Osgood, William F. (William Fogg), 1864-1943, Graustein, William C. (William Caspar), 1888-1941, joint author · New York : The Macmillan Company · leaf 568
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^… … As k increases from 0 toward c as its limit, this ellipse, risingfrom the section by the (x, 2/)-plane, grows continuouslysmaller and shrinks finally to a point, — the point (0, 0, c).Similarly, if k decreases from 0 toward — c as its limit. The surface generated by thechanging ellipse is the…
