 | Thomas Leybourn - Mathematics - 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 rad.... | |
 | Charles Hutton - Mathematics - 1822 - 616 pages
...as BE : BD ;; AE : DF ; that is, as the sum of the sides is to the difference of the sides, so is. the tangent of half the sum of the opposite angles, to the tangent of half their difference. EXAMPLE J. In the plane triangle ABC, i AB .145 yards Given < AC 174-07 yards I Z. A 37° 20' Required... | |
 | Rev. John Allen - Astronomy - 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 to... | |
 | Adrien Marie Legendre - Geometry - 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 the... | |
 | Peter Nicholson - Architecture - 1823 - 210 pages
...40, page 41) AD+BD : AC + 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 - 492 pages
...DCA= BCD, 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 - 440 pages
...THE OPPOSITE ANGLES ; To THE TANGENT OF HALF THEIR DIFFERENCE. Thus the sum of AB and AC (Fig. 25) is to their difference ; as the tangent of half the sum of the angles ACB and ABC. to the tangent of half their difference. Demonstration. Extend CA to G, making... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 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... | |
 | Nathaniel Bowditch - Nautical astronomy - 1826 - 732 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... | |
 | Silvestre François Lacroix - Geometry, Analytic - 1826 - 190 pages
...^r;» ^'otn which tang i (a' -f- 6') sin a' + sin 6' we infer, that the sum of the sines of two arcs is to their difference, as the tangent of half the sum of these arcs is to the tangent of half their difference, is obtained immediately by a very elegant geometrical... | |
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The sum of any two 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. 
