Osgood, William F. (William Fogg), 1864-1943, Graustein, William C. (William Caspar), 1888-1941, joint author · New York : The Macmillan Company · leaf 163
hecircle of contact, C, of thesphere with the cone.As the sphere grows still larger, it cuts the plane M, butfinally passes beyond on the other side. In its last position, inwhich it still meets M, it will be tangent to M. Let the pointof tangency be denoted by F, and the circle of contact of… … FiQ. 15 THE HYPERBOLA 145 the frustum * cut from the cone by the planes of C and C, isof the same length, 2 a, for all points P. Join P with F. Then PF and PE, being tangents from Pto the same sphere, are equal. Similarly, PF and PR areequal. Hence FP + FP =RP+ RP = i^i?, or FP-\- FP = 2a. But this…
