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1.1     ! root        1: .\"    @(#)e1  6.1 (Berkeley) 5/22/86
        !             2: .\"
        !             3: .2C $gsize 9$
        !             4: .nr PS 9
        !             5: .nr VS 11p
        !             6: .NH
        !             7: Introduction
        !             8: .PP
        !             9: ``Mathematics is known in the trade as
        !            10: .ul
        !            11: difficult,
        !            12: or
        !            13: .ul
        !            14: penalty, copy
        !            15: because it is slower, more difficult,
        !            16: and more expensive to set in type
        !            17: than any other kind of copy normally
        !            18: occurring in books and journals.''
        !            19: [1]
        !            20: .PP
        !            21: One difficulty with mathematical text
        !            22: is the multiplicity of characters,
        !            23: sizes, and fonts.
        !            24: An expression such as
        !            25: .EQ
        !            26: lim from {x-> pi /2} ( tan~x) sup{sin~2x}~=~1
        !            27: .EN
        !            28: requires an intimate mixture of roman, italic and greek letters, in three sizes,
        !            29: and a special character or two.
        !            30: (``Requires'' is perhaps the wrong word,
        !            31: but mathematics has its own typographical conventions
        !            32: which are quite different from those
        !            33: of ordinary text.)
        !            34: Typesetting such an expression by traditional methods
        !            35: is still an essentially manual operation.
        !            36: .PP
        !            37: A second difficulty is the two dimensional character
        !            38: of mathematics,
        !            39: which the superscript and limits in the preceding example
        !            40: showed in its simplest form.
        !            41: This is carried further by
        !            42: .EQ
        !            43: a sub 0 + b sub 1 over
        !            44:   {a sub 1 + b sub 2 over
        !            45:     {a sub 2 + b sub 3 over
        !            46:       {a sub 3 + ... }}}
        !            47: .EN
        !            48: .sp
        !            49: and still further by 
        !            50: .EQ
        !            51: define emx "{e sup mx}"
        !            52: define mab "{m sqrt ab}"
        !            53: define sa "{sqrt a}"
        !            54: define sb "{sqrt b}"
        !            55: int dx over {a emx - be sup -mx} ~=~
        !            56: left { lpile {
        !            57:      1 over {2 mab} ~log~ {sa emx - sb} over {sa emx + sb}
        !            58:    above
        !            59:      1 over mab ~ tanh sup -1 ( sa over sb emx ) 
        !            60:    above
        !            61:      -1 over mab ~ coth sup -1 ( sa over sb emx )
        !            62: }
        !            63: .EN
        !            64: These examples also show line-drawing, built-up characters like braces and radicals,
        !            65: and a spectrum of positioning problems.
        !            66: (Section 6 shows
        !            67: what a user has to type to produce these
        !            68: on our system.)

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