Principles of modern geometry, with numerious applications to plane and spherical figures; and an appendix, containing questions for exercise. Intended chiefly for the use of junior students (1862)
Mulcahy, John, 1810?-1853 · Dublin Hodges, Smith · leaf 136
10. If three arcs of great circles be drawn from theangles of a spherical triangle to meet in one point, the productsof the sines of the alternate segments so made on the sines areequal. HAEMONIC PROPERTIES ON THE SPHERE. 125 Let ABC be the spherical triangle, and 0 the point (see fig.); then, B… … sin AOB. sin COA. sin BOG7sin ABO • sin CAO • sin sin AOB • sin COA. sin BOC sin BO • sin AO • sin CO sin BAO • sin ACO . sin CBOthe right-hand members of these two equations are evidentlyequal, therefore so are those on the left hand, and therefore wehave sin AB. sin CA. sin BC= sin AB. sin CA .…
Geometry -- Problems, exercises, etc · Geometry
Internet Archive · Gerstein Library, University of Toronto · Public Domain Mark 1.0. Free to use for anything.
