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 133
ore AB, AC AD, are in harmonic proportion. We shall now prove the same result directly from the trigo-nometrical relation:— Since (Art. 121) sin AD • sin BC = sin AB . sin CD,we have sin AD • sin (AC - AB) = sin AB . sin (AD - AC) ;therefore sin AD • sin AC • cos AB - sin AD • cos AC • sin AB =sin… … HARMONIC PROPERTIES ON THE SPHERE. 123 tion, and therefore (Art. 5, 3°) the tangents are in harmonicproportion. Q. E. D. Again, by drawing a tangent plane at C, we shall have (Art.6,3°) 2 cot CA = cot CB - cot CD. This also follows readily from the trigonometrical relation:—For, sin (AC + CD). sin…
Geometry -- Problems, exercises, etc · Geometry
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