| Jeremiah Day - Logarithms - 1848 - 354 pages
...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 - Trigonometry - 1849 - 384 pages
...2 (/i 2 +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... | |
| Jeremiah Day - Geometry - 1851 - 418 pages
...THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, (Fig. 25.) **is to their difference ; as the tangent of half the sum of the** angles ACB and ABC, to the tangent of half their difference. Demonstration. Extend CA to G, making... | |
| 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 - 340 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... | |
| 1853 - 476 pages
...the sides opposite. 5. Find the value of tang. (a+b). 6. In a plane triangle, show that the sum of **two sides is to their difference as the tangent of half the sum** is to tangent of half the difference of the angles opposite. 7. Find the sin. \ A, and prove that 1... | |
| 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 - Geometry - 1854 - 436 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, in which the right... | |
| 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),... | |
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