Osgood, William F. (William Fogg), 1864-1943, Graustein, William C. (William Caspar), 1888-1941, joint author · New York : The Macmillan Company · leaf 556
e directed line L and the axis of z form in the plane M a system of coordinate axes, with respect to which the point P has the coordinates (r, z). The equation of the ruling i2, as a line of Mj is r = z tan <^. Since P lies on R, its coordinates (?*, z)satisfy this equation. But, clearly. where… … Fig. 3 or (1) ± Va;2 + 2/2 = 2: tan ^, a;2 + 2/2_;22tan2<^ = 0. Conversely, every point whose coordinates satisfy this equa-tion lies on the cone, for the steps can be retraced. Hencethis is the equation of the cone. Equation (1) is homogeneous in x, y, z. This is characteristicof the equation…
