\input Amiga.tex
\hsize=6.3in
\vsize=9.85in
\tolerance=10000
\voffset=-0.35in
\parskip=8pt
\font\Pa = cmss12 scaled \magstep 0
\font\Pb = cmr12 scaled \magstep 0
\font\Pc = cmr10 scaled \magstep 0
\font\Pd = cmr12 scaled \magstep 3
\font\Pe = cmsl12 scaled \magstep 0
\font\Pf = cmsy8 scaled \magstep 0
\font\Pg = cmtt9 scaled \magstep 0
\font\Pz = cmbxsl10 scaled \magstep 1

\def\ss{\char124 \hskip2pt}
\def\\{\char92{}}          %%%%% backslash %%%%%
\def\lb{\char'173{}}       %%%%% left brace %%%%%
\def\rb{\char'175{}}       %%%%% right brace %%%%%
\def\sp{\char32{}}         %%%%% special space symbol %%%%%
\def\beginliteral{
\vskip\baselineskip
\begingroup
\Pg
\obeylines
%{\obeyspaces\global\let =\ }
\catcode`\@=0
\parskip=0pt\parindent=0pt
\catcode`\$=12\catcode`\&=12\catcode`\^=12\catcode`\#=12
\catcode`\_=12\catcode`\~=12
\def\par{\leavevmode\endgraf}
\catcode`\{=12\catcode`\}=12\catcode`\%=12\catcode`\\=12
}
\def\endliteral{\endgroup}

\Pc
\centerline {\TeX\ C'est aussi les Mathématiques. Voici d'autres exemples:}

\goodbreak \vskip 2pt \hrule
\beginliteral
$\phi(t) = {1 \over \sqrt{2\pi}} \int_0^t e^{-x^2/2}\,dx$.
@endliteral
$\phi(t) = {1 \over \sqrt{2\pi}} \int_0^t e^{-x^2/2}\,dx$.
\vskip \baselineskip \hrule


\goodbreak \vskip 2pt \hrule
\beginliteral
$\underline x \quad \overline y \quad \underline{\overline{x+y}}$.
@endliteral
$\underline x \quad \overline y \quad \underline{\overline{x+y}}$.
\vskip \baselineskip \hrule



\goodbreak \vskip 2pt \hrule
\beginliteral
$\sin(2\theta) = 2\sin\theta\cos\theta
\quad \cos(2\theta) = 2\cos^2\theta - 1  $.
@endliteral
$\sin(2\theta) = 2\sin\theta\cos\theta
\quad \cos(2\theta) = 2\cos^2\theta - 1  $.
\vskip \baselineskip \hrule


\goodbreak \vskip 2pt \hrule
\beginliteral
$$\int \csc^2x\, dx = -\cot x+ C
\qquad \lim_{\alpha\to 0} {\sin\alpha \over \alpha} = 1
\qquad \lim_{\alpha\to \infty} {\sin\alpha \over \alpha} = 0.$$
@endliteral
$$\int \csc^2x\, dx = -\cot x+ C
\qquad \lim_{\alpha\to 0} {\sin\alpha \over \alpha} = 1
\qquad \lim_{\alpha\to \infty} {\sin\alpha \over \alpha} = 0.$$
\vskip \baselineskip \hrule


\goodbreak \vskip 2pt \hrule
\beginliteral
$$\tan(2\theta) = {2\tan\theta \over 1-\tan^2\theta}.$$
@endliteral
$$\tan(2\theta) = {2\tan\theta \over 1-\tan^2\theta}.$$
\vskip \baselineskip \hrule


\goodbreak \vskip 2pt \hrule
\beginliteral
\proclaim Theorem (Euclid). There exist an infinite number of primes.
@endliteral
\proclaim Theorem (Euclid). There exist an infinite number of primes.

\vskip \baselineskip \hrule


\goodbreak \vskip 2pt \hrule
\beginliteral
\proclaim Proposition 1.
$\root n \of {\prod_{i=1}^n X_i} \leq
{1 \over n} \sum_{i=1}^n X_i$ with equality if and only if $X_1=\cdots=X_n$.
@endliteral
\proclaim Proposition 1.
$\root n \of {\prod_{i=1}^n X_i} \leq
{1 \over n} \sum_{i=1}^n X_i$ with equality if and only if $X_1=\cdots=X_n$.

\vskip \baselineskip \hrule



\goodbreak \vskip 2pt \hrule
\beginliteral
$$ I_4 = \pmatrix{
1 &0 &0 &0 \cr
0 &1 &0 &0 \cr
0 &0 &1 &0 \cr
0 &0 &0 &1 \cr}$$
@endliteral
$$ I_4 = \pmatrix{
1 &0 &0 &0 \cr
0 &1 &0 &0 \cr
0 &0 &1 &0 \cr
0 &0 &0 &1 \cr}$$
\vskip \baselineskip \hrule


\goodbreak \vskip 2pt \hrule
\beginliteral
$$ |x| = \left\{ \matrix{
x & x \ge 0 \cr
-x & x \le 0 \cr} \right.$$
@endliteral
$$ |x| = \left\{ \matrix{
x & x \ge 0 \cr
-x & x \le 0 \cr} \right.$$
\vskip \baselineskip \hrule


\beginliteral
$$\pmatrix{
a & b & c & d \cr
b & a & c+d & c-d \cr
0 & 0 & a+b & a-b \cr
0 & 0 & ab  & cd \cr
}.$$
@endliteral

$$\pmatrix{
a & b & c & d \cr
b & a & c+d & c-d \cr
0 & 0 & a+b & a-b \cr
0 & 0 & ab  & cd \cr
}.$$
\vskip \baselineskip \hrule




\beginliteral
$$ \left |
\matrix{
a & b & c & d \cr
b & a & c+d & c-d \cr
0 & 0 & a+b & a-b \cr
0 & 0 & ab  & cd \cr
}
\right | $$
@endliteral


$$ \left |
\matrix{
a & b & c & d \cr
b & a & c+d & c-d \cr
0 & 0 & a+b & a-b \cr
0 & 0 & ab  & cd \cr
}
\right | $$
\vskip \baselineskip \hrule

\beginliteral
$$ \left [
\matrix{
aa     & \cdots & az     \cr
\vdots & \ddots & \vdots \cr
za     & \cdots & zz     \cr
}
\right ] $$
@endliteral

$$ \left [
\matrix{
aa     & \cdots & az     \cr
\vdots & \ddots & \vdots \cr
za     & \cdots & zz     \cr
}
\right ] $$
\vskip \baselineskip \hrule




\end

}