 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...- b : : tan %(A + B) : tan %(A - B) : that is, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles to the tangent of half thtir difference. 91. In case of a right•angled triangle, in which the right angle is B, we have... | |
 | W. Davis Haskoll - Civil engineering - 1858 - 422 pages
...expressed in words is the following rule. As the sum of the two given sides is to their differenee, so is the tangent of half the sum of the opposite angles to the twngtnt of half the differenee. -When the given parts are the three sides of a plane triangle. Figs.... | |
 | Frederick Augustus Griffiths - 1859 - 422 pages
...given side. Case 2. — When two sides, and their contained angle, are given. As the sum of the two sides, is to the difference of the sides ; so is the tangent of half the sum of their opposite angles, to the tangent of half the difference of the same angles. Then by adding half... | |
 | Frederick Augustus Griffiths - Artillery - 1859 - 426 pages
...given side. Case 2. — When two sides, and their contained angle, are given. As the sum of the two sides, is to the difference of the sides ; so is the tangent of half the sum of their opposite angles, to the tangent of half the difference of the same angles. Then by adding half... | |
 | William Thomas Read - 1862 - 144 pages
...Proposition HI. may here be written as a rule. " As the sum of the given sides is to their difference, so is the tangent of half the sum of the opposite angles to the tangent of half their difference. And the half difference added to half the sum gives the angle opposite the greater side, and, subtracted,... | |
 | Oliver Byrne - Engineering - 1863 - 600 pages
...same radius AD, by the definition of a tangent. But, the tangents AE, DF, being parallel, it will be as BE : BD :: AE : DF ; that is, as the sum of the...opposite angles, to the tangent of half their difference. The sum of the unknown angles is found, by taking the given angle from 180°. In the plane triangle... | |
 | William Thomas Read - Nautical astronomy - 1869 - 176 pages
...: sin B : : a : Ъ. (2) In any plane triangle, as the sum of any two sides is to their difference, so is the tangent of half the sum of the opposite angles, to the tangent of half their difference. From the preceding, we have, a^_ sin A Ъ ~~ sin В . Add 1 to both sides, a . , sin A ., . , then... | |
 | Edwin Pliny Seaver - Trigonometry - 1889 - 306 pages
...modulus. Formula [117] .... 131, 132 179-181. The sum of two sides of a triangle to their difference as the tangent of half the sum of the opposite angles to the tangent of half their, difference. Analytic proof. Geometric proof. Ratio of the sum and of the difference of two sides to the third side.... | |
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DF; that is, as the sum of the sides is to the difference of the sides, so is the tangent of half the sum of the opposite angles, to the tangent of half their difference. 
