% --- start of displayed preamble in the book --- vardef magnify(expr pic,p,c,f)= save A;picture A; A=pic;clip A to p; unfill (p shifted -c scaled f shifted c); draw A shifted -c scaled f shifted c; draw p shifted -c scaled f shifted c; enddef; picture pic[]; % ptext=btex ... etex; % image with text not shown % --- end of displayed preamble in the book --- verbatimtex %&latex \documentclass{article} \begin{document} etex picture ptext; ptext=btex \parbox{10cm}{\parindent20pt\noindent Proposition LX. Theorem XXIII.\hfill\break \strut\hskip\parindent \emph{If two bodies $S$ and $P$, attracting each other with forces reciprocally proportional to the squares of their distance, revolve about their common centre of gravity; I say, that the principal axis of the ellipsis which either of the bodies, as $P$, describes by this motion about the other $S$, will be to the principal axis of the ellipsis, which the same body $P$ may describe in the same periodical time about the other body $S$ quiescent, as the sum of the two bodies $S+P$ to the first of the two mean proportionals between that sum and the other body $S$.\hfill\break} \strut\hskip\parindent For if the ellipses described were equal to each other, their periodic times by the last Theorem would be in a subduplicate ratio of the body $S$ to the sum of the bodies $S+P$. Let the periodic time in the latter ellipsis be diminished in that ratio, and the periodic times will become equal; but, by Prop. XV, the principal axis of the ellipsis will be diminished in a ratio sesquiplicate to the former ratio; that is, in a ratio to which the ratio of $S$ to $S+P$ is triplicate; and therefore that axis will be to the principal axis of the other ellipsis as the first of two mean proportionals between $S+P$ and $S$ to $S+P$. And inversely the principal axis of the ellipsis described about the movable body will be to the principal axis of that described round the immovable as $S+P$ to the first of two mean proportionals between $S+P$ and $S$. Q.E.D.\hfill\break \strut\hskip\parindent (Newton, \emph{The mathematical principles of natural philosophy}, translated by Andrew Motte, 1848.)} etex; defaultfont:="ptmr8r"; warningcheck:=0; beginfig(1) pic0=ptext scaled 0.4;label(pic0,origin);pic1=thelabel(pic0,origin); path p[]; p1=fullcircle xscaled 1.2cm yscaled .8cm shifted (0,1cm); magnify(pic1,p1,center p1,2.5); p2=unitsquare shifted (-.5,-.5) xscaled 2.5cm yscaled 1cm shifted (-2cm*up); magnify(pic1,p2,center p2,2); endfig; end;