Mathematics for engineering students, Analytical geometry and calculus (1907)
Keller, S. S. (Samuel Smith), 1867-1923, Knox, W. F., [from old catalog] joint author · New York : D. Van Nostrand company · leaf 134
focal mdii to any point on theellipse is bisected by the normal at that point. Geometry tells us that the bisector of an angle of a tri-angle divides the opposite side into segments proportional Analytical Geometry. 5 to the other sides, hence, if we can prove (Fig. 49) thatFN : FN : : FP : FP our… … Fig. 49. Let P (Fig. 49) be (x, /). Then FN = FO + ON = c + e2x = ae + e2x, (since — = e, hence ae), But FN = FO - ON = ae - e2x. FP = a + ex and FP = a - exf . . (Art. 75) ae + e2x _ e{a + ex)_ a + exrae — e2x e(a — ex) a — ex FN FP FN FP or FN : FN : : FP : FP. It follows from the law of…
Geometry, Analytic · Calculus
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