| Jeremiah Day - Logarithms - 1815 - 126 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)... | |
| Jeremiah Day - Measurement - 1815 - 96 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 +... | |
| Olinthus Gregory - Plane trigonometry - 1816 - 244 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. and div. AC + BC; AC... | |
| Euclides - Euclid's Elements - 1816 - 528 pages
...tangent 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... | |
| Olinthus Gregory - Plane trigonometry - 1816 - 244 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 - 432 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
...: 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...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 W being in equilibrio on... | |
| John Playfair - Circle-squaring - 1819 - 333 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... | |
| Miles Bland - Geometry - 1819 - 377 pages
...preceding expressions not being easy for calculation, values i . may PROP. XIII. (88.) In any triangle, the **sum of any two sides is to their difference as the tangent of** the semi-sum of the angles at the base is to the tangent of their semi-difference. Let ABC be any triangle,... | |
| Euclid, Robert Simson - Mathematics, Greek - 1821 - 516 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...sum of the angles at the base to the tangent of half** their difference. PROP. IV. FIG. 18. IN any plane triangle BAC, whose two sides are BA, AC, and base... | |
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