| Jeremiah Day - Mathematics - 1853 - 5 pages
...therefore, from the preceding proposition, (Alg. 38'.>.) that the sum of any two sides of a. triangle, **is to their difference ; as the tangent of half the sum of** tin; opposite angles, to the tangent of half their difference. This is the second theorem npplied to... | |
| Charles Davies, Adrien Marie Legendre - Geometry - 1854 - 432 pages
...oppo• rile sides. 90. We also have (Art. 22), a + b : ab :: tan $(A + B) : ta.n$(A — B): tha| is, the **sum of any two sides is to their difference, as the tangent of half the sum of the** opposite angles to the tangent of half their difference. 91. In case of a right•angled triangle,... | |
| Allan Menzies - 1854
...Suppose AC, CB, and angle C to be given, then rule is, — Sum of the two sides (containing given angle) **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 ; half the sum = ^ (180 — angle C), then having found... | |
| Charles Davies - Navigation - 1854 - 322 pages
...AC :: sin G : sin B. THEOREM II. In any triangle, the sum of the two sides containing either *ngle, **is to their difference, as the tangent of half the sum of the** two oilier angles, to the tangent of half their difference. 22. Let ACS be a triangle: then will AB+AC... | |
| W.M. Gillespie, A.M., Civ. Eng - 1855
...angles are to each other as the opposite sides. THEOREM II. — 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. THEOREM III. — In every plane triangle,... | |
| Gerardus Beekman Docharty - Geometry - 1867 - 283 pages
...A+sin. B :: 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.)... | |
| James Pryde - Navigation - 1867 - 458 pages
...add the sides a and b and also subtract them, this will give a + b and a — b/ then the sum of the **sides is to their difference as the tangent of half the sum of the** remaining angles to the tangent of half their difference. The half sum and half difference being added,... | |
| Lefébure de Fourcy (M., Louis Etienne) - Trigonometry - 1868 - 288 pages
...a + I _ tang } (A + B) a — b tang} (A — B) *• ; which shows that, in any triangle, the sum of **two sides is to their difference as the tangent of half the sum of the angles** opposite to those sides is to the tangent of half their difference. We have A + B=180° — C; hence... | |
| W.M. GILLESPIE, L.L. D., CIV. ENG. - 1868
...angles are to each other as the opposite sides. THEOREM II. — 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. THEOREM III.— In every plane triangle,... | |
| Eli Todd Tappan - Geometry - 1868 - 420 pages
...BA-cos. A. That is, b = a cos. C -J- e cos. A. 869. Theorem — The sum of any two sid.es of a triangle **is to their difference as the tangent of half the sum of the** two opposite angles is to the tangent of half their difference. By Art. 867, a : b : : sin. A : sin.... | |
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