Selected propositions in geometrical constructions and applications of algebra to geometry. Being a key to the appendix of Davies' Legendre (1875)
Legendre, A. M. (Adrien Marie), 1752-1833, Davies, Charles, 1798-1876 · New York, Chicago [etc.] A.S. Barnes & company · leaf 55
nd E. From the similar triangles DSP andDBC, we have, DP : DC : : SP : CB . . . (1). From the similar triangles EPR and EBC, we have, EP : EB : : PR, or PS : BC . . . (2). From (1) and (2), we have, DP : DC : : EP : EB . . . (3). Whence, by division (Bk. II, Prop. 6), we have, DP : DC — DP : : EP :… … PROPOSITIONS FROM LEGENDRE. 49 APPLICATIONS OF ALGEBRA TO GEOMETRY. Prop. LXVII.—In a right-angled triangle ABC, given the baseBA, and the sum of the hypothenuse and perpendicular to find thehypothenuse and the perpendicular. Solution.—Denote BA by c, BC by x, AC by y, and the sum ofBC and AC by s.…
Geometry
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