 | Euclid - 1810 - 554 pages
...of half their difference. • Let ABC be a plane triangle, the sum of any two sides, AB, AC will be to their difference as the tangent of half the sum of -;' the angles at the base ABC, ACB to the tangent of half their difference. About A as a centre, with AB the... | |
 | Francis Nichols - 1811 - 162 pages
...ACB, which is the supplement of the angles at A and B, may be found by Cor. 32. 1. PROP VI. 61. In any triangle, the sum of any two sides is to their difference,...the tangent of half the sum of the opposite angles is to the tangent of half their difference. Let ABC be the proposed triangle, whose sides are AC, BC,... | |
 | Charles Hutton - 1811 - 442 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 I. In the plane triangle ABC, f AB 345 yards Given j AC 174-07 yards I / A 37° 20' Required... | |
 | Charles Hutton - 1811 - 494 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 th«ir difference. EXAMPLE I. In the plane triangle ABC, f AB 345 yards Given } AC 174-07 yards C /A... | |
 | William Enfield - 1811 - 476 pages
...side MR. In the triangle SRM, the sides RS, RM, being thus found, the sum of the two sides RS, RM, is to their difference, as the tangent of half the sum of the angles at the base RSM, RMS, is to the tangent of half their difference. To half the sum add half the... | |
 | Robert Gibson - 1811 - 580 pages
...In any Jilane triangle ABC, the sum of the two given sides AB and BC, including a given angle ABC, is to their difference, as the tangent of half the sum of the two unknown angles A and C is to Che tangent of half their difference. Produce AB and make HB=BC, and... | |
 | Charles Hutton - 1811 - 424 pages
...k readily converted into a very nsefnl proportion, viz, The sum of the sines of two arcs or angles, is to their difference, as the tangent of half the sum of those arcs ' or angles, is to the tangent of half their difference. 2f . Operating with the third and... | |
 | Charles Hutton - 1812 - 624 pages
...readily converted into a very useful proportion, viz, The sum of the sines of tiuo arcs or angles, is to their difference, as the tangent of half the sum of those arcs or angles, is to the tangent of half their difference. 26. Operating with the third and... | |
 | Charles Butler - 1814 - 582 pages
...by means of this proposition, without letting fall a perpendicular, as in the preceding article. 72. In a plane triangle, the sum of any two sides : is...difference : : as the tangent of half the sum of the angles at the base : to the tangent of half the difference. Let ABC be a triangle, from € as a centre... | |
 | Charles Butler - 1814 - 528 pages
...proposition, without letting fall a perpendicular, as in the preceding article. 71. In a plane triangle, tte 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 the difference. Let ABC be a triangle, from C as a centre... | |
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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. 
