| Horatio Nelson Robinson - Mathematics - 1851 - 96 pages
...Demonstrate that radius is to the tangent of the difference between this angle and half a right angle, **as the tangent of half the sum of the angles at the base** of the triangle, is to the tangent of half their difference, To obtain that certain angle, we must... | |
| William Smyth - Plane trigonometry - 1852 - 198 pages
...AC : : tang — - — - tang ; "•" /^ a proportion, which we may thus enunciate : the sum of tioo **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. parts. Subtracting the angle C 45° from... | |
| William Chauvenet - 1852 - 268 pages
...The 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 =... | |
| 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... | |
| 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
...opposite angles. It follows, 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... | |
| Horatio Nelson Robinson - History - 1853 - 334 pages
...circle, by theorem 18, book 3, we have, Hence, . . AB : AE=AF : AG QED PROPOSITION 7. The sum of any **two sides of a triangle, is to their difference, as the tangent of** the half sum of the angles opposite to these sides, to the tangent of half their difference. Let ABC... | |
| 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... | |
| 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,... | |
| William Smyth - Navigation - 1855 - 236 pages
...— AC : : tan — i— : 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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