Davies, Charles, 1798-1876 · New York and Chicago, A. S. Barnes and company · leaf 104
may be shown that the trianglesAED and FKI are similar: and, hence, whatever be thenumber of sides of the polygons, they may be divided into anequal number of similar triangles. THEOREM XXI. Similar polygons are to each other as the squares described on their homologous sides. Let ABODE and FGNIK,… … F G ber of similar triangles. Then, by Theorem XIX, we have triangles ABC : FGN : : AJ? . FG2 ADC : FIN : : DC? : m2 ADE FIK : : DE2 : IK2 But since the polygons are similar, the ratio of the last ante-cedent to its consequent, in each of the proportions, is thesame: hence, we have (Bk. III. Th.…
Geometry · Plane trigonometry
Internet Archive · Library of Congress · Public Domain Mark 1.0. Free to use for anything.
