 | Nathaniel Bowditch - 1846 - 854 σελίδες
...: DH : AF or HB ; that is, AD, the sum of the legs, AC and СЁ, is to AE, their difference, as DH, the tangent of half the sum of the angles at the base (the radius teing AH), is to HB, the tangent of half the difference of the same angles (to the same... | |
 | Jeremiah Day - 1848 - 354 σελίδες
...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 AG equal... | |
 | Charles Davies - 1849 - 372 σελίδες
...—^— _ R * x 2/ic-R 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 A (Theorem... | |
 | Horatio Nelson Robinson - 1850 - 370 σελίδες
...45°, and call the difference «. Lastly, radius is to the tangent, «, as the tangent of the half sum of the angles at the base is to the tangent of half their difference. III. Resolution of right-angled spherical triangles. side, #.a given angle, and x the quantity sought.... | |
 | Jeremiah Day - 1851 - 418 σελίδες
...equal to 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... | |
 | Horatio Nelson Robinson - 1851 - 96 σελίδες
...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... | |
 | Charles William Hackley - 1851 - 524 σελίδες
...: 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... | |
 | Adrien Marie Legendre - 1852 - 436 σελίδες
...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... | |
 | William Chauvenet - 1852 - 268 σελίδες
...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 - 340 σελίδες
...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... | |
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In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of... 
