 4320 1429 4001 1500 Dl 5 R f (91)4206 1504 w 10 R f 0.1 setlinewidth 5040 486 3024 486 Dl 5040 1195 5040 486 Dl 3024 1554 3024 486 Dl 4328 1426 4477 1387 Dl (92)3922 989 w 4351 1438 4443 1474 Dl 20 R f 16 setlinewidth 5040 2502 3024 2502 Dl 5040 486 5040 2502 Dl 3024 486 5040 486 Dl 3024 2502 3024 486 Dl 10 B f (Fig. 162:)1 372 1 904 2700 t 10 R f (pr.p.it. 15,)1 414 1 1301 2700 t 10 I f (d)1740 2700 w 10 S f (=)1815 2700 w 10 I f (ahead)1895 2700 w 10 R f (, nat. vars.)2 413 1 2139 2700 t 10 B f (Fig. 163:)1 372 1 3194 2700 t 10 R f (pr.p.it. 15,)1 414 1 3591 2700 t 10 I f (d)4030 2700 w 10 S f (=)4105 2700 w 10 I f (behind)4185 2700 w 10 R f (, nat. vars.)2 413 1 4457 2700 t 0.1 setlinewidth 1573 3774 1 1 De 1574 3773 1573 3773 Dl 1573 3774 1 1 De 1525 3759 1557 3786 Dl 1557 3786 1558 3786 Dl 1559 3786 1565 3785 Dl 1566 3784 1573 3774 Dl 1525 3759 1573 3773 Dl 1513 3736 1574 3772 Dl 1501 3731 1514 3735 Dl 1499 3731 1496 3733 Dl 1496 3733 1501 3740 Dl 1502 3740 1509 3747 Dl 1509 3748 1524 3759 Dl 1567 3785 1565 3785 Dl 1575 3785 1567 3785 Dl 1575 3785 1574 3773 Dl 1577 3786 1576 3786 Dl 1575 3785 1 1 De 1577 3785 1574 3773 Dl 1581 3785 1579 3785 Dl 1579 3785 1578 3785 Dl 1580 3785 1574 3773 Dl 1584 3784 1583 3785 Dl 1583 3785 1581 3785 Dl 1583 3783 1574 3772 Dl 1587 3781 1587 3782 Dl 1587 3784 1584 3784 Dl 1588 3780 1575 3772 Dl 1593 3777 1591 3780 Dl 1591 3781 1589 3781 Dl 1593 3776 1575 3772 Dl 1587 3768 1574 3772 Dl 1597 3767 1597 3775 Dl 1597 3776 1596 3776 Dl 1597 3767 1588 3767 Dl 1598 3767 1 1 De 1596 3776 1594 3776 Dl 1569 3786 1567 3785 Dl 1575 3787 1570 3787 Dl 1576 3788 1576 3786 Dl 1578 3789 1576 3789 Dl 1576 3788 1 1 De 1579 3787 1579 3785 Dl 1583 3787 1579 3788 Dl 1583 3787 1583 3785 Dl 1586 3788 1585 3788 Dl 1588 3784 1586 3788 Dl 1585 3787 1584 3787 Dl 1588 3782 1587 3782 Dl 1594 3782 1594 3783 Dl 1594 3784 1589 3784 Dl 1593 3781 1591 3780 Dl 1597 3782 1594 3782 Dl 1597 3781 1596 3776 Dl 1591 3765 1588 3767 Dl 1597 3764 1596 3764 Dl 1598 3764 1598 3766 Dl 1595 3764 1591 3764 Dl 1585 3790 1580 3790 Dl 1579 3789 1578 3789 Dl 1585 3788 1 1 De 1595 3787 1591 3790 Dl 1591 3788 1586 3788 Dl 1596 3785 1594 3783 Dl 1604 3775 1 1 De 1605 3776 1605 3777 Dl 1604 3778 1599 3781 Dl 1604 3775 1597 3775 Dl 1598 3781 1597 3781 Dl 1586 3789 1585 3789 Dl 1600 3785 1599 3781 Dl 1600 3785 1596 3785 Dl 1606 3769 1 1 De 1600 3767 1598 3767 Dl 1604 3768 1600 3767 Dl 1606 3770 1604 3775 Dl 1605 3768 1604 3768 Dl 1573 3790 1571 3790 Dl 1571 3789 1570 3787 Dl 1575 3791 1576 3789 Dl 1574 3792 1574 3791 Dl 1579 3792 1575 3792 Dl 1580 3792 1580 3790 Dl 1584 3792 1581 3792 Dl 1579 3792 1578 3792 Dl 1584 3791 1584 3789 Dl 1592 3791 1589 3792 Dl 1589 3792 1585 3792 Dl 1591 3791 1591 3790 Dl 1601 3788 1601 3786 Dl 1600 3789 1594 3791 Dl 1594 3791 1593 3791 Dl 1600 3785 1 1 De 1607 3783 1 1 De 1607 3781 1605 3777 Dl 1606 3784 1601 3786 Dl 1605 3768 1 1 De 1592 3762 1591 3764 Dl 1594 3762 1596 3764 Dl 1576 3792 1575 3792 Dl 1579 3793 1576 3793 Dl 1581 3793 1581 3792 Dl 1584 3795 1580 3795 Dl 1585 3794 1585 3792 Dl 1586 3797 1584 3795 Dl 1587 3797 1589 3794 Dl 1584 3795 1 1 De 1589 3793 1589 3792 Dl 1595 3795 1593 3795 Dl 1593 3794 1589 3794 Dl 1595 3793 1594 3791 Dl 1602 3790 1596 3795 Dl 1596 3794 1 1 De 1602 3790 1602 3789 Dl 1602 3787 1601 3787 Dl 1609 3785 1 1 De 1609 3785 1607 3783 Dl 1608 3787 1602 3789 Dl 1617 3780 1 1 De 1616 3779 1609 3776 Dl 1609 3776 1 1 De 1617 3780 1607 3782 Dl 1607 3776 1605 3776 Dl 1612 3768 1607 3769 Dl 1613 3769 1609 3776 Dl 1605 3764 1605 3768 Dl 1605 3765 1600 3767 Dl 1560 3788 1558 3786 Dl 1569 3791 1560 3789 Dl 1569 3790 1571 3790 Dl 1570 3794 1569 3791 Dl 1573 3794 1575 3792 Dl 1578 3795 1576 3793 Dl 1580 3796 1580 3795 Dl 1583 3796 1578 3796 Dl 1592 3795 1586 3798 Dl 1614 3792 1612 3794 Dl 1615 3791 1609 3786 Dl 1612 3794 1603 3790 Dl 1617 3782 1617 3780 Dl 1616 3782 1609 3785 Dl 1619 3766 1619 3769 Dl 1617 3766 1612 3768 Dl 1618 3770 1609 3776 Dl 1604 3762 1599 3762 Dl 1605 3762 1604 3762 Dl 1598 3763 1597 3764 Dl 1573 3797 1572 3795 Dl 1578 3797 1573 3797 Dl 1586 3800 1582 3800 Dl 1581 3800 1578 3797 Dl 1586 3800 1586 3798 Dl 1589 3801 1586 3800 Dl 1596 3797 1589 3801 Dl 1596 3797 1596 3795 Dl 1610 3797 1612 3794 Dl 1609 3797 1597 3797 Dl 1616 3792 1615 3792 Dl 1617 3790 1617 3782 Dl 1622 3775 1619 3769 Dl 1621 3777 1617 3779 Dl 1620 3761 1607 3763 Dl 1619 3761 1618 3766 Dl 1561 3792 1560 3789 Dl 1566 3794 1562 3792 Dl 1566 3795 1571 3795 Dl 1582 3800 1572 3800 Dl 1572 3799 1573 3797 Dl 1611 3801 1611 3798 Dl 1611 3802 1591 3804 Dl 1590 3803 1589 3801 Dl 1651 3779 1647 3778 Dl 1646 3778 1622 3776 Dl 1651 3780 1617 3790 Dl 1593 3757 1599 3762 Dl 1593 3759 1593 3762 Dl 1570 3800 1566 3798 Dl 1566 3797 1566 3795 Dl 1570 3800 1572 3800 Dl 1576 3804 1569 3803 Dl 1570 3802 1570 3800 Dl 1576 3804 1581 3800 Dl 1586 3811 1581 3811 Dl 1581 3811 1576 3805 Dl 1588 3810 1591 3804 Dl 1622 3817 1587 3810 Dl 1621 3816 1611 3800 Dl 1685 3782 1651 3780 Dl 1623 3818 1622 3818 Dl 1685 3782 1623 3818 Dl 1646 3777 1622 3757 Dl 1622 3759 1620 3761 Dl 1622 3755 1622 3757 Dl 1621 3755 1604 3762 Dl 1591 3755 1593 3762 Dl 1591 3755 1593 3757 Dl 1558 3799 1558 3797 Dl 1558 3796 1562 3792 Dl 1559 3799 1566 3798 Dl 1558 3823 1556 3823 Dl 1557 3823 1557 3805 Dl 1559 3823 1571 3816 Dl 1571 3816 1563 3805 Dl 1558 3805 1563 3805 Dl 1768 3871 1686 3782 Dl 1769 3871 1622 3837 Dl 1622 3836 1623 3818 Dl 1586 3748 1590 3754 Dl 1623 3751 1586 3748 Dl 1622 3752 1622 3754 Dl 1556 3804 1555 3804 Dl 1556 3804 1558 3800 Dl 1563 3804 1569 3803 Dl 1572 3816 1581 3811 Dl 1621 3837 1558 3824 Dl 1642 3728 1627 3742 Dl 1627 3742 1623 3752 Dl 1685 3782 1642 3728 Dl 1552 3794 1557 3786 Dl 1552 3795 1558 3797 Dl 1545 3800 1545 3797 Dl 1546 3797 1551 3795 Dl 1544 3801 1555 3804 Dl 1525 3816 1527 3804 Dl 1528 3803 1544 3800 Dl 1526 3818 1556 3823 Dl 720 4878 2736 4878 Dl 2736 4878 2736 4320 Dl 720 4877 720 3934 Dl 720 3934 1398 3795 Dl 1400 3794 1526 3817 Dl 2735 4319 1769 3872 Dl (86)1596 4430 w 2735 2862 2024 2862 Dl 2736 2862 2736 4320 Dl 1594 3665 1642 3728 Dl 2024 2862 1594 3664 Dl (87)2230 3535 w 1626 3743 1585 3748 Dl 1545 3795 1509 3747 Dl 1527 3804 1501 3740 Dl 1399 3794 1496 3733 Dl 720 2862 2024 2862 Dl 720 2862 720 3934 Dl 1593 3665 1499 3731 Dl (92)1190 3333 w 1586 3747 1514 3735 Dl 20 R f 16 setlinewidth 2736 4878 720 4878 Dl 2736 2862 2736 4878 Dl 720 2862 2736 2862 Dl 720 4878 720 2862 Dl 10 R f 0.1 setlinewidth 3024 4878 5040 4878 Dl 5040 4220 5040 4878 Dl 3024 4354 3024 4878 Dl 3845 3973 5040 4219 Dl 3844 3973 3024 4353 Dl (86)3998 4514 w 3248 2862 3024 2862 Dl 3024 4353 3024 2862 Dl 3844 3973 3248 2862 Dl (87)3259 3666 w 3249 2862 5040 2862 Dl 5040 4219 5040 2862 Dl (92)4262 3455 w 20 R f 16 setlinewidth 5040 4878 3024 4878 Dl 5040 2862 5040 4878 Dl 3024 2862 5040 2862 Dl 3024 4878 3024 2862 Dl 10 B f (Fig. 164:)1 372 1 904 5076 