 | William Mitchell Gillespie - Surveying - 1856 - 478 pages
...triangle, the sines of the angles are to each other a* the opposite sides. THEOREM II. — In every plane triangle, the sum of two sides is to their difference...of half the sum of the angles opposite those sides is to the tangent of half their difference. THEOREM III. — In every plane triangle, the cosine of... | |
 | George Roberts Perkins - Geometry - 1856 - 460 pages
...B. . . (2.) In the same way it may be shown that THEOREM II. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Theorem I., we have 5 : c : : sin. B... | |
 | Peter Nicholson - Cabinetwork - 1856 - 518 pages
...+ BC :: AC-BC : AD — BD. TRIGONOMETRY. — THEOREM 2. 151. The sum of the two sides of a triangle is to their difference as the tangent of half the sum of the angles at the base is to the tangent of half their difference. Let ABC be a triangle 4 then, of the two sides,... | |
 | William Mitchell Gillespie - Surveying - 1857 - 538 pages
...to each other at the opposite sides. THEOREM II.— In every plane triangle, the turn of two tides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. THEOREM III. — In every plane triangle, the cosine of... | |
 | W. M. Gillespie - Surveying - 1859 - 540 pages
...the angles are to each other at the opposite sides. THEOREM II — In every plane triangle, the turn of two sides is to their difference as the tangent...of half the sum of the angles opposite those sides is to the tangent of half their difference. THEOREM III. — In every plane triangle, t/m cosine of... | |
 | Elias Loomis - Trigonometry - 1859 - 218 pages
...AxAC=sin. BxBC, or sin. A : sin. B : : BC : AC. THEOREM II. (50.) In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference. Let ABC be any triangle ; then will CB+CA... | |
 | Elias Loomis - Logarithms - 1859 - 372 pages
...|(A+B) ^ sin. A~sin. B~sin. i(AB) cos. J(A+B)~tang. J(AB) ' that is, 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. .Dividing formula (3) "by (4), and considering... | |
 | George Roberts Perkins - Geometry - 1860 - 472 pages
...same way it may be shown that §«.] TRIGONOMETRY. THEOREM It In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the op? posite angles is to the tangent of half their difference. By Theorem I., we have o : c : : sin.... | |
 | McGill University - 1865 - 332 pages
...latter formula, determine tan. 15°, first finding tan. 30°. 5. The sum of the two sides of a triangle is to their difference as the tangent of half the sum of the base angles is to the tangent of half the difference. 6. Prove that if A" be the number of seconds... | |
 | Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...cos. A— sin. B : cos. (AB) ....... (44) THEOREM in. (ART. 9.) In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the ai,(/lei opposite to^them is to the tangent of half then- difference. „ . a sin. A , (Theorem 2.)... | |
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In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. 
