C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. A Treatise of Practical Surveying, ... - Side 94av Robert Gibson - 1808 - 440 siderUten tilgangsbegrensning - Om denne boken
| Enoch Lewis - 1844 - 228 sider
...to any radius whatever (Art. 27). QED ART. 30. In any right lined triangle, the sum of any two sides **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 the triangle;... | |
| 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,... | |
| 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... | |
| James Thomson - 1845 - 358 sider
...proposition is a particular case of this PROP. III. 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, is to the tangent of half their difference. Let ABC be a triangle,... | |
| 1845
...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,... | |
| 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)... | |
| 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:... | |
| 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,... | |
| 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... | |
| John Playfair - 1846 - 317 sider
...BC is parallel to FG, CE : CF : : BE : BG, (2. 6.) that is, the sum of the two sides of the triangle **ABC 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. PROP. V. THEOR. If a perpendicular... | |
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