Osgood, William F. (William Fogg), 1864-1943, Graustein, William C. (William Caspar), 1888-1941, joint author · New York : The Macmillan Company · leaf 326
all distances perpen-dicular to E are stretched, is the ratio ofelongation. Let us take the central line as axis of x.Since the slope of the diagonal S of thesquare is 1, the slope of the diagonal S of the rectangle is I.If the angle <^i is as shown, Fig. 16, the slopes of the twolines D and D… … Fig. 17 308 ANALYTIC GEOMETRY But then W =1% and, according to Th. 5, § 4, the lines D and D are conjugatediameters of a hyperbola, of which the diagonals of the rec-tangle are the asymptotes. The ratio b/a of the axes of thehyperbola equals the ratio of elongation, I: a Finally, let us show that…
