| Euclides - 1816 - 528 sider
...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 - 244 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 - 432 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—... | |
| Thomas Leybourn - 1819
...: 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.* 60 = 3 tan. 60 to rad. =: i.... | |
| John Playfair - 1819 - 333 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... | |
| Adrien Marie Legendre - 1822 - 367 sider
...principles of Art. 42 and 43 are easily deducible. XL VII. In any rectilineal 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 the difference of those same angles. From the proportion... | |
| Rev. John Allen - 1822 - 494 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
...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
...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 =... | |
| Jeremiah Day - 1824
...the sum, and FH to the difference of AC and AB. And by theorem II, [Art. 1 44.] 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 ^(ACB+B)... | |
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