t 10 R f (pr.p.it. 16,)1 414 1 1301 5076 t 10 I f (d)1740 5076 w 10 S f (=)1815 5076 w 10 I f (ahead)1895 5076 w 10 R f (, nat. vars.)2 413 1 2139 5076 t 10 B f (Fig. 165:)1 372 1 3194 5076 t 10 R f (pr.p.it. 16,)1 414 1 3591 5076 t 10 I f (d)4030 5076 w 10 S f (=)4105 5076 w 10 I f (behind)4185 5076 w 10 R f (, nat. vars.)2 413 1 4457 5076 t 0.1 setlinewidth 720 7254 892 7254 Dl 720 7253 720 6717 Dl 720 6717 1861 6175 Dl 892 7253 1861 6175 Dl (77)1063 6777 w 2735 7254 892 7254 Dl 2736 7253 2736 5477 Dl 2735 5478 1861 6175 Dl (86)2049 6654 w 720 5238 2736 5238 Dl 2736 5238 2736 5477 Dl 720 5238 720 6717 Dl (87)1459 5795 w 20 R f 16 setlinewidth 2736 7254 720 7254 Dl 2736 5238 2736 7254 Dl 720 5238 2736 5238 Dl 720 7254 720 5238 Dl 10 R f 0.1 setlinewidth 4553 6534 1 1 De 4552 6534 4553 6534 Dl 4552 6534 1 1 De 4532 6544 4517 6520 Dl 4533 6544 4532 6544 Dl 4540 6545 4533 6545 Dl 4551 6535 4541 6544 Dl 4552 6533 4517 6520 Dl 4553 6533 4520 6510 Dl 4520 6510 4514 6508 Dl 4512 6508 4514 6508 Dl 4511 6510 4511 6508 Dl 4511 6512 4510 6510 Dl 4517 6519 4512 6513 Dl 4541 6545 4543 6545 Dl 4544 6546 4553 6546 Dl 4553 6535 4553 6546 Dl 4554 6546 4556 6546 Dl 4554 6546 1 1 De 4554 6534 4556 6546 Dl 4557 6546 4559 6546 Dl 4555 6546 4556 6546 Dl 4554 6534 4559 6546 Dl 4561 6546 4562 6545 Dl 4559 6546 4561 6546 Dl 4554 6534 4562 6545 Dl 4566 6545 4566 6543 Dl 4562 6544 4565 6544 Dl 4554 6534 4566 6543 Dl 4569 6542 4570 6539 Dl 4567 6542 4569 6542 Dl 4554 6534 4570 6539 Dl 4554 6533 4564 6531 Dl 4573 6537 4572 6531 Dl 4573 6538 1 1 De 4565 6531 4572 6531 Dl 4572 6531 1 1 De 4570 6539 4572 6539 Dl 4544 6546 4546 6548 Dl 4547 6547 4553 6549 Dl 4553 6547 4553 6549 Dl 4554 6551 4556 6551 Dl 4553 6550 1 1 De 4556 6547 4556 6550 Dl 4556 6550 4561 6549 Dl 4561 6547 4561 6549 Dl 4563 6551 4564 6551 Dl 4566 6546 4564 6551 Dl 4562 6550 4563 6551 Dl 4565 6545 4566 6546 Dl 4572 6544 4572 6546 Dl 4567 6546 4572 6546 Dl 4570 6543 4572 6544 Dl 4573 6543 4575 6543 Dl 4573 6538 4575 6543 Dl 4564 6529 4566 6528 Dl 4570 6529 4571 6529 Dl 4571 6530 4571 6529 Dl 4566 6528 4569 6528 Dl 4558 6552 4563 6552 Dl 4556 6551 4557 6552 Dl 4563 6551 4563 6552 Dl 4571 6553 4574 6549 Dl 4565 6551 4571 6553 Dl 4572 6547 4574 6549 Dl 4581 6539 1 1 De 4581 6540 4581 6539 Dl 4577 6543 4581 6541 Dl 4573 6539 4579 6539 Dl 4575 6544 4576 6544 Dl 4563 6551 4564 6551 Dl 4577 6544 4579 6549 Dl 4575 6549 4579 6549 Dl 4579 6534 1 1 De 4573 6531 4574 6531 Dl 4574 6531 4577 6532 Dl 4579 6539 4579 6534 Dl 4578 6533 4579 6533 Dl 4548 6552 4551 6553 Dl 4547 6549 4547 6552 Dl 4553 6551 4551 6553 Dl 4551 6553 4551 6555 Dl 4551 6555 4556 6555 Dl 4557 6552 4556 6555 Dl 4558 6556 4563 6556 Dl 4556 6556 4558 6557 Dl 4563 6552 4563 6556 Dl 4568 6557 4572 6555 Dl 4563 6556 4568 6557 Dl 4571 6553 4572 6555 Dl 4580 6550 4580 6552 Dl 4574 6555 4580 6552 Dl 4573 6556 4574 6556 Dl 4579 6549 1 1 De 4584 6545 1 1 De 4581 6541 4584 6545 Dl 4580 6548 4584 6546 Dl 4579 6533 1 1 De 4567 6528 4567 6527 Dl 4567 6527 4569 6528 Dl 4551 6556 4552 6557 Dl 4552 6557 4556 6559 Dl 4557 6557 4556 6559 Dl 4557 6559 4562 6559 Dl 4556 6560 1 1 De 4562 6556 4562 6559 Dl 4564 6561 4566 6565 Dl 4568 6560 4566 6565 Dl 4563 6560 4563 6561 Dl 4569 6558 4569 6560 Dl 4575 6561 4577 6561 Dl 4569 6560 4574 6561 Dl 4575 6556 4577 6561 Dl 4579 6561 4584 6555 Dl 4577 6562 4578 6562 Dl 4583 6554 4584 6555 Dl 4580 6552 4582 6553 Dl 4588 6550 1 1 De 4584 6547 4587 6549 Dl 4583 6552 4588 6550 Dl 4584 6540 4592 6543 Dl 4584 6539 1 1 De 4585 6545 4592 6544 Dl 4581 6539 4583 6539 Dl 4581 6533 4584 6533 Dl 4584 6538 4584 6533 Dl 4577 6531 4577 6529 Dl 4574 6530 4577 6529 Dl 4535 6546 4535 6549 Dl 4535 6549 4545 6553 Dl 4547 6552 4545 6553 Dl 4545 6553 4546 6558 Dl 4550 6557 4546 6559 Dl 4554 6557 4556 6562 Dl 4557 6560 4556 6562 Dl 4556 6562 4563 6561 Dl 4567 6566 4574 6561 Dl 4566 6566 4566 6567 Dl 4598 6559 4597 6562 Dl 4588 6552 4598 6559 Dl 4585 6555 4597 6562 Dl 4593 6544 4593 6546 Dl 4588 6549 4593 6546 Dl 4587 6532 4589 6534 Dl 4584 6532 4587 6531 Dl 4584 6539 4589 6534 Dl 4572 6528 4576 6528 Dl 4576 6529 4577 6529 Dl 4572 6528 1 1 De 4547 6559 4548 6562 Dl 4549 6563 4555 6563 Dl 4555 6563 1 1 De 4560 6571 4565 6571 Dl 4555 6564 4559 6571 Dl 4565 6568 4565 6571 Dl 4565 6572 4570 6574 Dl 4580 6567 4570 6574 Dl 4578 6563 4580 6566 Dl 4597 6563 4597 6568 Dl 4580 6566 4597 6568 Dl 4599 6558 4599 6557 Dl 4594 6547 4599 6557 Dl 4590 6535 4595 6540 Dl 4593 6542 4595 6540 Dl 4578 6528 4586 6528 Dl 4586 6531 4586 6528 Dl 4534 6549 4534 6554 Dl 4535 6554 4539 6558 Dl 4546 6558 4539 6558 Dl 4559 6571 1 1 De 4546 6568 4559 6571 Dl 4548 6562 4545 6567 Dl 4598 6568 4600 6575 Dl 4573 6580 4600 6575 Dl 4570 6574 4572 6580 Dl 4618 6543 4623 6545 Dl 4596 6541 4617 6543 Dl 4600 6557 4623 6545 Dl 4567 6525 4572 6528 Dl 4566 6527 4566 6525 Dl 4536 6564 4541 6569 Dl 4538 6559 4536 6564 Dl 4544 6568 4541 6569 Dl 4539 6575 4549 6580 Dl 4541 6570 4539 6575 Dl 4559 6571 4549 6580 Dl 4555 6600 4566 6598 Dl 4549 6581 4555 6601 Dl 4571 6580 4566 6598 Dl 4567 6598 4646 6636 Dl 4600 6575 4646 6636 Dl 4623 6546 4655 6549 Dl 4647 6637 4653 6642 Dl 4655 6549 4653 6642 Dl 4587 6527 4617 6543 Dl 4587 6527 4587 6526 Dl 4586 6526 4586 6525 Dl 4577 6528 4586 6525 Dl 4566 6527 4564 6523 Dl 4566 6525 4564 6523 Dl 4526 6560 4525 6565 Dl 4533 6554 4526 6559 Dl 4535 6564 4525 6565 Dl 4469 6663 4474 6668 Dl 4517 6577 4469 6663 Dl 4530 6620 4474 6668 Dl 4528 6577 4530 6620 Dl 4527 6576 4517 6576 Dl 5009 7254 5040 7254 Dl 5040 6732 5040 7254 Dl 4656 6550 5040 6732 Dl 4877 7108 5008 7254 Dl 4654 6642 4876 7107 Dl (77)4837 6890 w 4564 6522 4561 6519 Dl 4561 6519 4585 6523 Dl 4585 6524 4585 6523 Dl 4517 6574 4517 6576 Dl 4524 6566 4516 6573 Dl 4539 6575 4528 6577 Dl 4554 6602 4530 6620 Dl 4475 6669 4876 7107 Dl 5 R f (81)4631 6797 w 10 R f 0.1 setlinewidth 4584 6519 4587 6514 Dl 4584 6523 4584 6519 Dl 4588 6515 4655 6549 Dl 4532 6544 4520 6554 Dl 4519 6554 4526 6559 Dl 4509 6558 4503 6564 Dl 4519 6555 4509 6557 Dl 4503 6563 4516 6573 Dl 4470 6566 4416 6607 Dl 4503 6564 4470 6566 Dl 4416 6607 4469 6663 Dl 5008 7254 3024 7254 Dl 3024 5440 3024 7254 Dl 4320 6509 3024 5439 Dl 4416 6607 4320 6510 Dl (86)3662 6654 w 3024 5238 5040 5238 Dl 5040 6732 5040 5238 Dl 3024 5348 3024 5238 Dl 4587 6513 4558 6498 Dl 4558 6497 3024 5348 Dl (87)4265 5785 w 4561 6519 4584 6519 Dl 4511 6514 4509 6557 Dl 4510 6511 4470 6566 Dl 4511 6509 4320 6510 Dl 3024 5439 3024 5348 Dl 4515 6508 4558 6498 Dl (92)3772 6039 w 4521 6510 4561 6519 Dl 20 R f 16 setlinewidth 5040 7254 3024 7254 Dl 5040 5238 5040 7254 Dl 3024 5238 5040 5238 Dl 3024 7254 3024 5238 Dl 10 B f (Fig. 166:)1 372 1 904 7452 t 10 R f (pr.p.it. 17,)1 414 1 1301 7452 t 10 I f (d)1740 7452 w 10 S f (=)1815 7452 w 10 I f (ahead)1895 7452 w 10 R f (, nat. vars.)2 413 1 2139 7452 t 10 B f (Fig. 167:)1 372 1 3194 7452 t 10 R f (pr.p.it. 17,)1 414 