Osgood, William F. (William Fogg), 1864-1943, Graustein, William C. (William Caspar), 1888-1941, joint author · New York : The Macmillan Company · leaf 339
is in-structive concerning the rela-tive positions of pole and polarwith regard to a central conic. Theorem 9. Let the point Piand the line Li he pole and polarin a central conic, center at 0 ;let D he the diameter through Fig. 26 * These methods are not very serviceable if accurate constructions… … DIAMETERS. POLES AND POLARS 321 Pi, D the diameter conjugate to D, and P^ the point of inter-section of Li with D. Then L^ is parallel to D and the half-length, d, of D is a mean proportional betiveen OPi and OF2: (1) OP, OP. = d\ We will prove the second part of the theorem first. By thedefinition…
