| Dennis M'Curdy - 1846 - 138 páginas
...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 páginas
...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 páginas
...+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... | |
| Ralph Smyth, Sir Henry Edward Landor Thuillier - 1851 - 718 páginas
...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 páginas
...: 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 páginas
...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 páginas
...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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