1 3591 7452 t 10 I f (d)4030 7452 w 10 S f (=)4105 7452 w 10 I f (behind)4185 7452 w 10 R f (, nat. vars.)2 413 1 4457 7452 t (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 41 42 %%Page: 42 43 /saveobj save def mark 43 pagesetup 10 R f (- 42 -)2 216 1 2772 282 t 0.1 setlinewidth 720 2502 847 2502 Dl 720 2501 720 1758 Dl 720 1759 1823 1435 Dl 848 2501 1823 1435 Dl (77)1043 1953 w 2735 2502 847 2502 Dl 2736 2501 2736 851 Dl 2735 852 1823 1435 Dl (86)2021 1930 w 720 486 2736 486 Dl 2736 486 2736 851 Dl 720 486 720 1758 Dl (87)1512 997 w 20 R f 16 setlinewidth 2736 2502 720 2502 Dl 2736 486 2736 2502 Dl 720 486 2736 486 Dl 720 2502 720 486 Dl 10 R f 0.1 setlinewidth 4357 1672 4358 1672 Dl 4357 1671 4358 1671 Dl 4357 1672 4357 1671 Dl 4334 1685 4315 1658 Dl 4336 1685 4335 1685 Dl 4345 1686 4337 1686 Dl 4356 1672 4345 1684 Dl 4356 1671 4315 1658 Dl 4359 1669 4317 1643 Dl 4315 1643 4309 1642 Dl 4307 1643 4309 1642 Dl 4307 1646 4307 1643 Dl 4309 1649 4307 1646 Dl 4315 1657 4309 1650 Dl 4346 1685 4348 1686 Dl 4348 1686 4358 1686 Dl 4358 1672 4358 1686 Dl 4359 1686 4361 1686 Dl 4359 1687 1 1 De 4359 1671 4361 1686 Dl 4363 1686 4365 1686 Dl 4362 1686 4363 1686 Dl 4359 1671 4365 1686 Dl 4368 1686 4369 1685 Dl 4366 1686 4368 1686 Dl 4359 1671 4369 1685 Dl 4374 1683 4375 1681 Dl 4370 1685 4374 1684 Dl 4360 1671 4375 1681 Dl 4379 1681 4381 1676 Dl 4376 1681 4379 1681 Dl 4360 1671 4381 1676 Dl 4359 1670 4372 1665 Dl 4385 1674 4383 1664 Dl 4384 1674 4385 1674 Dl 4372 1663 4382 1663 Dl 4383 1664 1 1 De 4381 1675 4384 1675 Dl 4347 1687 4350 1689 Dl 4351 1689 4358 1691 Dl 4359 1688 4358 1691 Dl 4358 1692 4361 1692 Dl 4358 1692 1 1 De 4362 1692 1 1 De 4362 1688 4362 1692 Dl 4362 1691 4368 1690 Dl 4368 1688 4368 1690 Dl 4370 1692 4372 1692 Dl 4374 1687 4372 1692 Dl 4369 1691 4370 1692 Dl 4374 1685 4375 1686 Dl 4382 1684 4382 1682 Dl 4375 1685 4381 1685 Dl 4379 1680 4382 1682 Dl 4382 1681 4386 1681 Dl 4384 1675 4386 1681 Dl 4373 1664 4375 1662 Dl 4380 1661 4382 1661 Dl 4382 1663 4382 1661 Dl 4375 1661 4380 1661 Dl 4364 1693 4370 1693 Dl 4362 1692 4363 1693 Dl 4370 1692 4370 1693 Dl 4380 1694 4385 1689 Dl 4373 1692 4380 1694 Dl 4382 1686 4385 1689 Dl 4395 1676 4396 1676 Dl 4396 1678 4396 1676 Dl 4388 1681 4395 1677 Dl 4385 1674 4394 1674 Dl 4387 1682 4389 1682 Dl 4370 1692 4372 1692 Dl 4389 1683 4391 1689 Dl 4386 1689 4391 1689 Dl 4393 1667 4394 1667 Dl 4384 1663 4386 1663 Dl 4387 1664 4392 1665 Dl 4394 1674 4394 1667 Dl 4391 1666 4393 1666 Dl 4352 1693 4356 1694 Dl 4352 1689 4352 1693 Dl 4358 1692 4356 1694 Dl 4356 1695 4356 1697 Dl 4356 1697 4361 1697 Dl 4363 1694 4361 1697 Dl 4364 1697 4369 1697 Dl 4362 1697 4364 1698 Dl 4369 1693 4369 1697 Dl 4376 1699 4381 1697 Dl 4371 1698 4376 1699 Dl 4380 1695 4381 1697 Dl 4393 1690 4393 1692 Dl 4384 1697 4393 1692 Dl 4382 1697 4384 1697 Dl 4391 1689 4392 1689 Dl 4400 1684 4400 1683 Dl 4396 1678 4400 1683 Dl 4392 1689 4399 1684 Dl 4392 1666 4393 1666 Dl 4376 1661 4376 1659 Dl 4377 1659 4380 1661 Dl 4356 1698 4357 1699 Dl 4357 1699 4362 1701 Dl 4364 1699 4362 1701 Dl 4362 1702 4368 1702 Dl 4362 1702 1 1 De 4369 1699 4368 1702 Dl 4369 1703 4371 1707 Dl 4375 1702 4371 1707 Dl 4368 1702 4368 1703 Dl 4376 1700 4376 1702 Dl 4382 1702 4386 1702 Dl 4376 1702 4381 1703 Dl 4384 1697 4386 1702 Dl 4388 1703 4397 1696 Dl 4386 1703 4387 1704 Dl 4396 1694 4397 1696 Dl 4393 1693 4395 1694 Dl 4404 1688 4404 1689 Dl 4400 1685 4403 1688 Dl 4396 1693 4404 1689 Dl 4413 1679 1 1 De 4401 1675 4413 1679 Dl 4400 1674 1 1 De 4400 1683 4412 1680 Dl 4396 1674 4399 1674 Dl 4396 1667 4401 1665 Dl 4400 1675 4401 1665 Dl 4391 1665 4391 1660 Dl 4386 1663 4391 1660 Dl 4337 1686 4338 1690 Dl 4339 1690 4349 1694 Dl 4351 1693 4349 1694 Dl 4350 1699 1 1 De 4349 1694 4350 1699 Dl 4355 1697 4350 1699 Dl 4359 1699 4361 1704 Dl 4362 1702 4361 1704 Dl 4360 1703 4368 1703 Dl 4371 1708 4381 1703 Dl 4371 1708 4371 1709 Dl 4414 1703 4416 1699 Dl 4404 1689 4416 1699 Dl 4397 1697 4413 1704 Dl 4413 1681 4413 1683 Dl 4404 1688 4413 1683 Dl 4407 1662 4409 1666 Dl 4401 1664 4406 1661 Dl 4401 1674 4409 1666 Dl 4383 1659 4389 1659 Dl 4389 1660 4391 1660 Dl 4383 1662 4383 1660 Dl 4351 1700 4352 1703 Dl 4353 1703 4360 1704 Dl 4360 1704 1 1 De 4364 1712 4370 1712 Dl 4360 1705 4364 1712 Dl 4371 1709 4370 1712 Dl 4370 1713 4375 1715 Dl 4376 1715 4389 1708 Dl 4388 1704 4389 1708 Dl 4413 1704 4411 1710 Dl 4389 1708 4411 1710 Dl 4416 1699 4417 1697 Dl 4412 1683 4417 1697 Dl 4409 1667 4417 1674 Dl 4413 1679 4417 1674 Dl 4392 1659 4405 1656 Dl 4405 1661 4405 1656 Dl 4338 1690 4338 1695 Dl 4339 1695 4343 1699 Dl 4350 1699 4343 1699 Dl 4363 1712 1 1 De 4349 1708 4363 1712 Dl 4351 1703 4348 1708 Dl 4412 1710 4412 1717 Dl 4376 1720 4412 1717 Dl 4376 1716 4376 1721 Dl 4452 1672 4461 1674 Dl 4418 1674 4453 1673 Dl 4418 1697 4461 1674 Dl 4376 1656 4383 1660 Dl 4376 1658 4375 1655 Dl 4340 1704 4345 1709 Dl 4342 1699 4340 1704 Dl 4348 1708 4345 1709 Dl 4343 1714 4352 1719 Dl 4345 1709 4343 1713 Dl 4363 1713 4352 1719 Dl 4355 1734 4366 1734 Dl 4352 1719 4355 1734 Dl 4376 1722 4366 1734 Dl 4367 1735 4441 1771 Dl 4412 1718 4441 1771 Dl 4462 1674 4528 1670 Dl 4442 1772 4446 1776 Dl 4446 1775 4528 1670 Dl 4407 1653 4453 1673 Dl 4406 1656 4406 1653 Dl 4405 1652 4404 1650 Dl 4389 1659 4404 1650 Dl 4375 1659 4371 1653 Dl 4373 1655 4371 1653 Dl 4330 1699 4330 1704 Dl 4337 1694 4330 1699 Dl 4340 1704 4330 1704 Dl 4297 1750 4299 1752 Dl 4322 1713 4297 1750 Dl 4332 1741 4299 1752 Dl 4332 1713 4332 1740 Dl 4331 1712 4323 1712 Dl 4996 2502 5040 2502 Dl 5040 1821 5040 2502 Dl 4529 1671 5040 1820 Dl 4432 1886 4995 2502 Dl 4445 1776 4431 1885 Dl (77)4744 2036 w 4371 1653 4366 1648 Dl 4367 1648 4403 1648 Dl 4403 1650 4403 1648 Dl 4323 1710 4323 1712 Dl 4329 1705 4322 1710 Dl 4342 1714 4332 1714 Dl 4354 1734 4332 1740 Dl 4300 1753 4431 1885 Dl 4401 1638 4404 1626 Dl 4403 1647 4401 1639 Dl 4405 1627 4528 1670 Dl 4335 1685 4323 1695 Dl 4323 1694 4330 1699 Dl 4314 1697 4310 1702 Dl 4322 1695 4314 1696 Dl 4310 1701 4322 1710 Dl 4286 1700 4265 1718 Dl 4309 1701 4286 1701 Dl 4265 1719 4297 1750 Dl 4995 2502 3024 2502 Dl 3024 847 3024 2502 Dl 4193 1652 3947 1437 Dl 4264 1718 4194 1652 Dl 3947 1436 3024 846 Dl (86)3672 1934 w 3024 486 5040 486 Dl 5040 1820 5040 486 Dl 3024 846 3024 486 Dl 4404 1627 4350 1607 Dl 4350 1606 3947 1437 Dl (87)4159 1015 w 4366 1647 4401 1639 Dl 4309 1650 4314 1696 Dl 4306 1647 4286 1701 Dl 4307 1643 4194 1652 Dl 4309 1642 4350 1607 Dl 5 R f (92)4148 1581 w 10 R f 0.1 setlinewidth 4317 1644 4366 1648 Dl 20 R f 16 setlinewidth 5040 2502 3024 2502 Dl 5040 486 5040 2502 Dl 3024 486 5040 486 Dl 3024 2502 3024 486 Dl 10 B f (Fig. 168:)1 372 1 904 2700 t 10 R f (pr.p.it. 18,)1 414 1 1301 2700 t 10 I f (d)1740 2700 w 10 S f (=)1815 2700 w 10 I f (ahead)1895 2700 w 10 R f (, nat. vars.)2 413 1 2139 2700 t 10 B f (Fig. 169:)1 372 1 3194 2700 t 10 R f (pr.p.it. 18,)1 414 1 