 | Euclides - 1816 - 588 pàgines
...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 pàgines
...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—... | |
 | Thomas Leybourn - 1819 - 430 pàgines
...: 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... | |
 | John Playfair - 1819 - 350 pàgines
...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... | |
 | Charles Hutton - 1822 - 680 pàgines
...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,...article, as we have already done with the first and seeondrwe shall obtain i! ' !':, 'ti-\ ' •i. 14 ANM&yiCZL PLANE TRIGONOMETRY. n* B^ vfapvA, cos.-... | |
 | Rev. John Allen - 1822 - 516 pàgines
...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... | |
 | Adrien Marie Legendre - 1822 - 394 pàgines
...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... | |
 | Peter Nicholson - 1823 - 210 pàgines
...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... | |
 | Jeremiah Day - 1824 - 440 pàgines
...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)... | |
 | 1824 - 492 pàgines
...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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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. 
