| John Playfair - 1819 - 317 pages
...BC is parallel to FG, CE : CF : : BE : BG, (2. 6.) that is, the sum of the two sides of the triangle **ABC 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. QED PROP. V. If a perpendicular... | |
| John Playfair - Circle-squaring - 1819 - 333 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 - Mathematics - 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.... | |
| Euclid, Rev. John Allen - Astronomy - 1822 - 494 pages
...the 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... | |
| Adrien Marie Legendre - Geometry - 1822 - 367 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 the... | |
| Peter Nicholson - Architecture - 1823 - 596 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 the... | |
| Industrial arts - 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... | |
| Jeremiah Day - Geometry - 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)... | |
| Peter Nicholson - Mathematics - 1825 - 372 pages
...: AC— CB:: tangí (B+C) : tang-i (B—C) it follows that in any triangle the sum of any two sides **is to their difference, as the tangent of half the sum of the two** angles opposite these sides, is to the tangent of half the difference of these same angles. Let then'AC=a,... | |
| Nathaniel Bowditch - Nautical astronomy - 1826 - 617 pages
...triangle (supposing any side to be the basr, and calling the other two the sides) the sum of the sides **is to their difference, as the tangent of half the sum of the** angles at the base is to the tangent of half the difference of the tame angles. Thus, in the triangle... | |
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