 | Nautical astronomy - 1821 - 708 pages
...same angle*. Thus, in the triangle ABC, if we call AB the base, it will he as the sum of AC and CB is to their difference, so is the tangent of half the sum of the angles ABC, BAG', to the tangent of half their difference. Dem. With the longest leg CB as radius, describe... | |
 | William Nicholson - Natural history - 1821 - 356 pages
...of either angle to the co-tangent of the other angle. As the sum of the sines of two unequal arches is to their difference, so is the tangent of half the sum of those arches to the tangent of half their difference : and as the sum of their co-sines is to their... | |
 | William Nicholson - Natural history - 1821 - 356 pages
...of either angle to the co-tangent of the other angle. As the sum of the sines of two unequal arches is to their difference, so is the tangent of half the sum of those arches to the tangent of half their difference : and as the sum of their co-sines a to their... | |
 | Charles Hutton - Mathematics - 1822 - 680 pages
...that the base is to the sum of the other two sides as ^ SPHERICAL TRIGONOMETRY. 25 | as the cosine of half the sum of the angles at the base, to the if cosine of half their difference. . I Ex. 14. How must three trees, A, B, c, be planted, so that... | |
 | 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... | |
 | Edward Riddle - Nautical astronomy - 1824 - 572 pages
...Or the angles opposite the given sides may be determined as follows. As the sum of the given sides is to their difference, so is the tangent of half the sum of their opposite angles to the tangent of half the difference of the same angles, (Trig. Prop. 6.) And... | |
 | Abel Flint - Surveying - 1825 - 252 pages
...this CASE depends on the following PROPOSITION. In every Plane Triangle, as the sum of any two Sides is to their difference, so is the Tangent of half the sum of the two opposite Angles to the Tangent of half the difference between them. Add this half difference to... | |
 | Nathaniel Bowditch - Nautical astronomy - 1826 - 764 pages
...the tame angla. Thus, in the triangle ABC, if we call AB the base, it will be as the sum of AC and CB is to their difference, so is the tangent of half the sum of the angles ABC, ВАС, to the tangent of half their difference. Dan. With the longest leg CB as radius, , describe... | |
 | Nathaniel Bowditch - Nautical astronomy - 1826 - 732 pages
...Thus, in the triangle ABC, if we call AB the base, it will he, as the sum of AC and >* CB is to theip difference, so is the tangent / of half the sum of the angles ABC, ВАС, to / the tangent of half their difference. / Dem. With the longest leg CB as radius, /... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...difference. Let ABC be a plane triangle, the sum of any two sides AB, AC will be to their difference as the tangent of half the sum of the angles at the base ABC, ACB, to the tangent of half their difference. About A as a centre, with AB the greater side for... | |
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AC, (Fig. 25.) is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half their difference. 
