Plane and solid analytic geometry; an elementary textbook (1901)
Ashton, Charles H. (Charles Hamilton), 1866- · New York, C. Scribner's sons · leaf 153
- = 1 at the point Pv We wish to show thata1 bl 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 ON on the X-axis is — xv or, since in a? — b2 a the ellipse — = e2, a1 CN=e2xvAlso, FfC=CF=ae. Hence FN= FC+CN=ae + e2xx = e (a + ex{),and NF=CF - CN = ae - e2xx = e(a - exj. But (by [45]) FF1 = a + g^, and FPX = a — e#r Ch. X, § 78] TANGENTS 135 FP FNHence l = ,…
Geometry, Analytic
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