| 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,... | |
| Jeremiah Day - Measurement - 1815 - 388 pages
...opposite angles. It follows, therefore, from the preceding proposition, (Alg. 389.) that the sum of any **two sides of a triangle, is to their difference; as the tangent of half the sum of the** opposite angles, to the tangent of half their difference. This is the second theorem applied to the... | |
| Jeremiah Day - Logarithms - 1815 - 126 pages
...opposite angles. It follows, therefore, from the preceding proposition, (Alg. 389.) that the sum of any **two sides of a triangle, is to their difference; as the tangent of half the sum of the** opposite angles, to the tangent of half their difference. This is the second theorem appKed to the... | |
| Euclides - 1816 - 528 pages
...being given, the fourth is also given. PROP. III. FIG. 8. 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 their difference. . Let ABC be a plane triangle, the sum of any two sides AB,... | |
| Olinthus Gregory - Plane trigonometry - 1816 - 276 pages
...cosines being the sines of the complements, it follows from the proposition that the sum of the cosines, **is to their difference, as the tangent of half the sum of the** complements, is to the tangent of halt' their difference. But half the sum of the complements of two... | |
| Sir John Leslie - Geometry - 1817 - 454 pages
...cos la + 7 cos5a + 21 cos3a + 35c. ' &e. &c. &c. PROP. IV. THEOR. The sum of the sines of two arcs **is to their difference, as the tangent of half the sum of** those arcs to the tangent of half the difference. If A and B denote two arcs ; smA+«'wB : sin A—... | |
| John Playfair - 1819 - 317 pages
...the radius to the tangent of the difference between either of them and 4 So. PROP. IV. The-sUm of any **two sides of a triangle is to their difference, as the tangent of half the sum of the angles** opposite to those sides, to the tangent of half their difference. Let ABC be any plane triangle ; CA+AB... | |
| Euclid, John Playfair - Circle-squaring - 1819 - 348 pages
...radius to the tangent of the difference between either of them and 45o. * PROP. IV. The sum of any troo **sides of a triangle is to their difference, as the tangent of half the sum of the angles** opposite to those sides, to the tangent of half their difference. Let ABC be any plane triangle ; CA+AB... | |
| Thomas Leybourn - Mathematics - 1819 - 430 pages
...: AC*. Required a proof. 8. Prove, geometrically, that in any plane triangle, 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. 9. Shew that tan.* 60 = 3 tan. 60 to rad. =: i. ID. P and... | |
| Rev. John Allen - Astronomy - 1822 - 516 pages
...legs AC and CB, and AD their difference ; therefore the sum of the legs AC, CB of the triangle ABC **is to their difference, as the tangent of half the sum of the angles** CAB and CBA at the Ijase is tQ the tangent of half their difference. PROP. VII. THEOR. If to half the... | |
| |