3591 2700 t 10 I f (d)4030 2700 w 10 S f (=)4105 2700 w 10 I f (behind)4185 2700 w 10 R f (, nat. vars.)2 413 1 4457 2700 t 0.1 setlinewidth 720 4878 1182 4878 Dl 720 4877 720 3865 Dl 720 3864 1787 3837 Dl 1183 4877 1787 3837 Dl (77)1073 4317 w 2735 4878 1182 4878 Dl 2736 4877 2736 3268 Dl 2735 3268 1787 3837 Dl (86)2103 4290 w 720 2862 2736 2862 Dl 2736 2862 2736 3268 Dl 720 2862 720 3865 Dl (87)1562 3326 w 20 R f 16 setlinewidth 2736 4878 720 4878 Dl 2736 2862 2736 4878 Dl 720 2862 2736 2862 Dl 720 4878 720 2862 Dl 10 R f 0.1 setlinewidth 4167 3927 1 1 De 4166 3926 4167 3926 Dl 4165 3926 1 1 De 4148 3939 4132 3917 Dl 4149 3939 4148 3939 Dl 4156 3938 4149 3939 Dl 4165 3929 4156 3939 Dl 4166 3927 4132 3917 Dl 4167 3926 4132 3906 Dl 4132 3904 4127 3904 Dl 4125 3905 4127 3904 Dl 4124 3908 4124 3906 Dl 4125 3910 4124 3908 Dl 4132 3916 4127 3911 Dl 4156 3939 4158 3939 Dl 4158 3939 4167 3939 Dl 4167 3927 4167 3939 Dl 4168 3939 4170 3939 Dl 4168 3940 1 1 De 4168 3927 4170 3939 Dl 4171 3939 4173 3939 Dl 4170 3939 4171 3939 Dl 4168 3927 4173 3939 Dl 4176 3939 4177 3938 Dl 4174 3939 4176 3939 Dl 4168 3927 4177 3938 Dl 4181 3936 4181 3934 Dl 4178 3937 4181 3936 Dl 4167 3926 4181 3934 Dl 4185 3933 4186 3929 Dl 4183 3934 4185 3934 Dl 4168 3926 4186 3929 Dl 4167 3925 4178 3920 Dl 4190 3926 4188 3918 Dl 4190 3928 1 1 De 4179 3919 4187 3918 Dl 4188 3918 1 1 De 4187 3929 4189 3929 Dl 4159 3940 4161 3942 Dl 4162 3942 4167 3943 Dl 4167 3941 4167 3943 Dl 4168 3944 4170 3944 Dl 4168 3944 1 1 De 4170 3941 4170 3944 Dl 4171 3943 4176 3942 Dl 4176 3940 4176 3942 Dl 4178 3944 4179 3944 Dl 4181 3939 4179 3944 Dl 4177 3943 4178 3944 Dl 4181 3937 4182 3938 Dl 4188 3937 4188 3935 Dl 4183 3937 4188 3937 Dl 4185 3934 4188 3935 Dl 4189 3935 4192 3934 Dl 4190 3929 4192 3934 Dl 4179 3919 4181 3917 Dl 4184 3916 4186 3916 Dl 4186 3918 4186 3916 Dl 4181 3917 4185 3916 Dl 4173 3945 4178 3945 Dl 4171 3945 4172 3945 Dl 4178 3943 4178 3944 Dl 4187 3945 4191 3940 Dl 4180 3944 4186 3945 Dl 4188 3938 4191 3940 Dl 4198 3928 4199 3928 Dl 4199 3930 4199 3928 Dl 4194 3934 4199 3930 Dl 4191 3927 4198 3927 Dl 4193 3934 4194 3934 Dl 4178 3944 4180 3944 Dl 4194 3935 4196 3940 Dl 4191 3940 4196 3940 Dl 4197 3920 4198 3920 Dl 4188 3918 4190 3918 Dl 4190 3918 4195 3918 Dl 4198 3927 4198 3920 Dl 4195 3919 4196 3919 Dl 4162 3946 4165 3947 Dl 4162 3942 4162 3945 Dl 4167 3945 4165 3947 Dl 4165 3947 4165 3949 Dl 4165 3948 4170 3948 Dl 4171 3945 4170 3948 Dl 4172 3949 4177 3949 Dl 4170 3948 4172 3949 Dl 4177 3945 4177 3949 Dl 4182 3949 4187 3947 Dl 4178 3950 4183 3950 Dl 4186 3945 4187 3947 Dl 4198 3941 4198 3943 Dl 4191 3948 4198 3943 Dl 4187 3948 4189 3948 Dl 4197 3941 1 1 De 4204 3935 4204 3934 Dl 4200 3929 4204 3934 Dl 4197 3941 4203 3936 Dl 4195 3919 4196 3919 Dl 4181 3916 4181 3914 Dl 4182 3915 4185 3916 Dl 4165 3950 4166 3950 Dl 4166 3950 4170 3952 Dl 4171 3950 4170 3952 Dl 4171 3952 4176 3952 Dl 4170 3952 1 1 De 4177 3949 4176 3952 Dl 4176 3954 4178 3957 Dl 4181 3952 4178 3957 Dl 4176 3953 4176 3954 Dl 4182 3950 4182 3952 Dl 4188 3953 4191 3953 Dl 4183 3953 4188 3953 Dl 4189 3948 4191 3953 Dl 4194 3954 4201 3947 Dl 4192 3954 4193 3954 Dl 4200 3946 4201 3947 Dl 4197 3943 4199 3944 Dl 4207 3940 1 1 De 4203 3937 4206 3939 Dl 4200 3944 4207 3940 Dl 4214 3929 1 1 De 4204 3927 4214 3929 Dl 4204 3926 1 1 De 4204 3935 4214 3931 Dl 4200 3927 4202 3926 Dl 4198 3920 4203 3918 Dl 4203 3927 4203 3918 Dl 4195 3918 4194 3914 Dl 4190 3917 4194 3914 Dl 4150 3940 4150 3943 Dl 4151 3944 4159 3947 Dl 4161 3946 4159 3947 Dl 4160 3947 4160 3951 Dl 4165 3949 4161 3951 Dl 4167 3950 4169 3954 Dl 4170 3953 4169 3954 Dl 4169 3954 4176 3954 Dl 4179 3958 4188 3953 Dl 4178 3957 4178 3958 Dl 4216 3952 4218 3948 Dl 4208 3941 4218 3948 Dl 4201 3946 4215 3952 Dl 4214 3931 4214 3933 Dl 4207 3938 4214 3933 Dl 4208 3915 4210 3918 Dl 4203 3917 4207 3914 Dl 4204 3926 4210 3918 Dl 4187 3913 4192 3913 Dl 4192 3914 4194 3914 Dl 4187 3915 4187 3914 Dl 4161 3952 4162 3954 Dl 4162 3955 4168 3955 Dl 4168 3955 1 1 De 4172 3962 4177 3962 Dl 4169 3956 4172 3962 Dl 4178 3960 4177 3962 Dl 4177 3962 4181 3964 Dl 4182 3963 4194 3957 Dl 4193 3954 4194 3957 Dl 4215 3954 4213 3959 Dl 4194 3958 4213 3959 Dl 4218 3948 4219 3946 Dl 4215 3934 4219 3946 Dl 4211 3919 4218 3925 Dl 4215 3930 4218 3925 Dl 4195 3914 4206 3909 Dl 4207 3914 4206 3909 Dl 4150 3943 4150 3947 Dl 4151 3948 4154 3951 Dl 4160 3951 4154 3951 Dl 4171 3962 1 1 De 4159 3959 4171 3962 Dl 4162 3954 4159 3958 Dl 4214 3959 4214 3965 Dl 4183 3969 4214 3965 Dl 4182 3964 4182 3969 Dl 4248 3921 4256 3921 Dl 4218 3925 4248 3920 Dl 4220 3946 4256 3921 Dl 4180 3911 4187 3914 Dl 4181 3913 4180 3911 Dl 4151 3955 4155 3959 Dl 4154 3951 4152 3955 Dl 4157 3959 4155 3959 Dl 4154 3963 4161 3967 Dl 4155 3959 4153 3962 Dl 4171 3962 4161 3967 Dl 4163 3980 4173 3980 Dl 4162 3968 4163 3980 Dl 4182 3970 4173 3980 Dl 4172 3980 4233 4009 Dl 4214 3966 4233 4009 Dl 4258 3920 4314 3908 Dl 4234 4010 4237 4013 Dl 4237 4013 4314 3908 Dl 4207 3907 4248 3920 Dl 4206 3908 4206 3906 Dl 4206 3905 4204 3903 Dl 4193 3913 4204 3903 Dl 4181 3914 4177 3909 Dl 4179 3911 4177 3909 Dl 4143 3952 4143 3955 Dl 4150 3948 4144 3952 Dl 4151 3955 4143 3955 Dl 4114 3989 4116 3991 Dl 4137 3962 4114 3989 Dl 4142 3984 4116 3991 Dl 4144 3964 4143 3984 Dl 4144 3962 4137 3962 Dl 4660 4878 5040 4878 Dl 5040 3927 5040 4878 Dl 4315 3908 5040 3926 Dl 4199 4087 4659 4878 Dl 4236 4013 4198 4086 Dl (77)4652 4359 w 4177 3909 4172 3906 Dl 4173 3904 4203 3901 Dl 4204 3903 4203 3901 Dl 4137 3961 4137 3962 Dl 4143 3956 4137 3960 Dl 4153 3962 4145 3962 Dl 4162 3980 4143 3984 Dl 4116 3991 4198 4086 Dl 4201 3893 4201 3882 Dl 4202 3901 4200 3894 Dl 4201 3883 4314 3908 Dl 4148 3939 4138 3947 Dl 4139 3948 4144 3952 Dl 4130 3948 4127 3952 Dl 4138 3948 4131 3948 Dl 4128 3953 4137 3960 Dl 4107 3952 4091 3964 Dl 4126 3952 4108 3951 Dl 4091 3964 4114 3989 Dl 4659 4878 3024 4878 Dl 3024 3261 3024 4878 Dl 4043 3913 3947 3816 Dl 4091 3963 4044 3913 Dl 3947 3815 3024 3260 Dl (86)3589 4293 w 3024 2862 5040 2862 Dl 5040 3926 5040 2862 Dl 3024 3260 3024 2862 Dl 4199 3882 4152 3871 Dl 4152 3871 3947 3816 Dl (87)4113 3343 w 4172 3905 4200 3894 Dl 4127 3912 4131 3948 Dl 4124 3908 4108 3951 Dl 4124 3906 4044 3913 Dl 4127 3904 4152 3871 Dl 4132 3905 4171 3905 Dl 20 R f 16 setlinewidth 5040 4878 3024 4878 Dl 5040 2862 5040 4878 Dl 3024 2862 5040 2862 Dl 3024 4878 3024 2862 Dl 10 B f (Fig. 170:)1 372 1 904 5076 t 10 R f (pr.p.it. 19,)1 414 1 1301 5076 t 10 I f (d)1740 5076 w 10 S f (=)1815 5076 w 10 I f (ahead)1895 5076 w 10 R f (, nat. vars.)2 413 1 2139 5076 t 10 B f (Fig. 171:)1 372 1 3194 5076 t 10 R f (pr.p.it. 19,)1 414 1 3591 5076 t 10 I f (d)4030 5076 w 10 S f (=)4105 5076 w 10 I f (behind)4185 5076 w 10 R f (, nat. vars.)2 413 1 4457 5076 t 0.1 setlinewidth 720 7254 1840 7254 Dl 720 7253 720 5702 Dl 720 5702 1710 6258 Dl 1840 7253 1710 6258 Dl (77)1156 6642 w 2735 7254 1840 7254 Dl 2736 7253 2736 5662 Dl 2736 5662 1710 6258 Dl (86)2238 6598 w 2736 5238 720 5238 Dl 2736 5238 2736 5662 Dl 720 5238 720 5702 Dl (87)1666 5643 w 20 R f 16 setlinewidth 2736 7254 720 7254 Dl 2736 5238 2736 7254 Dl 720 5238 2736 5238 Dl 720 7254 720 5238 Dl 10 R f 0.1 setlinewidth 3986 6219 3984 6215 Dl 3988 6219 3987 6219 Dl 3990 6216 3988 6218 Dl 3990 6216 3984 6215 Dl 3990 6214 3984 6212 Dl 3983 6212 1 1 De 3983 6213 1 1 De 3988 6219 3990 6219 Dl 3990 6217 3990 6219 Dl 3991 6217 3991 6219 Dl 3992 6217 3993 6219 Dl 3991 6216 3993 6218 Dl 3994 6218 1 1 De 3992 6215 3995 6217 Dl 3996 6217 3996 6216 Dl 3996 6217 1 1 De 3991 6216 3996 6216 Dl 3991 6215 3993 6214 Dl 3996 6215 3996 6213 Dl 3994 6213 3996 6213 Dl 3996 6216 1 1 De 3989 6219 1 1 De 3989 6220 3990 6220 Dl 3990 6220 1 1 De 3992 6220 1 1 De 3992 6220 1 1 De 3992 6220 3993 6220 Dl 3993 6220 1 1 De 3994 6219 3994 6220 Dl 3995 6218 3996 6218 Dl 3996 6217 1 1 De 3997 6217 3998 6217 Dl 3998 6216 3998 6217 Dl 3994 6213 1 1 De 3995 6213 1 1 De 3992 6220 3993 6220 Dl 3997 6220 3998 6219 Dl 3994 6220 3996 6220 Dl 3997 6219 3998 6219 Dl 3999 6217 4000 6216 Dl 3997 6215 3999 6215 Dl 3999 6218 3999 6219 Dl 3998 6219 3999 6219 Dl 3997 6213 3998 6213 Dl 3999 6214 3999 6213 Dl 3990 6220 1 1 De 3990 6220 1 1 De 3990 6220 1 1 De 3991 6221 3992 6221 Dl 3992 6221 1 1 De 3992 6221 3993 6221 Dl 3993 6220 3993 6221 Dl 3995 6221 3996 6221 Dl 3994 6222 3995 6222 Dl 3996 6221 1 1 De 4000 6220 1 1 De 3998 6221 4000 6220 Dl 4000 6216 4001 6217 Dl 3999 6218 4001 6217 Dl 3995 6213 1 1 De 3991 6222 3992 6222 Dl 3992 6222 3993 6222 Dl 3993 6222 1 1 De 3994 6223 3994 6224 Dl 3994 6223 3994 6224 Dl 3995 6222 1 1 De 3997 6222 3998 6222 Dl 3996 6222 3997 6222 Dl 3998 6221 3998 6222 Dl 3999 6223 4001 6221 Dl 4001 6221 1 1 De 4001 6220 1 1 De 4002 6218 4003 6218 Dl 4001 6220 4003 6219 Dl 4001 6215 4005 6215 Dl 4002 6217 4005 6216 Dl 4001 6215 1 1 De 4000 6212 4001 6212 Dl 4001 6214 4001 6212 Dl 3998 6212 1 1 De 3998 6212 1 1 De 3987 6220 1 1 De 3987 6220 3989 6220 Dl 3989 6221 3989 6222 Dl 3989 6222 1 1 De 3991 6221 3991 6222 Dl 3991 6222 3993 6222 Dl 3995 6223 3997 6222 Dl 4008 6223 4008 6222 Dl 4003 6220 4008 6222 Dl 4001 6221 4007 6223 Dl 4006 6217 1 1 De 4004 6219 4006 6217 Dl 4002 6212 4003 6212 Dl 4000 6212 4001 6212 Dl 4002 6214 4003 6212 Dl 3996 6212 3997 6212 Dl 3990 6222 1 1 De 3990 6222 3991 6222 Dl 3993 6225 3994 6225 Dl 3992 6223 3992 6225 Dl 3994 6225 1 1 De 3994 6226 3995 6226 Dl 3996 6225 3999 6224 Dl 3999 6223 3999 6224 Dl 4007 6223 4007 6225 Dl 4000 6224 4007 6225 Dl 4008 6221 1 1 De 4006 6217 4008 6221 Dl 4003 6213 4006 6214 Dl 4006 6215 4006 6214 Dl 3998 6211 4001 6210 Dl 4001 6211 4001 6210 Dl 3987 6220 1 1 De 3988 6222 1 1 De 3988 6222 3989 6222 Dl 3990 6224 3992 6225 Dl 3989 6223 1 1 De 4008 6226 4008 6228 Dl 3996 6228 4008 6228 Dl 3996 6227 3996 6228 Dl 4020 6210 4025 6210 Dl 4007 6213 4020 6211 Dl 4009 6220 4025 6210 Dl 3994 6212 3996 6212 Dl 3993 6212 1 1 De 3988 6223 3988 6224 Dl 3987 6222 1 1 De 3988 6224 1 1 De 3988 6225 3989 6226 Dl 3988 6225 1 1 De 3991 6225 3989 6226 Dl 3991 6230 3993 6230 Dl 3990 6227 3990 6230 Dl 3995 6228 3993 6230 Dl 3993 6231 4026 6256 Dl 4008 6228 4026 6256 Dl 4026 6210 4078 6197 Dl 4027 6257 4031 6261 Dl 4032 6261 4078 6197 Dl 4001 6210 4020 6211 Dl 4001 6210 1 1 De 4000 6209 1 1 De 3998 6211 4000 6209 Dl 3994 6212 3993 6212 Dl 3993 6212 1 1 De 3985 6222 1 1 De 3986 6222 3985 6222 Dl 3987 6222 3985 6222 Dl 3985 6225 3980 6230 Dl 3985 6230 3980 6230 Dl 3985 6225 3985 6230 Dl 3984 6224 3985 6224 Dl 3881 7254 5040 7254 Dl 5040 5657 5040 7254 Dl 4079 6196 5040 5656 Dl 4005 6298 3880 7254 Dl 4031 6261 4006 6297 Dl (77)4486 6624 w 3992 6211 3991 6211 Dl 3992 6211 3999 6209 Dl 3985 6223 3984 6223 Dl 3987 6224 3985 6224 Dl 3990 6230 3985 6230 Dl 3981 6231 4006 6297 Dl 3998 6207 3998 6205 Dl 3999 6208 3998 6207 Dl 3999 6205 4078 6197 Dl 3987 6218 3985 6220 Dl 3985 6222 1 1 De 3983 6222 1 1 De 3984 6220 3983 6220 Dl 3983 6221 3984 6223 Dl 3979 6221 3977 6223 Dl 3982 6221 3980 6221 Dl 3978 6224 3980 6230 Dl 3880 7254 3024 7254 Dl 3024 5658 3024 7254 Dl 3973 6214 3970 6207 Dl 3976 6222 3973 6215 Dl 3970 6207 3024 5657 Dl (86)3405 6591 w 5040 5238 3024 5238 Dl 5040 5656 5040 5238 Dl 3024 5657 3024 5238 Dl 3988 6205 3998 6205 Dl 3987 6206 3970 6207 Dl (87)3979 5630 w 3992 6210 3998 6207 Dl 3983 6213 3983 6220 Dl 3983 6214 3980 6221 Dl 3982 6213 3973 6215 Dl 3984 6212 3988 6206 Dl 3984 6212 3991 6211 Dl 20 R f 16 setlinewidth 5040 7254 3024 7254 Dl 5040 5238 5040 7254 Dl 3024 5238 5040 5238 Dl 3024 7254 3024 5238 Dl 10 B f (Fig. 172:)1 372 1 904 7452 t 10 R f (pr.p.it. 20,)1 414 1 1301 7452 t 10 I f (d)1740 7452 w 10 S f (=)1815 7452 w 10 I f (ahead)1895 7452 w 10 R f (, nat. vars.)2 413 1 2139 7452 t 10 B f (Fig. 173:)1 372 1 3194 7452 t 10 R f (pr.p.it. 20,)1 414 1 3591 7452 t 10 I f (d)4030 7452 w 10 S f (=)4105 7452 w 10 I f (behind)4185 7452 w 10 R f (, nat. vars.)2 413 1 4457 7452 t (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 42 43 %%Page: 43 44 /saveobj save def mark 44 pagesetup 10 R f (- 43 -)2 216 1 2772 282 t 0.1 setlinewidth 720 2498 720 1663 Dl 720 1663 1733 1491 Dl 720 2499 1733 1491 Dl (77)1007 1904 w 2736 2502 720 2502 Dl 2736 2501 2736 1085 Dl 720 2501 720 2499 Dl 2735 1085 1733 1491 Dl (86)1955 1991 w 720 486 2736 486 Dl 2736 486 2736 1085 Dl 720 486 720 1663 Dl (87)1575 994 w 20 R f 16 setlinewidth 2736 2502 720 2502 Dl 2736 486 2736 2502 Dl 720 486 2736 486 Dl 720 2502 720 486 Dl 10 R f 0.1 setlinewidth 4042 1499 1 1 De 4042 1499 4047 1498 Dl 4042 1499 4047 1498 Dl 5040 1668 5040 2494 Dl 4048 1498 5040 1667 Dl 4042 1501 5040 2494 Dl (77)4655 1906 w 4042 1499 1 1 De 4042 1497 4042 1496 Dl 4043 1497 4047 1498 Dl 5040 2502 3024 2502 Dl 5040 2495 5040 2502 Dl 3024 1087 3024 2502 Dl 4039 1498 4024 1491 Dl 4024 1491 3024 1086 Dl (86)3707 1992 w 3024 486 5040 486 Dl 5040 1667 5040 486 Dl 3024 1086 3024 486 Dl 4041 1496 4039 1496 Dl 4039 1496 4024 1491 Dl (87)4084 996 w 4042 1499 1 1 De 4039 1498 4039 1496 Dl 20 R f 16 setlinewidth 5040 2502 3024 2502 Dl 5040 486 5040 2502 Dl 3024 486 5040 486 Dl 3024 2502 3024 486 Dl 10 B f (Fig. 174:)1 372 1 904 2700 t 10 R f (pr.p.it. 21,)1 414 1 1301 2700 t 10 I f (d)1740 2700 w 10 S f (=)1815 2700 w 10 I f (ahead)1895 2700 w 10 R f (, nat. vars.)2 413 1 2139 2700 t 10 B f (Fig. 175:)1 372 1 3194 2700 t 10 R f (pr.p.it. 21,)1 414 1 3591 2700 t 10 I f (d)4030 2700 w 10 S f (=)4105 2700 w 10 I f (behind)4185 2700 w 10 R f (, nat. vars.)2 413 1 4457 2700 t 0.1 setlinewidth 720 4878 2736 4878 Dl 2736 4877 2736 4421 Dl 720 4877 720 3584 Dl 720 3584 1726 3869 Dl 2735 4420 1726 3869 Dl (77)1528 4395 w 2736 4421 2736 3938 Dl 2735 3938 1726 3869 Dl (86)2349 4096 w 2736 2862 720 2862 Dl 2736 2862 2736 3938 Dl 720 2862 720 3584 Dl (87)1739 3365 w 20 R f 16 setlinewidth 2736 