Plane and solid analytic geometry; an elementary textbook (1905)
Ashton, Charles H. (Charles Hamilton), 1866- · New York, C. Scribner's Sons · leaf 151
^ 4- ^ = 1 at the point P.. We wish to show that P^T bisects the angle FP^K, and that P^N 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. ^2 — 52 Its intercept ON on the X-axis is — x^, or, since id the ellipse ^2 _ p ^\ Also, FC=CF^ae, Hence FN= FC-\-CN=ae + e^x^ = e(a + ex{),and NF:=CF ~ ON = ae - eH^ = e(a - ex^. But (by [45]) F^ P-^ = a + ex^, and FP^ = a — ex^s Ch. X, § 78] TANGENTS 135 Hence FP^ NF and the normal…
Geometry, Analytic
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