| John Gummere - Surveying - 1814 - 400 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 - 562 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 - Mathematics - 1815 - 392 pages
...equal to the sum, and FH to the difference of AC and AB. And by theorem II, [Art. 144.] the sum of the **sides is to their difference ; as the tangent of half the sum of the** opposite angles, to the tangent of half their difference. Therefore, R:Tan (ACH-45°;::Tan A(ACB +... | |
| Jeremiah Day - Logarithms - 1815 - 172 pages
...equal to the sum, and FH to the difference of AC and AB. And by theorem II, [Art. 144.] the sum of the **sides is to their difference ; as the tangent of half the sum of the** opposite angles, to the tangent of half their difference. Therefore, R:Tan (ACH-45°;::Tan tfACB+B)... | |
| Euclides - 1816 - 592 pages
...three 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... | |
| Olinthus Gregory - Plane trigonometry - 1816 - 278 pages
...triangle it will be, as the sum of the sides about the vertical angle, is to their difference, so is **the tangent of half the sum of the angles at the base,** to the tangent of half their difference. By the preceding prop. AC : BC :: sin B : sin A, .-. by comp.... | |
| Sir John Leslie - Geometry - 1817 - 456 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—... | |
| Thomas Leybourn - Mathematics - 1819 - 430 pages
...: BC* : 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.3 60 = 3 tan. 60 to rad. == i. 10. P and... | |
| John Playfair - Circle-squaring - 1819 - 348 pages
...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... | |
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