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. A Treatise of Practical Surveying, ... - Side 94av Robert Gibson - 1808 - 440 siderUten tilgangsbegrensning - Om denne boken
| Dennis M'Curdy - 1846 - 138 sider
...triangle EFG, BC is drawn parallel to FG the base EC : CF : : EB : BG; that is, the sum of two sides **is to their difference, as the tangent of half the sum of the** angles at the base ia to the tangent of half their difference. * Moreover, the angles DBF, BFE are... | |
| Jeremiah Day - 1848 - 153 sider
...THE SUM OF THE OPPOSITE ANGLES ; TO THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, **is to their difference ; as the tangent of half the sum of the** angles ACB and ABC, to the tangent of half then- difference. Demonstration. Extend CA to G, making... | |
| Charles Davies - 1849 - 359 sider
...+c 2 —a 2 ) = R« x -R- x " * Hence THEOREM V. In every rectilineal triangle, the sum of two sides **is to their difference as the tangent of half the sum of the** angles opposite those sides, to the tangent of half their difference. * For. AB : BC : : sin C : sin... | |
| Sir Henry Edward Landor Thuillier - 1851 - 718 sider
...AH : IH : : CE :ED, that is, as the sum of the two sides AB and BC, is to their difference ; so is **the tangent of half the sum of the two unknown angles A and C,** to the tangent of half their difference. QED THEO. III. In any plane triangle A BD ; the base AD, will... | |
| Charles William Hackley - 1851 - 372 sider
...: tan £ (A + B) : tan ^ (A — B) That is to say, the sum of two of the 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. 76 This proportion is employed when two... | |
| Jeremiah Day - 1851
...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... | |
| A. M. LEGENDRE - 1852
...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
...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 - 1886 - 324 sider
...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 - 1853 - 5 sider
...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... | |
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