| 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 +... | |
| Euclides - 1816 - 528 pages
...them, in a plane triangle, any 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... | |
| 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—... | |
| 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 : CA—... | |
| Miles Bland - Euclid's Elements - 1819 - 444 pages
...* The 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,... | |
| 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.... | |
| John Playfair - 1819 - 317 pages
...the cosine of half their difference, as the cotangent of half the angle contained between them, to **the tangent of half the sum of the angles opposite to them.** COR. 2. If therefore A, B, C be the three angles of a spherical triangle, a, b, c the sides opposite... | |
| Adrien Marie Legendre - Geometry - 1822 - 367 pages
...principles of Art. 42 and 43 are easily deducible. XL VII. In any rectilineal triangle, the sum of **two sides is to their difference, as the tangent of half the sum of the angles opposite** those sides is to the tangent of half the difference of those same angles. From the proportion AB :... | |
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