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103. A circumference of a circle defcribed from c, with the radius ca, will cut 
the tangent pt in R, r. 
Whence the perpendiculars rf, rf, to that tangent, will cut the axis a« 
in the focii f, f. 
For TR XTrzTAXTfl. 
104. A circumference defcribed from E, with a-c, in the Ellipfis, or from c, 
with ab in the Hyperbola, will cut the axis a a, in the focii f, f 
For, in the Ellipfis, tt~cc-\-ff, or ac — (bc~4-cf*:=) bf*- 
And in the Hyperbola, ff—tt -f ce, or cf = (ac 1 + bc =) ab 1 . 
105. Let coproduced, cut pf, p f, in z, x \ draw mz , mx ^ and mz, MX, 
parallel to them, cutting pf, p f in z,. x. 
Then px = cr = ca = pz = /. 
106. Hence zLPxz^ Z.pzx; and z^mxz — /_mzx. 
For pm is perpendicular to zx. 
Confequently, the angles p zm, p xvi j pzm, pxm are equal- 
107. And the triangles p zm, Pxm, are fimilar and equal : 
And fo are the triangles pzm, pxm. 
Confequently, the trapezias p zmx, pzmx, are fimilar,. 
I 03 . Let cr, cr, cut pf, p /, in k, h 
Then ck= ^ C r ^ - P -==) 
And C/f = ^ c /^ f ^ pF __ pK _ RR> 
J09. Alfo PXi=pz= f— XPZ = — X — X/ = ) — — ( — = ) p- 
\?m t t c t \ t 
i to. The- 
