| Thomas Keith - 1839 - 498 pages
...to PROP, xxvi.) (413) In any spherical triangle, I. If the perpendicular fall within the triangle : **The cotangent of half the sum of the angles at the base, Is to the tangent of half their difference,** As the tangent of half the vertical angle, Is to tJie tangent of the excess of the greater of the two... | |
| Scottish school-book assoc - 1845 - 434 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
...the base EC : CF : : EB : BG; that is, 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.** Tharefore, in any triangle, &o. QED . 5 Th. The base of a triangle is to the sum of both the sides,... | |
| Nathaniel Bowditch - 1846 - 864 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... | |
| 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... | |
| Allan Menzies - 1854 - 520 pages
...then rule is, — Sum of the two sides (containing given angle) 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** ; half the sum = ^ (180 — angle C), then having found the half sum, J sum + £ diff. = greater angle,... | |
| Peter Nicholson - Cabinetwork - 1856 - 482 pages
...TRIGONOMETRY. — THEOREM 2. 151. The sum of the two sides of a triangle 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.** Let ABC be a triangle 4 then, of the two sides, CA and CB, let CB be the greater. Produce CA to E,... | |
| War office - 1861 - 714 pages
...one side the base, prove that the sum of the other 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.** 6. Observers on two ships a mile apart find the angles subtended by the other ship and a fort are respect... | |
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