Osgood, William F. (William Fogg), 1864-1943, Graustein, William C. (William Caspar), 1888-1941, joint author · New York : The Macmillan Company · leaf 571
ugatehyperbolic cylinders whose common asymptotic planes are (5) X m 4 + 1^-^=0. ,a 62 C2 Consequently, by Ch. XXII, § 6, Th. 2, their sections by theplane (4) are conjugate hyperbolas whose common asymptotes, defined by equations (4) and (5), pass throughthe origin, q. e. d. The equation of the… … (6) t + t-t = 0. a^ Fig. 5 The locus of the asymptotes is, therefore, acone whose vertex is at the origin. Thiscone is called the asymptotic cone of each of the hyperboloids(1) and (3). Evidently (1) lies wholly without the cone, thatis, on the convex side of it, while (3) lies wholly within it.…
