| Euclid - Geometry - 1810 - 518 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 greater side for... | |
| Thomas Keith - Navigation - 1810 - 482 pages
...xxvi.) (H) In any spherical triangle, I. If the perpendicular fall within the triangle. The co-tangent **of half the sum of the angles at the base, Is to** tangent of half their difference ; As the tangent of half the •vertical angle, Is to the tangent... | |
| John Dougall - 1810
...to EF; AD, however, is the sum of the sides, and AE their difference; while DC was shown above to be **the tangent of half the sum of the angles at the base,** and EF is the tangent of rulf their difference ; the proposition is, therefore, demonstrated. PROP.... | |
| 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, and... | |
| Francis Nichols - Plane trigonometry - 1811 - 128 pages
...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... | |
| 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
...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 the least... | |
| 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. IV. Fio.JS, .... | |
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