 In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.  Elements of Geometry and Trigonometry - Side 241av Adrien Marie Legendre - 1836 - 359 siderUten tilgangsbegrensning - Om denne boken
 | Benjamin Peirce - 1845 - 498 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... | |
 | Dennis M'Curdy - 1846 - 168 sider
...Therefore the sin. AC+sin. AB : sin. AC—sin. AB : : tan. J(AC-(AB): tan. J(AC—AB). QED 4 Th. In any triangle, the sum of two sides 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. Given the triangle ABC, the side AB being greater... | |
 | Euclid, John Playfair - 1846 - 334 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 : CA-AB... | |
 | Jeremiah Day - 1848 - 354 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 - 372 sider
...2 4.r"—« Q 2sin« iA=R 2 —R 2 x —^— _ R * x 2/ic-R 2 (/i 2 +c 2 —a 2 ) = R« x -R- x " * Hence THEOREM V. In every rectilineal triangle, the...AB— BC : : sin C + sin A : sin C — sin A. But sinC + sin A : sin C — sin A : : tang — - — : . . . C+A f~* A tang - (Art. XXIV.) ; hence, AB + BC... | |
 | Jeremiah Day - 1851 - 418 sider
...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... | |
 | Charles William Hackley - 1851 - 524 sider
...: 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... | |
 | William Chauvenet - 1852 - 268 sider
...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 =... | |
 | Adrien Marie Legendre - 1852 - 436 sider
...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 - 1886 - 340 sider
...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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