 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
 | Jeremiah Day - 1815 - 388 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 A(ACB +... | |
 | Euclides - 1816 - 588 sider
...three being given, the fourth is also given. PROP. III. FIG. 8. IN a plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the angles at the base, to the tangent of half their difference. . Let ABC be a plane triangle, the sum of any... | |
 | Olinthus Gregory - 1816 - 276 sider
...cosines being the sines of the complements, it follows from the proposition that the sum of the cosines, is to their difference, as the tangent of half the sum of the complements, is to the tangent of halt' their difference. But half the sum of the complements of two... | |
 | Sir John Leslie - 1817 - 456 sider
...cos la + 7 cos5a + 21 cos3a + 35c. ' &e. &c. &c. PROP. IV. THEOR. The sum of the sines of two arcs is to their difference, as the tangent of half the sum of those arcs to the tangent of half the difference. If A and B denote two arcs ; smA+«'wB : sin A—... | |
 | John Playfair - 1819 - 350 sider
...the difference between either of them and 45o. * PROP. IV. The sum of any troo 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—... | |
 | Thomas Leybourn - 1819 - 430 sider
...: BC* : AC*. Required a proof. 8. Prove, geometrically, that in any plane triangle, the sum of the sides is to their difference as the tangent of half the sum of the angles at the base to the tangent of half their difference. 9. Shew that tan.3 60 = 3 tan. 60 to rad. == i.... | |
 | Adrien Marie Legendre - 1822 - 394 sider
...principle ot Art. 44. And from this, the principles of Art. 42 and 43 are easily deducible. XL VII. In any rectilineal triangle, the sum of two sides is to their...of half the sum of the angles opposite those sides is to the tangent of half the difference of those same angles. From the proportion AB : AC : : sin... | |
 | Rev. John Allen - 1822 - 516 sider
...legs AC and CB, and AD their difference ; therefore the sum of the legs AC, CB of the triangle ABC is to their difference, as the tangent of half the sum of the angles CAB and CBA at the Ijase is tQ the tangent of half their difference. PROP. VII. THEOR. If to half the... | |
 | Peter Nicholson - 1823 - 210 sider
...BC : : AC - BC : AD - BD. TRIGONOMETRY. — THEOREM 2. 234. The sum of the two sides of a triangle 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. Let ABC be a triangle ; then, of the two sides,... | |
 | 1824 - 492 sider
...because DA C = AC B, (Euc. 1. 29.) Therefore, DAC+ DCA = 130o, and consequently ADC = of any triangle is to their difference, as the tangent of half the sum of the angles opposite them, is to the tangent of half their difference. Therefore, by logarithms, As, CD + DA = 9, = 0.954243... | |
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