| 1845
...b : a — b :: tan. | (A + в) : tan. ¿ (A — в).* Hence the sum of any two sides of a triangle, **is to their difference, as the tangent of half the sum of the angles** oppo-* site to those sides, to the tangent of half their difference. SECT. T. EESOLUTION OF TRIANGLES.... | |
| Nathan Scholfield - 1845 - 232 sider
...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 - 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,... | |
| Benjamin Peirce - 1845 - 449 sider
...triangle. j ¿ , C> ~! ' ' Ans. The question is impossible. 81. Theorem. The sum of two sides of a triangle **is to their difference, as the tangent of half the sum of the** opposite angles is to the tangent of half their difference. [B. p. 13.] Proof. We have (fig. 1.) a:... | |
| Benjamin Peirce - 1845 - 449 sider
...solve the triangle. -4n'. The question is impossible. 81. Theorem. The sum of two sides of a triangle **is to their difference, as the tangent of half the sum of the** opposite angles is to the tangent of half their difference. [B. p. 13.] Proof. We have (fig. 1.) a... | |
| 1845
...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 - 1846 - 317 sider
...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 - 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 halves... | |
| 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 AG equal... | |
| 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 A (Theorem... | |
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