Elements of geometry and trigonometry. Revised and adapted to the course of mathematical instruction in the United States (1856)
Legendre, A. M. (Adrien Marie), 1752-1833, Davies, Charles, 1798-1876 · New York : A.S. Barnes · leaf 150
f Q. For, from the points a and b, draw the lines aO, bO, tothe centre 0: they will pass through the points A and B(p. 7). Draw also OK to the point of contact K: it will BOOK V, 145 bii^ect AB in I, and be per-pendicular to it (b. hi., p. 6, s.)Prolong AO io E^ and drawBE. Let p represent the… … a Oh Hence, AOB ;p : P Oa0~a 0A\ or OK6K\ Again, since the triangles OaK^ EAB are similar, havingtheir sides respectively parallel (b iv., p. 21). Oil : OZ : : AE : EB, hence p : P : : AE : EB^ or by division (b. ii., p. 6), p : p-P :: Ilf : AE~EB, or AB\ But p is less than the square described on…
Geometry · Trigonometry
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