 | Roswell Park - 1847 - 632 pages
...triangle, the sides are proportional to the sines of the opposite angles : also, the sum of any two sides is to their difference, as the tangent of the half sum of the two opposite angles, is to the tangent of their half difference : and finally, the sine of half of... | |
 | Roswell Park - Best books - 1847 - 626 pages
...triangle, the sides are proportional to the sines of the opposite angles : also, the sum of any two sides is to their difference, as the tangent of the half sum of ihe two opposite angles, is to the tangent of their half difference : and finally, the sine of half... | |
 | Horatio Nelson Robinson - Astronomy - 1850 - 378 pages
...certain angle. Take this angle from 45°, and call the difference a. Lastly, radius is to the tangent, a, as the tangent of the half sum of the angles at the bose is to the tangent of half their difference. III. Resolution of right-angled spherical triangles.... | |
 | Jeremiah Day - Geometry - 1851 - 418 pages
...construction, 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—... | |
 | Horatio Nelson Robinson - History - 1853 - 334 pages
...book 3, we have, Hence, . . AB : AE=AF : AG QED PROPOSITION 7. The sum of any two sides of a triangle, is to their difference, as the tangent of the half sum of the angles opposite to these sides, to the tangent of half their difference. Let ABC be any plane triangle. Then,... | |
 | Horatio Nelson Robinson - Navigation - 1858 - 356 pages
...book 3, we have, Hence, . . AB : AE=AF : AO QED PROPOSITION 7. The sum of any two sides of a triangle, is to their difference, as the tangent of the half sum of the angles opposite to these sides, to the tangent of half their difference. Let AB C be any plane triangle. Then,... | |
 | James Pryde - Navigation - 1867 - 506 pages
...is |(A + B) ; add the sides a and b and also subtract them, this will give a + b and a — b/ then the sum of the sides is to their difference as the tangent of half the sum of the remaining angles to the tangent of half their difference. The half sum and half... | |
 | Nautical astronomy - 1880 - 880 pages
...angle C. LIX. h any triangle (supposing an;/ side to be the base, and calling the other two the sides, the sum of the sides is to their difference as the. tangent of half the sum of the angles at tht base is to the tangent of half the difference of the same angles.... | |
 | William Findlay Shunk - Railroad engineering - 1880 - 362 pages
...trigonometry, two sides and the included angle being known in any plane triangle, the sum of the known sides is to their difference as the tangent of the half sum of angles at base is to the tangent of half their difference. In triangle С DE, therefore, CD + DE or... | |
 | William Findlay Shunk - Railroad engineering - 1890 - 360 pages
...Ci.!,!« ,111,1 111,. ,.,..!,,. I... I „„~ln Iwlinn known in any plane triangle, the sum of the known sides is to their difference as the tangent of the half sum of angles at base is to the tangent of half their difference. In triangle С D E. therefore, CD + DE or... | |
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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. 