4878 720 4878 Dl 2736 2862 2736 4878 Dl 720 2862 2736 2862 Dl 720 4878 720 2862 Dl 10 R f 0.1 setlinewidth 4030 3870 4032 3870 Dl 4030 3870 4032 3870 Dl 3024 4878 5040 4878 Dl 5040 3585 5040 4878 Dl 3024 4421 3024 4878 Dl 4033 3869 5040 3584 Dl 4029 3871 3024 4420 Dl (77)4131 4395 w 4029 3870 4032 3870 Dl 3024 3940 3024 4420 Dl 4029 3871 3024 3939 Dl (86)3308 4096 w 5040 2862 3024 2862 Dl 5040 3584 5040 2862 Dl 3024 3939 3024 2862 Dl (87)3919 3365 w 20 R f 16 setlinewidth 5040 4878 3024 4878 Dl 5040 2862 5040 4878 Dl 3024 2862 5040 2862 Dl 3024 4878 3024 2862 Dl 10 B f (Fig. 176:)1 372 1 904 5076 t 10 R f (pr.p.it. 22,)1 414 1 1301 5076 t 10 I f (d)1740 5076 w 10 S f (=)1815 5076 w 10 I f (ahead)1895 5076 w 10 R f (, nat. vars.)2 413 1 2139 5076 t 10 B f (Fig. 177:)1 372 1 3194 5076 t 10 R f (pr.p.it. 22,)1 414 1 3591 5076 t 10 I f (d)4030 5076 w 10 S f (=)4105 5076 w 10 I f (behind)4185 5076 w 10 R f (, nat. vars.)2 413 1 4457 5076 t ( in iteration 16 \(figures 164\261165\) differs substantially from that in iterations 15)12 3296(The view direction)2 774 2 970 5232 t (and 17, despite monotonic reductions of both the linear objective)9 2597 1 720 5352 t 10 I f (c)3342 5352 w 7 R f (T)3397 5312 w 10 I f (x)3456 5352 w 10 R f (and the potential function.)3 1049 1 3525 5352 t ( appear to be mirror images.)5 1180(Notice how the forward and backward views of the last two iterations)11 2890 2 970 5508 t ( ``natural'' variables\) is much longer in the)7 1812(This is so because the transformed polytope \(as seen by the)10 2508 2 720 5628 t ( an outside view, analogous to figures)6 1608( Indeed,)1 362( or \(0,0,1\) directions.)3 891(\(0,1,0\) direction than in the \(1,0,0\))5 1459 4 720 5748 t ( up the)2 284( turning)1 321( By)1 174(101\261135, of the the transformed polytope from iteration 22 is simply a horizontal line.)13 3541 4 720 5868 t ( figure)1 297( nonbinding constraints have gone:)4 1435(magnification in figures 175 and 177, we can see where all the)11 2588 3 720 5988 t (178 is like figure 175, but with view angle 0.5)9 1963 1 720 6108 t 10 S f (\260)2683 6108 w 10 R f ( but with view angle)4 864(, and figure 179 is like figure 177,)7 1453 2 2723 6108 t (0.15)720 6228 w 10 S f (\260)895 6228 w 10 R f (.)935 6228 w (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 43 44 %%Page: 44 45 /saveobj save def mark 45 pagesetup 10 R f (- 44 -)2 216 1 2772 282 t 0.1 setlinewidth 2284 1855 1 1 De 2285 1854 1 1 De 2273 1861 2260 1848 Dl 2275 1862 1 1 De 2278 1862 2275 1862 Dl 2283 1855 2278 1861 Dl 2283 1854 2260 1848 Dl 2283 1853 2255 1836 Dl 2255 1836 2251 1836 Dl 2251 1837 2251 1836 Dl 2252 1840 2250 1838 Dl 2254 1843 2252 1841 Dl 2260 1847 2255 1843 Dl 2280 1862 1 1 De 2279 1862 2284 1862 Dl 2284 1855 2284 1862 Dl 2286 1862 1 1 De 2285 1855 2286 1862 Dl 2287 1862 2288 1862 Dl 2285 1855 2288 1862 Dl 2290 1861 1 1 De 2288 1862 2289 1862 Dl 2285 1854 2290 1861 Dl 2293 1860 2293 1859 Dl 2290 1861 2292 1861 Dl 2285 1854 2293 1859 Dl 2295 1858 2297 1856 Dl 2293 1859 2295 1859 Dl 2285 1854 2297 1856 Dl 2285 1853 2293 1848 Dl 2301 1853 2301 1846 Dl 2300 1854 1 1 De 2294 1848 2301 1846 Dl 2297 1855 2299 1855 Dl 2280 1863 2281 1863 Dl 2282 1864 2284 1864 Dl 2284 1863 2284 1864 Dl 2285 1864 2286 1864 Dl 2286 1862 2286 1864 Dl 2287 1864 2289 1864 Dl 2289 1863 2289 1864 Dl 2291 1864 1 1 De 2291 1863 2293 1861 Dl 2290 1864 1 1 De 2293 1861 1 1 De 2297 1860 2297 1859 Dl 2293 1861 2296 1861 Dl 2295 1859 2297 1859 Dl 2298 1859 2300 1859 Dl 2300 1856 2300 1859 Dl 2301 1846 1 1 De 2293 1847 2295 1845 Dl 2300 1844 2301 1844 Dl 2301 1846 2301 1844 Dl 2295 1844 2298 1843 Dl 2288 1864 2290 1864 Dl 2287 1864 1 1 De 2295 1864 2298 1862 Dl 2291 1865 2294 1865 Dl 2297 1861 2298 1862 Dl 2307 1854 1 1 De 2307 1855 2307 1854 Dl 2301 1858 2306 1856 Dl 2300 1854 2306 1854 Dl 2301 1859 1 1 De 2290 1864 2291 1864 Dl 2301 1859 2301 1862 Dl 2299 1862 2301 1862 Dl 2309 1847 1 1 De 2301 1846 2303 1846 Dl 2303 1846 2307 1846 Dl 2307 1853 2309 1847 Dl 2308 1846 2309 1846 Dl 2282 1865 2283 1865 Dl 2282 1863 2282 1864 Dl 2284 1865 2283 1865 Dl 2283 1866 1 1 De 2284 1866 2286 1866 Dl 2286 1865 2286 1866 Dl 2287 1866 2289 1866 Dl 2287 1866 1 1 De 2289 1865 2289 1866 Dl 2293 1866 2295 1866 Dl 2290 1866 2292 1866 Dl 2295 1866 1 1 De 2301 1863 2301 1864 Dl 2296 1866 2301 1864 Dl 2296 1866 1 1 De 2308 1859 1 1 De 2307 1856 2308 1859 Dl 2302 1862 2307 1860 Dl 2309 1846 1 1 De 2296 1844 2296 1842 Dl 2296 1842 2298 1843 Dl 2284 1866 1 1 De 2284 1867 2286 1867 Dl 2286 1867 1 1 De 2286 1867 2288 1867 Dl 2288 1866 2288 1867 Dl 2289 1868 2289 1869 Dl 2291 1868 2289 1869 Dl 2291 1868 1 1 De 2294 1868 2296 1868 Dl 2292 1868 2294 1868 Dl 2296 1866 2296 1868 Dl 2297 1867 2302 1865 Dl 2302 1865 1 1 De 2302 1864 1 1 De 2307 1860 2308 1861 Dl 2303 1864 2308 1862 Dl 2319 1855 1 1 De 2312 1853 2319 1855 Dl 2311 1853 1 1 De 2308 1858 2318 1856 Dl 2308 1853 2310 1853 Dl 2309 1846 2315 1844 Dl 2310 1853 2315 1844 Dl 2309 1846 2309 1841 Dl 2304 1846 2309 1841 Dl 2276 1863 2276 1864 Dl 2276 1864 2280 1865 Dl 2281 1865 2280 1865 Dl 2281 1866 2281 1867 Dl 2283 1867 2281 1867 Dl 2284 1867 2285 1868 Dl 2285 1868 1 1 De 2285 1868 2288 1868 Dl 2289 1869 2294 1868 Dl 2310 1868 2312 1866 Dl 2308 1862 2312 1866 Dl 2303 1866 2309 1868 Dl 2317 1858 2318 1856 Dl 2308 1861 2316 1858 Dl 2322 1843 2322 1839 Dl 2315 1844 2322 1839 Dl 2311 1852 2322 1843 Dl 2302 1841 2307 1840 Dl 2308 1841 2309 1841 Dl 2300 1844 2301 1842 Dl 2282 1868 1 1 De 2283 1869 2285 1869 Dl 2286 1871 2288 1871 Dl 2285 1869 2286 1871 Dl 2288 1871 1 1 De 2290 1872 2291 1872 Dl 2290 1871 2296 1869 Dl 2296 1868 2296 1869 Dl 2307 1870 2309 1868 Dl 2297 1870 2306 1870 Dl 2313 1865 2314 1865 Dl 2316 1858 2314 1865 Dl 2323 1844 2325 1851 Dl 2319 1855 2325 1851 Dl 2309 1840 2326 1831 Dl 2324 1838 2326 1831 Dl 2276 1865 2276 1866 Dl 2276 1865 2278 1866 Dl 2279 1867 2281 1867 Dl 2281 1870 2286 1871 Dl 2281 1868 2280 1869 Dl 2306 1870 2305 1872 Dl 2291 1872 2305 1872 Dl 2290 1872 2290 1873 Dl 2366 1842 2376 1842 Dl 2325 1850 2365 1842 Dl 2315 1865 2376 1842 Dl 2296 1839 2301 1842 Dl 2296 1842 2296 1838 Dl 2278 1868 2280 1869 Dl 2278 1867 2278 1868 Dl 2281 1869 2280 1869 Dl 2280 1871 2282 1872 Dl 2279 1871 1 1 De 2286 1871 2282 1872 Dl 2283 1875 2286 1875 Dl 2283 1873 2283 1875 Dl 2290 1873 2286 1875 Dl 2286 1875 2304 1881 Dl 2304 1872 2304 1881 Dl 2376 1842 2664 1776 Dl 2304 1882 1 1 De 2304 1882 2664 1776 Dl 2329 1825 2365 1842 Dl 2326 1831 2329 1825 Dl 2330 1825 2330 1820 Dl 2307 1840 2330 1820 Dl 2295 1842 2293 1836 Dl 2295 1838 2293 1836 Dl 2274 1867 2274 1868 Dl 2276 1866 2274 1867 Dl 2277 1868 2274 1868 Dl 2269 1876 1 1 De 2272 1871 2268 1876 Dl 2276 1876 2269 1876 Dl 2276 1870 2276 1875 Dl 2275 1870 2273 1870 Dl 2736 1786 2736 2331 Dl 2670 1775 2736 1786 Dl 2290 1887 2736 2331 Dl 2665 1775 2669 1774 Dl 2304 1883 2289 1887 Dl (77)2536 