 | Robert Gibson - Surveying - 1811 - 582 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... | |
 | William Enfield - Astronomy - 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... | |
 | Charles Hutton - Mathematics - 1811 - 422 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 - Mathematics - 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 - 568 pages
...this proposition, without letting fall a perpendicular, as in the preceding article. 72. 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 the difference. Let ABC be a triangle, from € as a centre... | |
 | Charles Butler - Mathematics - 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... | |
 | Euclides - 1814 - 558 pages
...difference; and since BC, FG are parallel (2. 6.), EC is to CF, as EB to BG ; that is, the sum of the sides is to their difference, as the tangent of half the sum of the angles at the base, tothe tangent of half their difference. •'• - °" •' • -.-.. • •> i... | |
 | Robert Gibson - Surveying - 1814 - 558 pages
...aIn any jilane triangle AUC, the sum of the two gruen 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 Cix tg the tangent of half their difference. Produce AB, and make HB— BC,... | |
 | John Gummere - Surveying - 1814 - 398 pages
...therefore since BC, FG are parallel EB : BF : : EC : CG (2. 6.) ; that is, the * sum of the sides AC, AB, is to their difference, as the tangent of half the sum of the angles ABC, ACB, is to the tangent of half their difference. • *• •• To demonstrate the latter... | |
 | Jeremiah Day - Logarithms - 1815 - 172 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... | |
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In every plane 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 their difference. 
