Elements of geometry and trigonometry. Revised and adapted to the course of mathematical instruction in the United States (1856)
Legendre, A. M. (Adrien Marie), 1752-1833, Davies, Charles, 1798-1876 · New York : A.S. Barnes · leaf 156
he squares OjiJ^Leir diameters. BOOK Y. 151 PKOPOSITION XIV. TIIEOKEM. Simihr arcs are to each other as their radii: and similar sec-tors are to each oilier as the squares of their radii. Let AB, BE, be similar arcs, and ACB^ BOB, sinuJarsectors: then • AB , BE \\and ACB : BOB CA OB CA 0B\ For,… … CA : circ. OB] but these circumferences are as the radii AC^ BO (p. 13);hence, AB : BE :: CA : OB, For a like reason, the sectors ACB^ BOE, are to eachother as the Avhole circles: which again are as the squaresof their radii (p, 13); therefore, sect. ACB : sect. BOB CA OB. PROPOSITION XV. THEOREM.…
Geometry · Trigonometry
Internet Archive · California Digital Library · Public Domain Mark 1.0. Free to use for anything.
