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\sizetest \arrowvert\Arrowvert \sizetest \uparrow\downarrow
\sizetest \updownarrow\Updownarrow \sizetest \Uparrow\Downarrow
\sizetest \bracevert{\delimiter"342} \sizetest \backslash/
\sizetest \langle\rangle \sizetest \lbrace\rbrace
\sizetest \lceil\rceil \sizetest \lfloor\rfloor
$$\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{-1}}}}}}}}}$$
\def\dobig{\do\bigvee \do\bigwedge \do\bigotimes \do\bigoplus \do\bigodot
\do\bigcap \do\bigcup \do\biguplus \do\bigsqcup
\do\int \do\ointop \do\smallint \do\prod \do\coprod \do\sum}
\def\do#1{#1_a^b A} $\dobig$ $$\dobig$$
\bye




Be sure of it: Giue me the Occular proofe.
” WILLIAM SHAKESPEARE, Othello (1604)

The ¬gure itself appears here
as a very necessary adjunct to the verbalization.
In Euclid™s presentation we cannot wholly follow the argumentation
without the ¬gure, and unless we are strong enough
to imagine the ¬gure in our mind™s eye, we would also be reduced
to supplying our own ¬gure if the author had not done it for us.
Notice also that the language of the proof has a
formal and severely restricted quality about it.
This is not the language of history, nor of drama,
nor of day to day life;
this is language that has been sharpened and re¬ned so as to serve
the precise needs of a precise but limited intellectual goal.
” P. J. DAVIS and R. HERSH, Proof (1981)
(page 344)




I
Index
Appendix I: Index 345


The author has tried to provide as complete an index as possible, so that people
will be able to ¬nd things that are tucked away in obscure corners of this long
book. Therefore the index itself is rather long. A short summary of the simpler
aspects of appears at the beginning of Appendix B; a summary of
the standard character classes for tokens can be found at the end of Chapter 6;
a summary of other special things appears under ˜tables™ below.
Page numbers are underlined in the index when they represent the de¬nition
or the main source of information about whatever is being indexed. (Underlined entries
are the most de¬nitive, but not necessarily the easiest for a beginner to understand.)
A page number is given in italics (e.g., ˜123 ™) when that page contains an instructive
example of how the concept in question might be used. Sometimes both underlining
and italics are appropriate. When an index entry refers to a page containing a relevant
exercise, the answer to that exercise (in Appendix A) might divulge further information;
an answer page is not indexed here unless it refers to a topic that isn™t included in the
statement of the relevant exercise.
Index entries for quoted symbols like ˜T™ refer to example programs that draw
the symbols in question.
Symbolic tokens that are preceded by an asterisk (*) in this index are primi-
tives of ; i.e., they are built in. It may be dangerous to rede¬ne them.

6test.mf, 312“313. *{ (left brace), 16“18, 60, 129, 213.
# (hash mark), see sharped dimensions. {{, 61, 289.
˜#™, 200“201. *} (right brace), 16“18, 60, 129, 213.
## (traced equation), 80“83, 239. }}, 61, 289.
### (removed independent variable), 83. *+ (plus sign), 62, 63, 72, 80, 211.
#### (deduced equation), 81. *++ (Pythagorean addition), 66, 67, 72, 211.
*#@ (pre¬x of at point), 177, 251. (double edge), 117, 296“297.
% (percent sign), 43, 50. +++ (triple edge), 296“297.
*& (ampersand), 213“214, see concatenation. *+-+ (Pythagorean subtraction), 66,
for preloaded bases, 35, 279. 72, 211, 238.
™ (apostrophe or prime), 25, 55, 81. *- (minus sign), 62, 63, 72, 80, 211, 297.
" (double-quote mark), 50“51. -- (straight join), 24“26, 127“129, 234, 262.
"" (empty string), 188, 236, 254, 276, (double edge), 117, 296“297.
294, 328. --- (tense join), 107, 127“129, 262.
˜(™, 103“105, 128, 318. (triple edge), 296“297.
( (left parenthesis), 59, 60, 61, 62“63, -> (macro expansion), 44, 160, 249, 251.
71“73, 165, 210“215. ˜”™ (em dash), 306.
((, 51. _ (underline), 49, 51, 173, 265, 270.
) (right parenthesis), 59, 60, 61, 62“63, * (asterisk), 285“286.
71“73, 165, 210“215. as prompt character, 31, 37, 279.
)), 51. *as times sign, 59, 62“64, 72, 73,
*[ (left bracket), 9“10, 54, 55, 60, 72, 80, 80, 211“212.
211“212, 298“299, 324. **, as command-line prompt, 31“32,
[[, 61. 35“40, 187, 269, 279.
[] (collective subscript), 56, 177, 273. as exponentiation sign, 59, 64, 72,
[1] (progress report), 37, 324. 237, 251, 265.
*] (right bracket), 9“10, 54, 55, 60, 72, 80, / (slash), 328, 329.
211“212, 298“299, 324. *as divided-by sign, 59, 62, 63, 72,
]], 61, 162, 262, 299. 80, 82, 210“211.
346 Appendix I: Index


