 | W. Davis Haskoll - Civil engineering - 1858 - 422 pages
...three given parts are two sides and the included angle. — As the sum of the two 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. In the triangle ABC, AB = 345, and BC = 174,... | |
 | Alfred Wilks Drayson - 1861 - 236 pages
...proceed as follows : — Suppose AB, BC, known, and the angle ABC. Then as the sum of the two sides Is to their difference, So is the tangent of half the sum of the two unknown angles To the tangent of half their difference. Half their difference thus found, added to... | |
 | William Thomas Read - 1862 - 144 pages
...find the rest. 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... | |
 | Olinthus Gregory - 1863 - 482 pages
...latter. 15. In any plane 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. 16. In any plane triangle it will be,... | |
 | Samuel Alsop - Surveying - 1865 - 440 pages
...: 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 Thomas Read - Nautical astronomy - 1869 - 176 pages
...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... | |
 | Horatio Nelson Robinson - 1875 - 288 pages
...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 - Railroad engineering - 1880 - 362 pages
...opposite to the latter. 3. In any plane trianf/le, 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. 4. In any plane triangle, as the cosine... | |
 | Simon Newcomb - Trigonometry - 1882 - 372 pages
...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... | |
 | Royal Society (Great Britain) - Mathematics - 1828 - 490 pages
...at the pole is obtained by 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... | |
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TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE. 
