 | 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 - 388 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 - 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. and div. AC + BC; AC... | |
 | Euclides - 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 - 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—... | |
 | 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...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... | |
 | Euclid, 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... | |
 | Miles Bland - Euclid's Elements - 1819 - 444 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 - Geometry - 1821 - 514 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... | |
| |
In any plane 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. 
