| William Nicholson - 1809 - 720 pages
...the tangent of half the difference of the same arches. In any spherical triangle A li С (fig. 27), **it will be, as the cotangent of half the sum of the** angle», at the base, is to tlie tañe ent of half their difference, »o ii tin- tangent of halt" the... | |
| Thomas Keith - Navigation - 1810 - 482 pages
...Fig. to PROP, xxvi.) (H) In any spherical triangle, I. If the perpendicular fall within the triangle. **The co-tangent of half the sum of the angles at the base, Is to** tangent of half their difference ; As the tangent of half the •vertical angle, Is to the tangent... | |
| Francis Nichols - Plane trigonometry - 1811 - 128 pages
...any spherical triangle, if a perpendicular arc be drawn from an angle to the opposite side, or base, **the cotangent of half the sum of the angles at the base** will be to the tangent of half their difference, as the tangent of half the sum of the segments of... | |
| William Nicholson - Natural history - 1821 - 356 pages
...to the tangent of half the difference of the same arches. In any spherical triangle, ABC (fig. 27,) **it will be, as the co-tangent of half the sum of the angles at the** case is to the tangent of half their difference, so is the tangent of half the vertical angle to the... | |
| Nautical astronomy - 1821 - 704 pages
...difference of the same angles, (to the same radius,) and therefore (by art. :<:».) 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. I ed in it M : ABC, if the Hoe CD be.... | |
| Peter Nicholson - Architecture - 1823 - 210 pages
...TRIGONOMETRY. — THEOREM 2. 234. 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 ; then, of the two sides, CA and CB, let CB be the greater. Produce CA to E,... | |
| Edward Riddle - Nautical astronomy - 1824 - 572 pages
...radius is to the tangent of the difference between this angle and half a right angle, as the tangent **of half the sum of the angles at the base is to the** tiuigcnt of half their difference. ELEMENTARY PRINCIPLES OP SPHERICAL TRIGONOMETRY. 1. A SPHERE is... | |
| Thomas Keith - Navigation - 1826 - 508 pages
...tang ECD, the same expression as when the perpendicular falls within the triangle. (Y) COROLLARY II. **The co-tangent 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 tangent of half the difference between the two... | |
| Nathaniel Bowditch - Nautical astronomy - 1826 - 710 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... | |
| Nathaniel Bowditch - Nautical astronomy - 1826 - 782 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... | |
| |