| (vertical line), 117, 297. abs (absolute value), 66, 82, 238, 264.
accents, 315, 317.
*\ (backslash), 179, 236, 262.
at beginning of command line, 31, 38, 40. accuracy, 50, 62“69, 143, 237.
\\, 262. ad hoc dimensions, 92, 95.
< (less than sign), 64, 65, 170, 210, 237. Adams, John, 359.
*
*<= (less than or equal to), 64, 65, 170, addition of pictures, 115, 117, 245.
210, 282. addition of vectors, 9, 68.
<- (argument value), 160. *addto, 118“119, 144, 151, 242“245.
<> (unequal to), 64, 65, 170, 210, 282. addto command , 220.
*
(angle brackets), 49“50. adjust_fit, 306“308.
*= (equals sign), 5, 6, 23, 64, 75“85, 88, 97, Æschylus, 47.
165, 167, 170, 171, 210, 218. Æsopus, 340.
==, 292. a¬ne transformations, 247.
*=: (ligature replacement), 305, 306, algebraic operations, 59“73, 209“215, 230.
316, 317. Algol, 57, 89.
|=:, 316, 317. Alingham, William, 189.
*
*|=:>, 317. Allen, Fred (= Sullivan, John Florence), 85.
*=:|, 317. almost digitized character, 296.
*=:|>, 317. *also, 118, 220, 242“245.
*|=:|, 317. \alternation, 338.
*|=:|>, 317. alternatives, 169.
*|=:|>>, 317. always_iff, 307, 311“312.
/ (unequals sign), 282. ambiguous points, 150, 198“200, 204.
=
> (greater than sign), 64, 170, 210, 237. American Mathematical Society, ii, ix.
*
>> (shown value), 41, 62. anatomy of , 169, 179,
217, 285, 344.
>= (greater than or equal to), 64, 65,
*
170, 210, 282. *and, 65, 129, 170, 210, 213, 288“289.
Anderson, Izett William, 299.
*, (comma), 57, 72, 73, 129, 155, 165“167,
171, 317, 318. *angle, 29, 67, 72, 107, 135, 211.
,, , 51. angle brackets, 49“50.
. (period), 43, 50, 51. angle of pen, 21“22, 26“28, 152, 164.
˜.™, 306. arguments, 159“160, 166“167, 210, 288.
*.. (free join), 7, 15“19, 24, 127“133, 213. arithmetic, 59“63.
... (bounded join), 18“19, 44, 127, arrays, 54“57.
248, 262. ASCII, 49, 188, 281“283, 317.
*; (semicolon), 155, 169, 171, 172, 187, *ASCII, 72, 188, 211.
217, 223“224, 263, 312. aspect_ratio, 94, 145, 204, 269, 335.
;; , 51. assignment , 88.
: (colon), 169, 317“319. assignments, 28, 33, 87“89, 98, 159.
*
*:: (local label), 317. *at, 191, 220, 252, 277, 312.
*||: (left boundary label), 317. at size, 96, 319.
*:= (gets), 28, 33, 87, 88, 97, 98, 155“156, *atleast, 129, 132, 213, 262.
159, 165, 167, 171, 176, 218, 282. *autorounding, 127, 195, 204“205, 206,
?, 41, 42“43. 212, 262, 264, 271“272.
???, 224, 262. axis, 103.
! (exclamation point), 41, 189.
˜b™, 308.
*@ (at point), 177, 251.
background character, 40, 338“339.
*@# (su¬x of at point), 176, 177, 178,
Backus, John Warner, 49.
251, 273“274.
backwards path, 119.
˜a™, 192. badio.mf, 41, 223.
˜A™, 163, 164, 248, 302“303. barheight, 96, 161, 199, 302“303.
abort, 312“313. base ¬le, 34“35, 261, 278“279, 304, 307.
Appendix I: Index 347


