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 138
IX.—ffHEOR.—In equal circles^ or in the same cir-cle^ angles, whether at the centers or circumferences^ have thesame ratio as the arcs on which they stand have to one another^so also have the sectors. Let, in the equal circles ALB, DNE, the angles LGK, KGC,CGB, DHN, NHM, and IMITF be at the… … Since (T. def. 19) all angles at the center of a circle aremeasured by the arcs intercepted by the sides of the angles, and all ancjles at the circum- ference are subtended by the arcs intercepted by the sides of the angles, and (III. 16) equal angles will have equal arcs whether they be at the…
Geometry · Trigonometry
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