\begin{picture}(0,0)% \includegraphics{fig1.eps}% \end{picture}% \setlength{\unitlength}{1699sp}% % \begingroup\makeatletter\ifx\SetFigFont\undefined% \gdef\SetFigFont#1#2#3#4#5{% \reset@font\fontsize{#1}{#2pt}% \fontfamily{#3}\fontseries{#4}\fontshape{#5}% \selectfont}% \fi\endgroup% \begin{picture}(5478,2944)(989,-3148) \put(2644,-1518){\makebox(0,0)[lb]{\smash{{\SetFigFont{5}{6.0}{\familydefault}{\mddefault}{\updefault}{$A'_1$}% }}}} \put(6144,-2375){\makebox(0,0)[lb]{\smash{{\SetFigFont{5}{6.0}{\familydefault}{\mddefault}{\updefault}{$D$}% }}}} \put(2929,-2447){\makebox(0,0)[lb]{\smash{{\SetFigFont{5}{6.0}{\familydefault}{\mddefault}{\updefault}{$A_1$}% }}}} \put(4215,-2304){\makebox(0,0)[lb]{\smash{{\SetFigFont{5}{6.0}{\familydefault}{\mddefault}{\updefault}{$A_2$}% }}}} \put(5073,-2232){\makebox(0,0)[lb]{\smash{{\SetFigFont{5}{6.0}{\familydefault}{\mddefault}{\updefault}{$A_3$}% }}}} \put(4572,-946){\makebox(0,0)[lb]{\smash{{\SetFigFont{5}{6.0}{\familydefault}{\mddefault}{\updefault}{$A'_3$}% }}}} \put(3858,-1161){\makebox(0,0)[lb]{\smash{{\SetFigFont{5}{6.0}{\familydefault}{\mddefault}{\updefault}{$A'_2$}% }}}} \put(5573,-875){\makebox(0,0)[lb]{\smash{{\SetFigFont{5}{6.0}{\familydefault}{\mddefault}{\updefault}{$D'$}% }}}} \put(5215,-2804){\makebox(0,0)[lb]{\smash{{\SetFigFont{5}{6.0}{\familydefault}{\mddefault}{\updefault}{$\triangle_3$}% }}}} \put(3072,-3090){\makebox(0,0)[lb]{\smash{{\SetFigFont{5}{6.0}{\rmdefault}{\mddefault}{\updefault}{$\triangle_1$}% }}}} \put(4430,-3018){\makebox(0,0)[lb]{\smash{{\SetFigFont{5}{6.0}{\familydefault}{\mddefault}{\updefault}{$\triangle_2$}% }}}} \end{picture}% |
\theo{ [de thales]} Soient $D$ et $D'$
deux droites du plan $\R^2$, $\triangle_1$, $\triangle_2$ et
$\triangle_3$ trois droites parall\`eles entre elles coupant $D$ en les
points $A_1$, $A_2$, $A_3$ et $D'$ en $A'_1$, $A'_2$, $A'_3$
respectivement. On suppose $\triangle_1$ et $\triangle_3$ non confondues alors on a l'\'egalit\'e $$\frac{\overline{A_1A_2}}{\overline{A_1A_3}}=\frac{\overline{A'_1A'_2}}{\overline{A'_1A'_3}}\ .$$ \begin{center} \input{fig1.eps_t} \end{center} |