2012 w 2293 1835 2289 1830 Dl 2290 1830 2331 1815 Dl 2331 1820 2331 1815 Dl 2275 1868 2273 1869 Dl 2278 1871 2275 1871 Dl 2282 1875 2276 1875 Dl 2270 1877 2289 1887 Dl 2340 1789 2388 1689 Dl 2332 1814 2339 1789 Dl 2389 1690 2669 1774 Dl 5 R f (82)2434 1781 w 10 R f 0.1 setlinewidth 2274 1862 2271 1865 Dl 2273 1866 2271 1865 Dl 2268 1866 2268 1867 Dl 2270 1866 2268 1866 Dl 2272 1869 2268 1867 Dl 2259 1867 2257 1870 Dl 2267 1866 2260 1866 Dl 2258 1871 2268 1876 Dl 2736 2502 720 2502 Dl 2736 2332 2736 2502 Dl 720 1126 720 2502 Dl 2218 1849 1280 1352 Dl 2257 1869 2219 1849 Dl 1280 1351 720 1125 Dl (86)1460 2019 w 720 486 2736 486 Dl 2736 1786 2736 486 Dl 720 1125 720 486 Dl 2387 1689 2229 1641 Dl 2229 1641 1280 1352 Dl (87)1788 1020 w 2289 1830 2339 1789 Dl 2256 1844 2268 1866 Dl 2253 1841 2260 1866 Dl 2250 1837 2219 1849 Dl 2250 1836 2229 1641 Dl (92)1870 1639 w 2255 1835 2288 1830 Dl 5 R f (93)2271 1744 w 20 R f 16 setlinewidth 2736 2502 720 2502 Dl 2736 486 2736 2502 Dl 720 486 2736 486 Dl 720 2502 720 486 Dl 10 R f 0.1 setlinewidth 3446 1612 3445 1610 Dl 3448 1613 1 1 De 3449 1611 3448 1613 Dl 3449 1610 3445 1610 Dl 3449 1611 3445 1609 Dl 3445 1609 1 1 De 3449 1613 3450 1613 Dl 3450 1611 3450 1613 Dl 3451 1611 3451 1613 Dl 3451 1611 3452 1613 Dl 3451 1611 3453 1613 Dl 3453 1612 1 1 De 3451 1611 3453 1612 Dl 3454 1611 1 1 De 3454 1612 1 1 De 3451 1611 3454 1611 Dl 3451 1610 3453 1609 Dl 3454 1610 3454 1609 Dl 3452 1609 3454 1609 Dl 3450 1614 1 1 De 3451 1614 1 1 De 3451 1614 3452 1614 Dl 3453 1613 3453 1614 Dl 3454 1612 3455 1612 Dl 3455 1612 1 1 De 3456 1612 1 1 De 3456 1611 3456 1612 Dl 3453 1609 1 1 De 3452 1614 3453 1614 Dl 3455 1614 3456 1613 Dl 3454 1614 3455 1614 Dl 3456 1613 1 1 De 3457 1612 3458 1611 Dl 3456 1610 3458 1610 Dl 3457 1612 3457 1613 Dl 3456 1613 3457 1613 Dl 3455 1609 3456 1609 Dl 3457 1610 3457 1609 Dl 3451 1614 1 1 De 3452 1615 3453 1615 Dl 3453 1615 1 1 De 3454 1615 3455 1615 Dl 3453 1615 3454 1615 Dl 3458 1614 1 1 De 3456 1614 3458 1614 Dl 3458 1611 3459 1612 Dl 3458 1613 3459 1612 Dl 3453 1609 1 1 De 3451 1615 1 1 De 3452 1616 3453 1616 Dl 3453 1616 1 1 De 3453 1617 1 1 De 3453 1617 1 1 De 3456 1617 1 1 De 3455 1617 3456 1617 Dl 3456 1616 3456 1617 Dl 3457 1616 3459 1615 Dl 3458 1614 1 1 De 3460 1613 3461 1613 Dl 3459 1614 3461 1613 Dl 3459 1610 3463 1610 Dl 3460 1612 3463 1611 Dl 3458 1610 1 1 De 3457 1608 3458 1608 Dl 3458 1610 3458 1608 Dl 3456 1608 1 1 De 3456 1608 1 1 De 3448 1614 3449 1614 Dl 3449 1615 1 1 De 3449 1615 1 1 De 3450 1616 1 1 De 3452 1616 3453 1616 Dl 3454 1617 3456 1617 Dl 3467 1617 3467 1616 Dl 3462 1614 3467 1616 Dl 3460 1615 3466 1617 Dl 3463 1612 1 1 De 3461 1613 3463 1612 Dl 3460 1608 3461 1608 Dl 3458 1607 3459 1607 Dl 3460 1610 3461 1608 Dl 3455 1608 3456 1608 Dl 3449 1616 3450 1616 Dl 3452 1618 3453 1618 Dl 3451 1616 3451 1617 Dl 3453 1618 1 1 De 3453 1619 3454 1619 Dl 3454 1618 3457 1617 Dl 3457 1617 1 1 De 3466 1618 3466 1620 Dl 3459 1618 3466 1620 Dl 3467 1615 1 1 De 3464 1611 3467 1615 Dl 3461 1608 3464 1609 Dl 3464 1610 3464 1609 Dl 3456 1608 3458 1607 Dl 3458 1607 1 1 De 3448 1614 1 1 De 3448 1615 1 1 De 3449 1615 1 1 De 3449 1616 3451 1617 Dl 3449 1617 1 1 De 3466 1620 3466 1622 Dl 3454 1620 3466 1622 Dl 3454 1619 3454 1620 Dl 3483 1604 3491 1604 Dl 3464 1608 3481 1605 Dl 3468 1614 3491 1604 Dl 3453 1608 3454 1608 Dl 3448 1617 1 1 De 3448 1616 1 1 De 3448 1617 3449 1618 Dl 3448 1617 1 1 De 3451 1618 3449 1618 Dl 3450 1622 3452 1622 Dl 3450 1619 3450 1621 Dl 3454 1620 3452 1622 Dl 3452 1622 3502 1668 Dl 3467 1622 3502 1668 Dl 3492 1604 4119 1463 Dl 3503 1668 3515 1682 Dl 3516 1682 4119 1463 Dl 5 R f (71)3673 1596 w 10 R f 0.1 setlinewidth 3458 1605 3481 1605 Dl 3458 1606 1 1 De 3456 1607 3458 1605 Dl 3452 1608 1 1 De 3447 1615 1 1 De 3448 1615 3447 1615 Dl 3445 1617 3443 1620 Dl 3446 1620 3443 1620 Dl 3446 1617 3446 1621 Dl 3447 1617 1 1 De 3024 2502 5040 2502 Dl 5040 1203 5040 2502 Dl 3024 1943 3024 2502 Dl 4124 1461 5040 1202 Dl 3467 1700 3024 1942 Dl 4120 1463 4123 1462 Dl 3515 1683 3467 1700 Dl (77)4102 2010 w 3451 1607 1 1 De 3452 1607 3458 1605 Dl 3445 1616 1 1 De 3448 1617 3447 1617 Dl 3449 1621 3446 1621 Dl 3444 1621 3467 1700 Dl 3456 1603 3456 1602 Dl 3457 1604 3456 1604 Dl 3457 1603 4123 1462 Dl 3447 1613 3446 1614 Dl 3447 1615 1 1 De 3445 1614 1 1 De 3445 1614 1 1 De 3445 1615 3445 1616 Dl 3442 1615 3441 1616 Dl 3444 1614 3443 1614 Dl 3442 1616 3443 1620 Dl 3024 1634 3024 1942 Dl 3439 1610 3438 1606 Dl 3441 1615 3440 1610 Dl 3438 1607 3024 1635 Dl (86)3152 1754 w 5040 486 3024 486 Dl 5040 1202 5040 486 Dl 3024 1635 3024 486 Dl 3449 1603 3456 1602 Dl 3447 1604 3438 1606 Dl (87)3903 1002 w 3451 1606 3456 1604 Dl 3445 1609 3445 1614 Dl 3445 1609 3443 1614 Dl 3445 1609 3440 1610 Dl 3446 1608 3448 1604 Dl 3446 1608 3451 1607 Dl 20 R f 16 setlinewidth 5040 2502 3024 2502 Dl 5040 486 5040 2502 Dl 3024 486 5040 486 Dl 3024 2502 3024 486 Dl 10 B f (Fig. 178:)1 372 1 1003 2700 t 10 R f (It. 21,)1 236 1 1400 2700 t 10 I f (d)1661 2700 w 10 S f (=)1736 2700 w 10 I f (behind)1816 2700 w 10 R f (,)2088 2700 w 10 I f (v)2138 2700 w 10 R f (= 0.5)1 206 1 2207 2700 t 10 S f (\260)2413 2700 w 10 B f (Fig. 179:)1 372 1 3282 2700 t 10 R f (It. 22,)1 236 1 3679 2700 t 10 I f (d)3940 2700 w 10 S f (=)4015 2700 w 10 I f (behind)4095 2700 w 10 R f (,)4367 2700 w 10 I f (v)4417 2700 w 10 R f (= 0.15)1 256 1 4486 2700 t 10 S f (\260)4742 2700 w 10 B f (Concluding Remarks)1 909 1 720 2940 t 10 R f ( the dual affine and dual projective algorithms come from solving the)11 2881(The pictures shown above of)4 1189 2 970 3096 t ( I)1 83( projective algorithm come from a closely related problem.)8 2354(same single problem, while those of the primal)7 1883 3 720 3216 t ( are)1 150(have not yet looked at enough other problems to make any claims about how typical the above pictures)17 4170 2 720 3336 t (\(of problems having three degrees of freedom\).)6 1886 1 720 3456 t ( \320 at least those corresponding to an orthogonal)8 1950(The algorithm's eye views shown above)5 1611 2 970 3612 t 10 I f (F)4557 3612 w 10 R f (in \(16\) \320)2 396 1 4644 3612 t ( primal affine vari-)3 768(change much faster for the affine dual variant than for the projective ones; views of the)15 3552 2 720 3732 t ( the dual affine variant, just as the primal and dual pro-)11 2262(ant presumably would behave similarly to those of)7 2058 2 720 3852 t ( \(For)1 228(jective views are qualitatively similar.)4 1547 2 720 3972 t 10 I f (F)2526 3972 w 10 R f ( it)1 111( has a nice interpretation:)4 1029(orthogonal, the search direction)3 1282 3 2618 3972 t (is the projection, by)3 800 1 720 4092 t 10 I f (FF)1547 4092 w 7 R f (T)1680 4052 w 10 R f ( final figures show that the pro-)6 1277( The)1 208( space.