Osgood, William F. (William Fogg), 1864-1943, Graustein, William C. (William Caspar), 1888-1941, joint author · New York : The Macmillan Company · leaf 363
y(6) lie on (9). Secondly, the locusdoes not extend to infinity in anydirection.* In general, this ellipse will notbe a circle. Let L be the extremityof an axis. Since the transforma-tion (8) carries any straight linethrough the origin into a straightline through the origin, OL willcorrespond to a… … Fig. 11 TRANSFORMATIONS OF THE PLANE 345 about the origin through an angle 0 such that OL comes to liealong the positive axis of x: .^^. [Xi = x cos ^ — 2/ sin 6, ^ ^ \y^ = x sin 0 + y cos 6. Furthermore, we rotate the (x, 2/)-plane about the originthrough such an angle 6 that OL comes to lie along…
