| Nathan Scholfield - 1845 - 896 pages
...B sin. A sin. C sin. B sin. C. 68 PROFOSITION in. In any plane triangle, the sum of any two sides, **is to their difference, as the tangent of half the sum of the angles** opposite to them, is to the tangent of half their difference. Let ABC be any plane triangle, then,... | |
| Nathan Scholfield - Conic sections - 1845 - 244 pages
...proposition, a sin. A.~ c b sin. 68 FROPOSITION III. In any plane triangle, the sum of any two sides, **is to their difference, as the tangent of half the sum of the angles** opposite to them, is to the tangent of half their difference. Let ABC be any plane triangle, then,... | |
| Nathan Scholfield - Conic sections - 1845
...a sin. B sin. A c sin. C sin. B b PROPOSITION III. In any plane triangle, the sum of any two sides, **is to their difference, as the tangent of half the sum of the angles** opposite to them, is to the tangent of half their difference. Let ABC be any plane triangle, then,... | |
| Scottish school-book assoc - 1845 - 278 pages
...6 tan. 4(A — B) opposite to the angles A and B, the expression proves, that the sum of the sides **is to their difference, as the tangent of half the sum of the** opposite angles is to the tangent of half their difference, which is the rule. (7.) Let (AD— DC)... | |
| John Playfair - Euclid's Elements - 1846 - 332 pages
...radius to the tangent of the difference between either of them and 45°. PROP. IV. THEOR. The sum of any **two sides of a triangle is to their difference, as the tangent of half the sum of the angles** opposite to those sides, to the tangent of half their difference. Let ABC be any plane triangle ; CA+AB... | |
| Dennis M'Curdy - Geometry - 1846 - 168 pages
...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 halves of the central... | |
| Jeremiah Day - Logarithms - 1848 - 153 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 AG equal... | |
| Charles Davies - Trigonometry - 1849 - 384 pages
...+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... | |
| Jeremiah Day - Geometry - 1851 - 418 pages
...opposite angles. It follows, therefore, from the preceding proposition, (Alg. 389.) that the sum of any **two sides of a triangle, is to their difference ; as the tangent of half the sum of the** opposite angles, to the tangent of half their difference. This is the second theorem applied to the... | |
| Charles William Hackley - Trigonometry - 1851 - 538 pages
...— 6 : : 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... | |
| |