Osgood, William F. (William Fogg), 1864-1943, Graustein, William C. (William Caspar), 1888-1941, joint author · New York : The Macmillan Company · leaf 441
(2) Xq = OP cos «, OP 2/o = OP cos ^, Zq = OP cos y; (3) cos a = Q- cos/8 = -^, COSy = ^0-. OP ^ OP Thus cos2 a + cos^ R + cos2 y = ^o + .Vo+ ^0. ^ ^ 0P2 But OP = x,^ + 2/0 + ^0, and the theorem is proved. We have shown, then, that every directed line has definitedirection cosines, the sum of whose… … verse is also true: Any three numbers, the sum of whose squaresis unity, are the direction cosines of some directed line. Preliminary to proving this, we revertto the proof of Theorem 1 and choosethe point P in particular as the pointin which the ray issuing from 0 in thedirection of V meets the…
