| Charles Hutton - Mathematics - 1811 - 422 pages
...k readily converted into a very nsefnl proportion, viz, The sum of the sines of two arcs or angles, **is to their difference, as the tangent of half the sum of** those arcs ' or angles, is to the tangent of half their difference. 2f . Operating with the third and... | |
| Charles Hutton - Mathematics - 1812 - 632 pages
...readily converted into a very useful proportion, viz, The sum of the sines of tiuo arcs or angles, **is to their difference, as the tangent of half the sum of** those arcs or angles, is to the tangent of half their difference. 26. Operating with the third and... | |
| Robert Gibson - Surveying - 1814 - 556 pages
...AB .- .- S. A ,• BC, 6fc. QED THEO. II. fig. aIn any jilane triangle AUC, the sum of the two gruen **sides AB and BC, including a given angle ABC, is to...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, and join HC: Jet fall the... | |
| Charles Butler - Mathematics - 1814 - 528 pages
...1.), V AF : FB : : AE : ED (4. 6.) and AF : AE : : FB : ED (16. 5.) ; that is, 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. QED When two sides and the included angle... | |
| John Gummere - Surveying - 1814 - 390 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... | |
| Jeremiah Day - Logarithms - 1815 - 126 pages
...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
...the opposite angles, !Ło the tangent of half their difference. Thus the sum of AB and AC (Fig. 25.) **is to their difference ; as the tangent of half the sum of the** angles ACB and ABC, to the tangent of half their difference. Demonstration. Extend CA to G, making... | |
| 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... | |
| 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—... | |
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