| Nathaniel Bowditch - Nautical astronomy - 1826 - 764 pages
...difference of the same angles, (to the same radius,) and therefore (by art. 55) as the tabular tangent of half the sum of the angles at the base is to the tabular tangent of half the difference of the same angles. t In any plane triangle ABC, if the line... | |
| Nathaniel Bowditch - Nautical astronomy - 1826 - 732 pages
...difference of the same angles, (to the same radius,) and therefore (by art. 55) as the tabular tangent of half the sum of the angles at the base is to the tabular tangent of half the difference of the same angles. ьх. In any plane triangle ABC, if the... | |
| Thomas Keith - 1839 - 498 pages
...III. (483) When the three angles are given, to find the sides. The cotangent of half the sum of die angles at the base, Is to the tangent of half their difference, As die tangent of half the vertical angle, Is to the tangent of die excess of die greater of the two vertical... | |
| Enoch Lewis - Conic sections - 1844 - 234 pages
...vertex on the base, and an arc described bisecting the vertical angle ; it will be, as the cotangent of half the sum of the angles at the base is to the tangent of half their difference, so is the tangent of half the vertical angle to the tangent of the angle formed by the perpendicular... | |
| Scottish school-book assoc - 1845 - 444 pages
...difference of the segments of the base made by a perpendicular upon it from the vertex, as the cosine of half the sum of the angles at the base, is to the cosine of half their difference. Also, that the sum of the sides, is to the lifference of the segments... | |
| Dennis M'Curdy - Geometry - 1846 - 166 pages
...i(AC— AB). QED 4 Th. In any triangle, the sum of two sides is to their difference, as the tangent of half the sum of the angles at the base is to the tangent of half their difference. Given the triangle ABC, the side AB being greater than AC; AB+AC : AB— AC : : tan. J(ACB+ABC) : tan.... | |
| Nathaniel Bowditch - 1846 - 854 pages
...difference of the same angles (to the same radius) ; and therefore (by Art. 55) as the tabular tangent of half the sum of the angles at the base is to the tabular tangent of half the difference of the same angles. LX. In any plane triangle, ABC, if the line... | |
| Anthony Dumond Stanley - Geometry - 1848 - 134 pages
...tanj(A + B) tanj(a + ft). that is, The tangent of half the sum of any two sides of a spherical triangle is to the tangent of half their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. 38. In the following articles... | |
| Horatio Nelson Robinson - Astronomy - 1850 - 370 pages
...45°, and call the difference «. Lastly, radius is to the tangent, «, as the tangent of the half sum of the angles at the base is to the tangent of half their difference. III. Resolution of right-angled spherical triangles. side, #.a given angle, and x the quantity sought.... | |
| Horatio Nelson Robinson - Mathematics - 1851 - 96 pages
...theorem : In any plane triangle, the sum of the sides is to their difference., as the tangent of the half sum of the angles at the base, is to the tangent of half their difference. This theorem is demonstrated in some form in every treatise on trigonometry. 5. Give a geometrical... | |
| |