Smith, David Eugene, 1860-1944 · Boston, New York [etc.] Ginn and Company · leaf 242
een inmany algebras. For, letting AP2 — a, PXP2 = b, P2B ~ c> we nave a a — b LEADING PROPOSITIONS OF BOOK III 231 which is also derived from taking the reciprocals of a, b, c, andplacing them in an arithmetical progression, thus : whence or 1 1 b a 1 1 c b a — b b- e ab be a — b ab a b — c be c… … It maybe noted thatZP2(?P1, being made up of halves oftwo supplementary angles, is a right angle. Furthermore, if theratio CA : CB is given, and AB is given, then Px and P2 are bothfixed. Hence C must lie on a semicircle with P1P2 as a diameter,and therefore the locus of a point such that its…
Geometry
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