 | Euclid - Geometry - 1776 - 326 pages
...PROP. XXIH. TN every* fpherical triangle, the cotangent of half thefum of the * angles at the bafe, is to the tangent of half their difference ; as the tangent of half the vertical angle to the tangent of the angle that the perpendicular makes tuith the line bifecling the vertical angle.... | |
 | Thomas Simpson - Trigonometry - 1810 - 168 pages
...of half £ THEOREM VII. In any spherical triangle, ABC (fig. 16.), it -will be, as the co-tangent 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 which the perpendicular CD... | |
 | Asiatick Society (Calcutta, India) - Asia - 1811 - 600 pages
...Yerracondah, and the observed angles PSY and PYS, we have, the tangent of half the sum of the first, to the tangent of half their difference, as the tangent of half the sum of the second, to tangent of 2° 54' 25"-9^i their half difference : from which we get the greater... | |
 | Francis Nichols - Plane trigonometry - 1811 - 162 pages
...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 the vertical angle is to the tangent of half their difference; that is, cot.... | |
 | William Nicholson - Natural history - 1821 - 356 pages
...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 base is to the tangent of half their difference, so is the tangent of half the vertical angle to the tangent of the angle which the perpendicular CD... | |
 | Nautical astronomy - 1821 - 708 pages
...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.... | |
 | Rev. John Allen - Astronomy - 1822 - 508 pages
...substituting the latter ratios for the former, the cotangent of the hull' sum of t!ie angles A and ABC is to the tangent of half their difference, as the tangent of the half sum of the angles ACD and BCD is to the tangent of half their difference; and, forming rectangles... | |
 | Peter Nicholson - Architecture - 1823 - 210 pages
...— 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 - 504 pages
...the proper rules. RULE III. (X) When the three angles are given, to find the sides. The co-tangent of half the sum of the angles at the base, Is to the...half their difference; As the tangent of half the verticle angle, Is to the tangent of the excess of the greater of the two vertical angles (formed by... | |
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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. 
