Plane and solid analytic geometry; an elementary textbook (1904)
Ashton, Charles Hamilton, 1866-1936 · New York, C. Scribner's Sons · leaf 151
^-=\ at the point Pv We wish to show thata2 b2 PXT bisects the angle FPXK, and that PXN bisects theangle FP^F. It is a well-known theorem of elementary geometry thatthe bisector of an interior angle of a triangle divides theopposite side into segments which are proportional to the 134 ANALYTIC… … Fig. 71. a2 — b2Its intercept CN on the X-axis is — xv or, since in a2 — b2 a the ellipse — = e2, a2 CJSr=e2xvAlso, FfO=CF=ae. Hence F,N=F,C+CN= ae + e2xx = e(a + exx),and NF=CF - CN= ae - e2xx = e(a - ex{). But (by [45]) F,P1 = a -f- exv and FPX = a — &rr Ch. X, § 78] TANGENTS 135 Hence and…
Geometry, Analytic
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