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 255
rm an equilateral triangle. On the three sides of any triangle ABC, let^the equilateraltriangles ABD, BCF, CAE be de-scribed externally, and find G, H,K, the centers of the circles de-scribed in those triangles; drawGH, HK, KG ; GHK is an equilat-eral triangle. Join GA, GB, HB, HC, HF, KC,AF. Then… … 252 EXERCISES. HB : BG; that is, in the triangles FBA, HBG the sides aboutthe angles FBA, HBG are proportional; and these angles aj-eequal, each of thorn being equal to the sum of the angle ABCand two thirds of a right angle. Hence (V. 6) these trianglesare equiangular; and therefore (V. 3) FB or…
Geometry · Trigonometry
Internet Archive · California Digital Library · Public Domain Mark 1.0. Free to use for anything.
