Geometry : the elements of Euclid and Legendre simplified and arranged to exclude from geomtrical reasoning the reductio ad absurdum : with the elements of plane and spherical trigonometry, and exercises in elementary geometry and trigonometry / /c By Lawrence S. Benson (1868)
Benson, Lawrence S. (Lawrence Sluter), Legendre, A. M. (Adrien Marie), 1752-1833 · New York : Pub. for the author by Davies & Kent · leaf 47
.),and BIT equal to BC, therefore (I. 3, case 1) the triangle ABHis equal to the triangle DBC. But (I. 15, cor. 4) the parallelo-gram BPIIL is double the ti-iangle ABH; for like reason thesquare BADE is double the triangle DBC ; hence (I. ax. 6)BPIIL is equivalent to BADE. In like manner, PCLK can… … OTHERWISE, Let the squares on AB andBC fall on the same side of BC.Describe the square BAED onthe side BA (L 23), and th.esquare BCMN on the side BC(L 23), and produce AE to F(I. post. 2); then tlirough D drawPF parallel to BC (I. 18). Because AF is parallel to BD(L def. 14, and 15, cor. 1), BC…
Geometry · Trigonometry
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