Osgood, William F. (William Fogg), 1864-1943, Graustein, William C. (William Caspar), 1888-1941, joint author · New York : The Macmillan Company · leaf 557
is anarbitrary number, is also a solution. On the other hand, acurved surface is a cone with its vertex at the origin if andonly if, when P: (x^, yi, z^) is a point of the surface other than0, an arbitrary point, (kx^, ky^, kz^), of OP is also a point of thesurface. Thus the algebraic condition… … Fig. 4 SPHERES AND OTHER SURFACES 539 curved surface be a cone with its vertex at the origin, and thetheorem is proved. ^^^^f^iadvic Cones. A cone represented by a homogeneous equa-tion of the second degree in x, y, z, i.e. by an equation of theform, (4) ax^ + by^ + cz^ + dxy + eyz + fzx = 0, is…
