| Robert Gibson - 1808 - 482 pages
...la any plane triangle ABC, the sum of the two. given sides AB and £C, 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 the tangent of half their difference. Fig. 11. PLANE TRIGONOMETRY.... | |
| Sir John Leslie - Geometry, Plane - 1809 - 522 pages
...dt 3"-V zp: « <f-*s"-*+n. n -- * 3 2 -7 s -6 &c . PROP. IV. THEOR. The sum of the sines of two arcs **is to their difference, as the tangent of half the sum of the** arcs to the tangent of half the difference. If A and B denote two arcs; the S,A + S,B : S, A — S,B... | |
| Euclid - Geometry - 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 greater side for... | |
| 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 difference, and... | |
| Francis Nichols - Plane trigonometry - 1811 - 162 pages
...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 - 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 - Mathematics - 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 - 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 - Mathematics - 1814 - 528 pages
...1.), V AF : FB : : AE : ED (4. 6.) and AF : AE : : FB : ED (16. 5.) ; that is, the sum of the sides : **is to their difference : : as the tangent of half the sum of the angles at the base** : to the tangent of half their difference. QED When two sides and the included angle are given, the... | |
| 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 part... | |
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