Osgood, William F. (William Fogg), 1864-1943, Graustein, William C. (William Caspar), 1888-1941, joint author · New York : The Macmillan Company · leaf 326
^ P of the conjugate diameter D has, byTh. 11, the coordinates (4) x = — a sin <^, y = b cos ^. Hence we obtain, for the squares of the half-lengths of D and a^ = a2 cos2 <^ + 62 sin2 <^, b^- = a- sin2 <f)-\-b- cos2 <^. Therefore, a{^ + b^^ = a2 + b^, and we have a simple proof of… … Hyperbola. Consider, now, a set of four steel girders A, B,C, and D in the form of a square, and a cross girder E throughthe center of the square parallel to A and C. Suppose thattie-rods are spanned into the frame along the diagonals ofthe square and along pairs of lines making equal angles…
