Wentworth, G. A. (George Albert), 1835-1906 · Boston, Ginn & company · leaf 126
cits three sides, A,B,C the anglesopposite to them, respectively. Through 0 draw an arc CD ofa great circle, perpendicular tothe side AB, meeting AB at D.For brevity let CD=p, AD=m,BD = n, ZACD = x, /.BCD 1. By §46 [38], in the righttriangles BDC and ADC, sinp = sin a sin B,and sinp = sin b sin A.… … [43] These equations may of course also be written in the formof proportions; as, for example, sin a: sin b = sin A : sin B. In Fig. 41 the arc of the great circle CD cuts the side ABwithin the triangle. In case it cut AB produced without thetriangle, sin(180°- A\ sin (180° -B), or sin (180°- C),…
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