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.nr PS 9
.nr VS 11p
.NH
Introduction
.PP
``Mathematics is known in the trade as
.ul
difficult,
or
.ul
penalty, copy
because it is slower, more difficult,
and more expensive to set in type
than any other kind of copy normally
occurring in books and journals.''
[1]
.PP
One difficulty with mathematical text
is the multiplicity of characters,
sizes, and fonts.
An expression such as
.EQ
lim from {x-> pi /2} ( tan~x) sup{sin~2x}~=~1
.EN
requires an intimate mixture of roman, italic and greek letters, in three sizes,
and a special character or two.
(``Requires'' is perhaps the wrong word,
but mathematics has its own typographical conventions
which are quite different from those
of ordinary text.)
Typesetting such an expression by traditional methods
is still an essentially manual operation.
.PP
A second difficulty is the two dimensional character
of mathematics,
which the superscript and limits in the preceding example
showed in its simplest form.
This is carried further by
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a sub 0 + b sub 1 over
  {a sub 1 + b sub 2 over
    {a sub 2 + b sub 3 over
      {a sub 3 + ... }}}
.EN
.sp
and still further by 
.EQ
define emx "{e sup mx}"
define mab "{m sqrt ab}"
define sa "{sqrt a}"
define sb "{sqrt b}"
int dx over {a emx - be sup -mx} ~=~
left { lpile {
     1 over {2 mab} ~log~ {sa emx - sb} over {sa emx + sb}
   above
     1 over mab ~ tanh sup -1 ( sa over sb emx ) 
   above
     -1 over mab ~ coth sup -1 ( sa over sb emx )
}
.EN
These examples also show line-drawing, built-up characters like braces and radicals,
and a spectrum of positioning problems.
(Section 6 shows
what a user has to type to produce these
on our system.)
