 | Nathan Scholfield - 1845 - 244 pages
...proposition, a sin. A.~ c b sin. 68 FROPOSITION III. In any plane triangle, the sum of any two sides, is to their difference, as the tangent of half the sum of the angles opposite to them, is to the tangent of half their difference. Let ABC be any plane triangle,... | |
 | Nathan Scholfield - 1845 - 894 pages
...B sin. A sin. C sin. B sin. C. 68 PROFOSITION in. In any plane triangle, the sum of any two sides, is to their difference, as the tangent of half the sum of the angles opposite to them, is to the tangent of half their difference. Let ABC be any plane triangle,... | |
 | Nathan Scholfield - 1845 - 542 pages
...a sin. B sin. A c sin. C sin. B b PROPOSITION III. In any plane triangle, the sum of any two sides, is to their difference, as the tangent of half the sum of the angles opposite to them, is to the tangent of half their difference. Let ABC be any plane triangle,... | |
 | John Playfair - 1846 - 332 pages
...difference as the radius to the tangent of the difference between either of them and 45°. PROP. IV. THEOR. 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. Let ABC be any plane triangle... | |
 | Dennis M'Curdy - 1846 - 168 pages
...triangle EFG, BC is drawn parallel to FG the base EC : CF : : EB : BG; that is, the sum of two sides is to their difference, as the tangent of half the sum of the angles at the base ia to the tangent of half their difference. * Moreover, the angles DBF, BFE are... | |
 | Anthony Dumond Stanley - 1848 - 134 pages
...is, The tangent of half the sum of any two sides of a spherical triangle is to the tangent of half their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. 38. In the following articles it is proposed to present... | |
 | Jeremiah Day - 1848 - 358 pages
...THE SUM OF THE OPPOSITE ANGLES ; TO THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half then- difference. Demonstration. Extend CA to G, making... | |
 | George Clinton Whitlock - 1848 - 336 pages
...A + sin5 : sinlA — sin 7?, or (333) a + b : a—b : : tani(A+B) : tan^(^-S) ; ie PROPOSITION VI. The sum of any two sides of a triangle is to their dif- (396) ference, as the tangent of the half sum of the angles opposite to the tangent of half their... | |
 | Charles Davies - 1849 - 380 pages
...+c 2 —a 2 ) = R« x -R- x " * Hence THEOREM V. In every rectilineal triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides, to the tangent of half their difference. * For. AB : BC : : sin C : sin... | |
 | Charles William Hackley - 1851 - 526 pages
...— 6 : : tan £ (A + B) : tan £ (A — B) That is to say, the sum of two of the sides of a plane triangle is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. 76 This proportion is employed when two sides and the included... | |
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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. 
