| Francis Nichols - Plane trigonometry - 1811 - 128 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, as 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... | |
| William Enfield - Astronomy - 1811 - 428 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 difference,... | |
| Robert Gibson - Surveying - 1811 - 592 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 - 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 - 632 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
...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 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 with... | |
| 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 with... | |
| 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 PROP.... | |
| John Gummere - Surveying - 1814 - 390 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 part... | |
| Robert Gibson - Surveying - 1814 - 556 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,... | |
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