| Euclides - 1816 - 588 pages
...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... | |
| Sir John Leslie - 1817 - 456 pages
...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— «'wB A—... | |
| Charles Hutton - 1818 - 652 pages
...This equation is readily converted into a very useful proportion, viz. The sum of the sines of two ara **or angles, is to their difference, as the tangent...angles, is to the tangent of half their difference.** 26. Operating with the third and fourth formulae of the preceding article, as we have already done... | |
| John Playfair - 1819 - 350 pages
...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... | |
| Thomas Leybourn - 1819 - 430 pages
...: 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... | |
| Charles Hutton - 1822 - 680 pages
...• '• .--""•'"• This equation is readily converted into a very useful proportion, viz. Tlie **sum of the sines of two arcs or angles, is to their difference** r,- a$ the tangent of: half the sum of those arcs or angles, is to the tangent of half their difference.... | |
| Adrien Marie Legendre - 1822 - 394 pages
...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... | |
| Rev. John Allen - 1822 - 516 pages
...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... | |
| Peter Nicholson - 1823 - 210 pages
...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... | |
| 1824 - 492 pages
...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,... | |
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