| Jeremiah Day - Geometry - 1851 - 418 pages
...the sum, and FH to the difference of AC and AB. And by theorem II, (Art. 144.) the sum of the sides **is to their difference ; as the tangent of half the sum of the** opposite angles, to the tangent of half their difference. Therefore, R : tan (ACH— 45°) : : tan... | |
| Adrien Marie Legendre - Geometry - 1852 - 436 pages
...AC :: sin 0 : sin jR THEOEEM II. In any triangle, the sum of the two sides containing either angle, **is to their difference, as the tangent of half the sum of the two** other angles, to the tangent of half their difference. 22. Let ACB be a triangle: then will AJ3 + AC... | |
| William Chauvenet - 1852 - 268 pages
...proposition is therefore general in its application.* 118. The sum of any two sides of a plane triangle **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 the preceding article, a : b =... | |
| Charles Davies - Geometry - 1886 - 334 pages
...C : sin B. Theorems. THEOREM 11. In any triangle, the sum of the two sides containing eithe1 angle, **is to their difference, as the tangent of half the sum of** (he t1eo other angles, to the tangent of half their di/ereMe. Let ACB be a triangle: then will With... | |
| Jeremiah Day - Mathematics - 1853 - 288 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 - Navigation - 1854 - 446 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... | |
| Allan Menzies - 1854 - 520 pages
...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),... | |
| Charles Davies - Geometry - 1854 - 436 pages
...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,... | |
| Charles Davies - Geometry - 1855 - 336 pages
...sin A : sin BTheorems.THEOREM IIIn any triangle, the sum of the two sides contain1ng either angle, **is to their difference, as the tangent of half the sum of the two** other angles, to the tangent of half their differenceLet ACB be a triangle: then will AB + AC:AB-AC::t1M)(C+£)... | |
| William Smyth - Navigation - 1855 - 236 pages
...tan — ~ ; lU —4 a proportion, which we may thus enunciate ; the sum of two sides of a triangle **is to their difference, as the tangent of half the sum of the** opposite angles is to the tangent of half their difference. Ex. 1. Let AC (fig. 30) be 52. 96 -yds,... | |
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