A general geometry and calculus : including book I. of the general geometry, treating of loci in a plane; and an elementary course in the differential and integral calculus (1881)
Olney, Edward, 1827-1887 · New York : Sheldon and Co. · leaf 215
Fia. 196. 203, JPtop*—The radii vectores drawn to any point in an ellipse ofhyperbola make equal angles with the tangent at that point. Dem.—Let PF and PF, be the radiivectores, and M T the tangent, Figs. 195,197. ThenFPT=F PM. For,AT = — {137, Bx. 1, ox 276, Ex. 4), and AF =:A F==Ae. Hence, in the… … and FT -(ex -f A), Wherefore in Fig. 197. either case we have FT : FT :: r : r {201). Now drawing FM parallel toPF we have FT : FT :: PF : FM, or r : r :: r : FM. .•. FM=r =FP, and F MP = FPT= FPM. q. e. d. 204:, CoE.—In the ellipse the normal bisects the angle included by theradii vectores to the…
Geometry, Analytic · Calculus
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