 | David Stewart Erskine Earl of Buchan, Walter Minto - Logarithms - 1787 - 164 pages
...difference. Cof af-cof b : cof a — cof b : : cot ^ : tang t±?. (4) Lem. 3. The fum of the fines of two arcs is to their difference as the tangent of half the fum of thofe arcs is to the tangent of half their their difference. * Sin a + fin b : fin a —... | |
 | Sir John Leslie - Geometry, Plane - 1809 - 522 pages
...odd number ; and that Cos,n« = dt 3"-V zp: « <f-*s"-*+n. n -- * 3 2 -7 s -6 &c . PROP. IV. THEOR. The sum of the sines of two arcs is to their difference, as the tangent of half the sum of the arcs to the tangent of half the difference. If A and B denote two arcs; the S,A + S,B... | |
 | Rev. John Allen - Astronomy - 1822 - 516 pages
...the tangent of half their difference (5 Pi. Tr.), and the sum of the sines of the angles ACD and BCD is to their difference, as the tangent of half their sum is to the tangent of half their difference (4 PL Tr ) ; therefore, substituting the latter ratios for the former, the cotangent of the half sum... | |
 | Rev. John Allen - Astronomy - 1822 - 508 pages
...5 Eu.); but the sum of the cosines of the angles A and ABC is to their difference, as the cotangent of half their sum is to the tangent of half their difference (5 PI. Tr.), and the sum of the sines of the angles ACD and BCD is to their difference, as the tangent... | |
 | Thomas Keith - Navigation - 1826 - 504 pages
...TANGENTS, &C. OF THE SUMS, AND OF THE DIFFERENCES OF ARCS. PROPOSITION xiii. (Plate L Fig. 2.J (P) The sum of the sines of two arcs is to their difference, as the tangent of half the sum of those arcs is to the tangent of half their difference. Let BA and во be the two arcs ;... | |
 | Silvestre François Lacroix - Geometry, Analytic - 1826 - 190 pages
...equation 2 >- — r- ~ = - — r~, — ^r;» ^'otn which tang i (a' -f- 6') sin a' + sin 6' we infer, that the sum of the sines of two arcs is to their difference, as the tangent of half the sum of these arcs is to the tangent of half their difference, is obtained immediately by a very... | |
 | Charles William Hackley - Trigonometry - 1838 - 328 pages
...expressed in a proportion thus : (he sum of the sines of any two arcs is to the difference of their sities as the tangent of half their sum is to the tangent of half t/teif difference' 75. Let ABC be any triangle ; then (Art. 64) a : b : : sin A : sin B or by composition,... | |
 | Thomas Keith - 1839 - 498 pages
...TANGENTS, ETC. OF THE SUMS, AND OF THE DIFFERENCES OF ARCS. PROPOSITION xin. (Plate I. Fig. 2.) (231) Tlie sum of the sines of two arcs is to their difference, as the tangent of half the sum of those arcs is to the tangent of half their difference. Let BA and BO be the two arcs ; draw... | |
 | Enoch Lewis - Conic sections - 1844 - 234 pages
...As IF : IB : : tan CGF : tan CGB :: tan $(AB — AC). tan QED to their difference, as the cotangent of half their sum is to the tangent of half their difference. Retaining the construction of the last article, it is easily perceived that GI is the sum, and 1C the... | |
 | Charles William Hackley - Trigonometry - 1851 - 524 pages
...expressed in a proportion thus : the sum of the sines of any two arcs is to the difference of their sines as the tangent of half their sum is to the tangent of half their difference. A 75. Let AB c be any triangle ; then (Art. 67) a : i : : sin A : sin B or by composition, (Alg. Art.... | |
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The sum of the sines of two arcs is to their difference, as the tangent of half the sum of those arcs is to the tangent of half their difference. 