\))1 307(, of a gradient vector into the viewing)7 1517 4 1731 4092 t (jective views can change more rapidly from the vantage point of a nonorthogonal)12 3249 1 720 4212 t 10 I f (F)3994 4212 w 10 R f (.)4055 4212 w (For any continuous choice of)4 1205 1 970 4368 t 10 I f (F)2210 4368 w 10 R f ( slowly as we want by taking)6 1226(, we can make the pictures change as)7 1543 2 2271 4368 t ( \320)1 127( 4])1 99( leads naturally to considering differential forms of the algorithms \320 see [1,)12 3072( This)1 230(small enough steps.)2 792 5 720 4488 t ( everyone who sees)3 805( \(Nearly)1 363(and to making movies in which the transformed polytope deforms smoothly.)10 3152 3 720 4608 t ( I look forward)3 607( And)1 224( would like to do so when time permits.)8 1602( I)1 85(the above pictures suggests making a movie.)6 1802 5 720 4728 t ( to display such a movie in real)7 1351(to some future time when we'll all have workstations powerful enough)10 2969 2 720 4848 t (time.\))720 4968 w ( feasible regions for the primal and dual projective variants visually)10 2731(Outside views of the transformed)4 1339 2 970 5124 t ( that the transformed polytopes have inscribed and circumscribed spheres)9 3128(support the well-known fact)3 1192 2 720 5244 t (whose diameters have a bounded ratio.)5 1552 1 720 5364 t ( solution paths \(figures 11\26114,)4 1239(Only the first few steps are long enough to be seen on the plots of the)15 2831 2 970 5520 t ( gives hope for the possibility of devising fast stopping tests.)10 2425( This)1 228(30\26133, 74\26177\).)1 608 3 720 5640 t ( to have)2 346(Many authors like to consider problems in Karmarkar's canonical form, i.e.,)10 3184 2 970 5796 t 10 I f (b)4540 5796 w 10 S f (=)4639 5796 w 10 I f (e)4743 5796 w 7 I f (m)4798 5816 w 10 R f (and)4896 5796 w 10 I f (A)720 5916 w 7 R f (T)792 5876 w 10 I f (e)851 5916 w 7 I f (m)906 5936 w 10 S f (=)1013 5916 w 10 I f (e)1117 5916 w 10 R f ( to this form should have little effect on the pictures considered in)12 2702( conversion)1 470( Explicit)1 374(in \(1b\).)1 301 4 1193 5916 t ( each in [8]\);)3 527(this paper, as it generally adds as many new variables as new equality constraints \(e.g. two of)16 3793 2 720 6036 t (the main effect would come from perturbing the orthogonalization of)9 2759 1 720 6156 t 10 I f (F)3504 6156 w 10 R f (in \(16\).)1 294 1 3590 6156 t ( of Karmarkar's algorithm to frac-)5 1385(We could also make pictures depicting Anstreicher's extension [2])8 2685 2 970 6312 t ( primal projective step)3 896( step computation is similar to the)6 1362( Anstreicher's)1 588(tional linear programming problems.)3 1474 4 720 6432 t (computation described above and should yield similar pictures.)7 2525 1 720 6552 t ( to arrange that)3 616(For starting, some authors also like)5 1425 2 970 6708 t 10 I f (e / n)2 138 1 3041 6708 t 10 R f (be feasible, usually by adding a new variable)7 1831 1 3209 6708 t ( cleaner than doing a separate)5 1192( is)1 95( This)1 231(\(at high cost\), with no corresponding additional constraint, as in [24].)10 2802 4 720 6828 t (phase-1 calculation to find a feasible starting point)7 2029 1 720 6948 t 10 I f (x)2775 6948 w 10 S f (\260)2819 6948 w 10 R f ( ``null variables'', i.e., compo-)4 1233(, as it is not troubled by)6 948 2 2859 6948 t (nents of)1 324 1 720 7068 t 10 I f (x)1074 7068 w 10 R f ( it adds a degree of freedom, which makes drawing pic-)10 2259( But)1 199( feasible solutions.)2 755(that vanish in all)3 679 4 1148 7068 t (tures of the transformed feasible regions much harder.)7 2161 1 720 7188 t (January 30, 1987)2 685 1 2537 7680 t cleartomark showpage saveobj restore %%EndPage: 44 45 %%Page: 45 46 /saveobj save def mark 46 pagesetup 10 R f (- 45 -)2 216 1 2772 480 t (One can regard Karmarkar's linear programming algorithm as an interior penalty-function method)11 4070 1 970 840 t ( may then be tempted to make other choices of the)10 2143( One)1 229( special choice of the penalty parameter.)6 1687(with a)1 261 4 720 960 t ( approach of this paper might)5 1208( is unclear how useful the)5 1053( It)1 117(penalty parameter; see [11] and [12] for details.)7 1942 4 720 1080 t ( problems like those considered)4 1321( For)1 203( such penalty methods.)3 958(be in presenting an algorithm's eye view of)7 1838 4 720 1200 t ( to turn the Hessian of)5 915(above having three degrees of freedom, we might make a linear change of variables)13 3405 2 720 1320 t ( into the identity matrix)4 977(the penalty function)2 817 2 720 1440 t 10 I f (I)2547 1440 w 10 R f (; pictures of the resulting transformed feasible region would)8 2460 1 2580 1440 t ( having two degrees of free-)5 1146( course, for problems)3 860( Of)1 159(then show the constraints as the algorithm sees them.)8 2155 4 720 1560 t (dom, conventional level contour plots would also be informative.)8 2609 1 720 1680 t 10 B f (Acknowledgements)720 1920 w 10 R f ( comments on the)3 780(I thank Bob Fourer, Eric Grosse, Norm Schryer, and Mike Todd for helpful)12 3290 2 970 2076 t (manuscript.)720 2196 w 10 B f (References)720 2436 w 10 R f ( Resende, and G. Veiga, ``An Implementation of Karmarkar's)8 2562( Adler, N. K. Karmarkar, M. G. C.)7 1450([1] I.)1 308 3 720 2628 t ( & Oper. Res., Univ.)4 843( of Indust. Engin.)3 712( Dept.)1 274(Algorithm for Linear Programming,'' draft manuscript,)5 2241 4 970 2748 t ( CA 94720 \(May 1986\).)4 963( Berkeley,)1 435(of California,)1 538 3 970 2868 t ( Programming for Lin-)3 928( M. Anstreicher, ``A Monotonic Projective Algorithm for Fractional Linear)9 3045([2] K.)1 347 3 720 3024 t (ear Programming,'')1 787 1 970 3144 t 10 I f (Algorithmica)1782 3144 w 10 B f (1)2335 3144 w 10 R f (\(4\), pp. 483\261498 \(1986\).)3 982 1 2385 3144 t ( R. Barnes, ``A Variation on Karmarkar's Algorithm for Solving Linear Programming Problems,'')12 3984([3] E.)1 336 2 720 3300 t 10 I f (Mathematical Programming)1 1141 1 970 3420 t 10 B f (36)2136 3420 w 10 R f (, pp. 174\261182 \(1986\).)3 866 1 2236 3420 t ( and)1 183( Affine)1 323( A. Bayer and J. C. Lagarias, ``The Nonlinear Geometry of Linear Programming I.)13 3467([4] D.)1 347 4 720 3576 t ( Hill, NJ 07974 \(Sept.)4 974( Murray)1 373( Labs,)1 268( Bell)1 217( AT&T)1 347(Projective Scaling Trajectories,'' manuscript,)3 1891 6 970 3696 t (1986\).)970 3816 w ( L. Soyster, ``Some Computational Experience and a Modification of the Kar-)11 3175( M. Cavalier and A.)4 809([5] T.)1 336 3 720 3972 t (markar Algorithm,'' manuscript \(Feb. 1985\).)4 1800 1 970 4092 t ( and B. S. Kochar, ``Exploiting Special Structures Using a Variant of Karmarkar's Algo-)13 3601( Chandru)1 372([6] V.)1 347 3 720 4248 t ( Engineering, Purdue University,)3 1360( of Industrial)2 546( School)1 343(rithm,'' Research Memorandum No. 86\26110,)4 1821 4 970 4368 t (West Lafayette, IN 47907 \(June 1986\).)5 1560 1 970 4488 t ( Linear Programming,'' Research Memo-)4 1684( Chandru and B. S. 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