Osgood, William F. (William Fogg), 1864-1943, Graustein, William C. (William Caspar), 1888-1941, joint author · New York : The Macmillan Company · leaf 353
ions away from the origin. This tranformationis evidently represented analyti-cally by the equations : where A; is a constant greaterthan unity. If k is positive, butless than unity, the transforma-tion represents a shrinking toward the origin. The stretchingsand shrinkings defined by (1) are known… … Fig. 6 TRANSFORMATIONS OF THE PLANE 335 Example. The equilateral hyperbola 3.2 _ 2^2 _ ^2 is carried by (1), if k is taken equal to -: x = -, 2/ = ^, or x=ax, y = ay\a a into the curve a2a;2 - a?y^ = a% or x^ — y^ = 1. Thus all equilateral hyperbolas are seen to be similar to oneanother, since each…
