| ELIAS LOOMIS, LL.D. - 1859
...|(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 - 1860 - 443 páginas
...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.... | |
| Euclides - 1860
...demonstrated that AB : BC = sin. C : sin. A. PROPOSITIOK VI. THEOREM. The sum of two sides of a triangle **is to their difference as the tangent of half the sum of the** angles at the base to the tangent of half their difference. Let ABC be any triangle, then if B and... | |
| War office - 1861 - 12 páginas
...=2 tan 2 A. 5. In any triangle, calling one side the base, prove that the sum of the other two sides **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. 6. Observers on two ships a mile apart... | |
| Benjamin Greenleaf - 1862 - 490 páginas
...^ (A — B) f(\7\ sin A — sin B ~ wt~i (A + B) ; ( ' that is, The sum of the sines of two angles **is to their difference as the tangent of half the sum of the** angles is to the tangent of half their difference, or as the cotangent of half their difference is... | |
| Charles Davies - 1862 - 393 páginas
...AC . : sin C : sin B. THEOREM IL In any triangle, the sum of the two sides containing either angle, **is to their difference, as the tangent of half the sum of** tt1e two oif1er angles, to the tangent of half their difference. 22. Let ACB be a triangle: then will... | |
| Benjamin Greenleaf - 1863 - 320 páginas
...a sin A sin B sin C' (89) (90) (91) (92) (93) 112. 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. For, by (90), a : b : : sin A : sin B;... | |
| 1863 - 256 páginas
...proposition is therefore general in its application.* 118. The »urn of any two side» of a plane triangle ie **to their difference as the tangent of half the sum of the** opposite angles is to the tangent of half their difference. For, by the preceding article, a : b =»... | |
| 1864
...the first proportion in Theorem I. THEOREM III. 41. 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 a triangle ; then AB + BC:BC—... | |
| 1865
...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... | |
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