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