Legendre, A. M. (Adrien Marie), 1752-1833, Brewster, David, Sir, 1781-1868, Davies, Charles, 1798-1876 · New York, Wiley & Long · leaf 224
sines and cosines of two arcs, a and b, being given,it is required to find the sine and cosine of the sum or differenceof these arcs. Let the radius AC=R,the arcAB=a, the arc BD=6, and con-sequently ABD=a + h. Fromthe points B and D, let fall theperpendiculars BE, DF upon AC ;from the point D, draw… … CB : CI BE cos h sm a IK: CB : CI :: CE : CK,or R : cos 6 : : cos a : CK- R cos a cos h. R The triangles DIL, CBE, having their sides perpendicular,each to each, are similar, and give the proportions, CB;DI : : CE : DL,or R : sin & : : cosa : DL^^^?^^ sin a sin h. CB : DI ; : BE : IL, or R :…
Trigonometry · Geometry
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