 | 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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The cotangent of half the sum of the angles at the base, Is to the tangent of half their difference... 
