Osgood, William F. (William Fogg), 1864-1943, Graustein, William C. (William Caspar), 1888-1941, joint author · New York : The Macmillan Company · leaf 567
uadric surfaces. We proceed to consider more general types. The surface defined by the equation (1) + ^ = 1 is known as an ellipsoid. If two of the three numbers a, b, c are equal, it is in particular an ellip-soid of revolution (Ch. XXII, § 8).To construct the surface in the generalcase when no… … Fia. 1 62 ^ c2 a2 + -=1, ^+y-=i. a^ The parts of these ellipses which lie in the quarter-planesbounding the first octant connect the points (a, 0, 0), (0, b, 0),(0, 0, c), as shown. The section of (1) by a plane z = k parallel to the {x, y)-plane has the equations : 548 QUADRIC SURFACES 549 If Ti^…