baseline, 75“77, 101. Burns, Robert, 299.
basic path join , 129, 213. bye, 278, 279, 306, 321, 324.
batchmode, 219, 226. byte, 264, 275.
*
BCPL strings, 320. byte list , 318.
bean-like shape, 15“16, 21“22, 24“25.
c code, 106, 324.
beauty, v, 185.
Camden, William, 51.
Beethoven, Ludwig van, 185.
Campbell, John Campbell, 359.
beginchar, 35, 76, 96, 102“103, 107, 115,
cand, 288“289.
148, 156, 197, 199, 204, 275, 316.
CAPSULE, 239.
begingroup, 155“157, 175, 178, 210“215,
*
capsule_def, 264.
217, 236, 243, 275, 289.
capsules, 159, 166, 172, 210, 239, 247,
beginlogochar, 160, 302.
254, 264.
Bell, Eric Temple, 11.
Carter, Matthew, 207.
bell-shaped distribution, 251.
Cartesian coordinates, 5“6, 191.
Bernshte˜ Serge˜ Natanovich, 14.
±n, ±
cc (cicero), 92, 267, 268.
polynomials, 14, 133, 152, 246, 298“299.
ceiling, 65, 66, 72, 264.
B´zier, Pierre Etienne, 14.
e
\centerlargechars, 340, 341.
Bibby, Duane Robert, i.
chance, 183“185.
Bierce, Ambrose Gwinnett, ix.
change_width, 199, 276, 309.
\bigtest, 341.
*char, 187, 188, 214, 263.
Billawala, Nazneen Noorudin, 266, 294.
*charcode, 106, 210, 212, 220, 275, 324.
binary search, 176“177, 293“294.
*chardp, 106, 212, 220, 275, 315“316, 324.
black, 270, 332“333.
*chardx, 106, 212, 220, 276, 324, 334.
black-letter, 294.
*chardy, 212, 324.
black/white reversal, 115.
*charexists, 106, 210, 316, 324.
blacker, 93“94, 268, 270“271.
*charext, 106, 212, 220, 316, 324.
blankpicture, 192, 263.
*charht, 106, 212, 220, 275, 315“316,
Boole, George, 170.
324, 334, 335.
*boolean, 55, 56.
*charic, 106, 212, 220, 275, 315“316, 324.
boolean expression , 170, 210.
*charlist, 317, 318, 331, 334, 335.
Boolean expressions, 170, 257.
charlist command , 318.
boolean primary , 170, 210.
charwd, 106, 212, 220, 275, 315“316,
*
boolean secondary , 170, 210.
324, 334, 335.
boolean tertiary , 170, 210.
cheapo, 91“93, 99, 278“279, 332“333.
bot, 23, 80, 147, 151, 204, 273.
check sums, 320, 324, 325.
boundaries, 24“29, 123“125.
Chinese characters, 3, 106, 324.
*boundarychar, 212, 317.
circles, 123“124, 148.
bounded curves, 19, 132.
clear_pen_memory, 147, 273, 278, 310.
bounding box, 22, 35, 76, 101“107,
clearit, 115, 242, 275, 277, 295.
276, 307, 315.
clearpen, 272, 275.
bounding triangle, 19, 132.
clearxy, 275, 277.
box, see bounding box.
cm (centimeter), 18, 92, 267, 268.
bp (big point), 92, 267, 268.
cm.base, 35, 279, 311.
braces, 16“18, 60, 129, 213.
cmchar, 306, 307, 312“313.
bracket notation, see mediation.
cmex10, 317“318.
brackets, 9“10, 54, 55, 60, 72, 80, 211“212,
cmmf, 35, 279.
298“299, 324.
cmr9, 203, 320.
broad-edge pens, 26“29, 151“152, 162“165.
cmr10, 101, 305“306, 319.
Bront¨, Emily Jane, 73.
e
cmr10.mf, 305.
Bruck, Richard Hubert, 29.
cmsl10, 101.
bu¬er size, 226, 286.
cmtt10, 306.
built-up symbols, 318.
Burkitt, William, 99. code , 317.
348 Appendix I: Index


