Commit | Line | Data |
---|---|---|
8340f87c BJ |
1 | .2C $gsize 9$ |
2 | .nr PS 9 | |
3 | .nr VS 11p | |
4 | .NH | |
5 | Introduction | |
6 | .PP | |
7 | ``Mathematics is known in the trade as | |
8 | .ul | |
9 | difficult, | |
10 | or | |
11 | .ul | |
12 | penalty, copy | |
13 | because it is slower, more difficult, | |
14 | and more expensive to set in type | |
15 | than any other kind of copy normally | |
16 | occurring in books and journals.'' | |
17 | [1] | |
18 | .PP | |
19 | One difficulty with mathematical text | |
20 | is the multiplicity of characters, | |
21 | sizes, and fonts. | |
22 | An expression such as | |
23 | .EQ | |
24 | lim from {x-> pi /2} ( tan~x) sup{sin~2x}~=~1 | |
25 | .EN | |
26 | requires an intimate mixture of roman, italic and greek letters, in three sizes, | |
27 | and a special character or two. | |
28 | (``Requires'' is perhaps the wrong word, | |
29 | but mathematics has its own typographical conventions | |
30 | which are quite different from those | |
31 | of ordinary text.) | |
32 | Typesetting such an expression by traditional methods | |
33 | is still an essentially manual operation. | |
34 | .PP | |
35 | A second difficulty is the two dimensional character | |
36 | of mathematics, | |
37 | which the superscript and limits in the preceding example | |
38 | showed in its simplest form. | |
39 | This is carried further by | |
40 | .EQ | |
41 | a sub 0 + b sub 1 over | |
42 | {a sub 1 + b sub 2 over | |
43 | {a sub 2 + b sub 3 over | |
44 | {a sub 3 + ... }}} | |
45 | .EN | |
46 | .sp | |
47 | and still further by | |
48 | .EQ | |
49 | define emx "{e sup mx}" | |
50 | define mab "{m sqrt ab}" | |
51 | define sa "{sqrt a}" | |
52 | define sb "{sqrt b}" | |
53 | int dx over {a emx - be sup -mx} ~=~ | |
54 | left { lpile { | |
55 | 1 over {2 mab} ~log~ {sa emx - sb} over {sa emx + sb} | |
56 | above | |
57 | 1 over mab ~ tanh sup -1 ( sa over sb emx ) | |
58 | above | |
59 | -1 over mab ~ coth sup -1 ( sa over sb emx ) | |
60 | } | |
61 | .EN | |
62 | These examples also show line-drawing, built-up characters like braces and radicals, | |
63 | and a spectrum of positioning problems. | |
64 | (Section 6 shows | |
65 | what a user has to type to produce these | |
66 | on our system.) |