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 231
v/21. 343, JProp,—The intercepts of a secant between the hyperbola andits asymptotes are equal. Dem.—Let DD be any secant, and Pand P, the points in which it cuts thecurve, be designated respectively as {x, y)and (x, y). Since DD is a line pass-ing through the two points (x, y), and{x, y), we have… … X y — y X Fig. 224. _ xy — yx y — y = X = y — y CP. Now as PCD and PCD are equiangular and have CD = CP,the triangles are equal, and PD = P D. Q. e. d. ScH.—This proposition afibrds an ele-gant and convenient method of construct-ing the hyperbola. If the axes are given,put them in position and draw…
Geometry, Analytic · Calculus
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