| 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.... | |
| Francis Nichols - Plane trigonometry - 1811 - 128 pages
...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, and... | |
| 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 - 1811
...of half their difference : also, that the base is to the sum of the other two sides, as the cosine **of half the sum of the angles at the base, to the** cosine of half their difference. Ex. 14. How must three trees, A, B, c, be planted, so that the angle... | |
| 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... | |
| 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, .... | |
| 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,... | |
| |