codes, 281“283. currentpicture, 114, 115, 116, 118, 120,
191, 271“272, 295.
Colburn, Dorothy, 107.
collective subscripts, 56, 177. currenttransform, 94, 145, 204, 269,
271, 301, 310.
command , 217.
command line, 38, 187, 269, 277, 301. currentwindow, 192, 312.
commands, 155, 217“220, 230, 321. curves, 13“19, see paths.
comments, 43, 50“51. cusps, 136.
commutativity, 247. cutdraw, 151, 271“272.
comparison, 65“66, 80, 170. cutoff, 150, 272.
compass directions, 26, 119, 206“207, *cycle, 15, 16, 24“28, 69, 129“131, 170,
228“229. 171, 210, 213.
complex numbers, 69.
d, 35, 76, 102, 204, 275.
compound , 217.
˜d™, 294.
compound statement, 155, 217.
da Vinci, Leonardo, 19.
Computer Modern, 35, 103“105, 203,
dangerous bend, vii, 11, 106“107, 115, 143.
206, 279, 304“313.
Darwin, Charles Robert, 57.
concatenation, of paths, 70“71, 123,
data structures, 53“57.
127, 129, 130, 245.
Davis, Philip Jacob, 343.
of strings, 69, 84“85, 187, 278, 286, 312.
*day, 212, 218, 323.
condition , 169.
dd (didot point), 92, 267, 268.
conditional and/or, 288“289.
de Casteljau, Paul de Faget, 14.
conditions, 169“171, 179, 219, 259.
debugging tricks, 229“231, 286.
constants, 59, 62, 263“264.
*decimal, 187“188, 214.
contents of this manual, table, x“xi.
decimal digit , 50.
*contour, 118“119, 220.
decimal point, 50“51.
control points, 13“19, 70“71, 133, 229.
decimal representation, 188.
*controls, 19, 70“71, 129“130, 133, 152, 213.
declaration , 56, 171.
controls , 129, 213.
declaration list , 57.
conversion to pixel units, 259, 268.
declarations, 56“57.
convex polygons, 119, 147, 297“298.
declarative versus imperative, 87.
Conway, John Horton, 121.
declared su¬x , 57.
coordinates, 5“11, 23, 109, 191, 193.
declared variable , 57, 175.
cor, 288“289.
decr, 266.
corner pixels, 93“94.
def, 36, 159“162, 165“167.
*cosd, 67, 72, 211. *
default_wt_, 271“272.
cosines, 67, 69.
define_blacker_pixels, 33, 92“93,
counterclockwise, 111, 119, 229, 255.
106, 268, 302.
counterclockwise, 264.
define_corrected_pixels, 93, 197, 268, 302.
Cowper, William, 51.
define_good_x_pixels, 199, 268, 302.
craziness, 184“185.
define_good_y_pixels, 199, 268, 302.
crispness, 103“104.
cube roots, 177. define_horizontal_corrected_pixels,
204, 268, 302.
cubes, 113.
define_pixels, 33, 92, 106, 199, 268, 302.
*cull, 118, 120, 151, 243“245.
define_whole_blacker_pixels, 202, 268.
cull command , 118, 220.
define_whole_pixels, 199, 268, 302.
culldraw, 271, 272.
culling, 113, 120, 151, 242“245, 296. define_whole_vertical_blacker_pixels,
268.
cullit, 113, 120, 242, 243, 277.
define_whole_vertical_pixels, 204,
Cundall, Frank, 299.
268, 302.
*curl, 17, 128“131, 213, 234.
de¬nition , 165.
currentbreadth, 310“311.
de¬nition heading , 165.
currentnull, 295.
currentpen, 118, 147, 150, 204, 271“272. de¬nitions, 159“167, 175“180.
Appendix I: Index 349


deleting tokens, 42“43, 225. driver ¬les, 304“306.
delimited parameters , 165. *dropping, 118, 120, 220.
delimiters, 61, 167, 210, 254, 288“289. D¨rer, Albrecht, 13, 19.
u
*delimiters, 61, 180, 210, 218, 221, *dump, 217, 221, 262, 279, 311.
262, 296, 299, 313. .dvi, 32, 40, 103, 106, 323, 327, 328.
delimiters command , 218.
e, 27“29, 273.
dependent variables, 81“83, 88, 224.
˜E™, 96“97, 204, 302“303.
depth, 101.
edge structure, 116“117, 296“297.
Derek, Bo, 287.
edges, 116.
Descartes, Ren´, 6, 11, 19.
e
editing, 46.
design size, 96, 319“320, 324, 329.
e¬ciency, 39, 99, 141, 144, 147, 228, 230,
designsize, 212, 320.
*
234, 244, 264, 265, 277, 291, 297, 298.
device drivers, 323, 325.
El Palo Alto, 124“126, 139, 228“229.
diagnostic aids, 229“231, 259, 286.
ellipses, 123, 126.
diamond-shaped nib, 148“149, 297.
Ellis, Henry Havelock, 11.
Dickens, Charles John Hu¬am, 145.
*else, 169“170, 179.
di¬erence of pictures, 115, 244.
*elseif, 169“170, 179.
digestion process, 179, 217“221.
em dash, 306.
digit string , 50.
emergency stops, 226.
digitization, 111, 149, 195“207, 230.
empty option in for list, 171, 299.
\digits, 339.
empty statement, 155, 217.
dimensions, 92, 267.
empty text argument, 299.
dir, 18, 67, 68, 83“84, 135, 163“164,

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