| 1863
...180°, the remainder will be the sum of the other two angles. Then say, — As the sum of the given **sides, Is to their difference ; So is the tangent of half the sum of** _ the remaining angles, To the tangent of half their difference. Then, secondly, say, — As the cosine... | |
| 1865 - 428 sider
...angle from 180° : the remainder will be the sum of the remaining angles. Then, As the sum of the given **sides is to their difference, so is the tangent of half the sum of the** remaining angles to the tangent of half their difference. This half difference added to the half sum... | |
| William Davis Haskoll - 1868 - 184 sider
...greater side, the required angle will be acute. When two sides and their included angle are given. — **As the sum of any two sides is to their difference, So is the tangent of half the sum of** their opposite angles, to the tangent of half their difference. Then the half difference of these angles,... | |
| William Thomas Read - 1869 - 154 sider
...= Therefore Sin A DC BC DC 0 DC a 1. Sin В Or Sin A : 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... | |
| 1875
...41' 36" i sum 71° 50' 48" Here we will apply the following theorem in trigonometry. As the sum of **two sides 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. Let x= the half difference between D and... | |
| William Findlay Shunk - 1880 - 318 sider
...remainder will be the sum of the other two angles. Then, by proposition 3, — As the sum of the given **sides is to their difference, So is the tangent of half the sum of the** remaining angles to the tangent of half their difference. Half the sum of the remaining angles added... | |
| Simon Newcomb - 1882 - 104 sider
...last section. But there is a more convenient method founded on the following theorem : THEOREM IV. **As the sum of any two sides is to their difference, so is the tangent of half the sum of the** angles opposite these sides to the tangent of half their difference. Proof. From the equation b : o... | |
| William Davis Haskoll - 1886 - 230 sider
...greater side, the required angle will be acute. When two sides and their included angle are given. — **As the sum of any two sides is to their difference, So is the tangent of half the sum of** their opposite angles to the tangent of half their difference. Then the half difference of these angles,... | |
| 1828
...the following method : As the tangent of half the sum of the co-latitudes is to the tangent of half **their difference ; so is the tangent of half the sum of the** observed angles, to the tangent of half their difference. The triangle is thus reduced to a spherical... | |
| Daniel Kinnear Clark - 1889 - 1011 sider
...sides and the included angle are given. RULE 4. To find the other side: — as the sum of the two given **sides is to their difference, so is the tangent of half the sum of** their opposite angles to the tangent of half their difference — add this half difference to the half... | |
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