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 246
s,describe a circle, and by the corol-lary referred to,it will pass throughB and F, Join AG and produceBA to H. Then the rectangleFG.GB=AG^-AK^ each beingequal to the square of GK ; that is,FB.BG+BG==AB^-fBG^—AK^Take awayBG^; the:i FB.BG=AB^-AK==(AB+AK) (AB— AK)=HB.EB. Hence BG becomes known. Then,… … Prop. XXIII.—Prob.— Given the base, the area, and the•ratio of the sides of a triangle; to construct it. Let AB be the given base, and (V. 3, and scho.) find thepoints C, D, so that AC, CB, and AD, DB are in the ratio of the sides; on CD as diame-ter describe the semicircleCED, and (II. 5, scho.)…
Geometry · Trigonometry
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