| Abel Flint - Deeds - 1818 - 184 pages
...: 0.37044=60° 30'. CASE III. Two Sides and their contained Angle given, to find the ether Jingles and Side. Fig. 49. The solution of this CASE depends...Tangent of half the Sum of the two opposite Angles ; To th« Tangent of half the Difference between them. Add this half difference to half the Sum of the Angles... | |
| Robert Gibson - Surveying - 1818 - 502 pages
...wholes are as their halves, ie AH : IH : : CE : ED, that is, as the snm of the two sides AB and BC, is to their difference ; so is the tangent of half the sum of the two unknown angles A and C, to the tangent of half their difference. QED THEOREM HI. In any right-lined... | |
| 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,... | |
| 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... | |
| 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... | |
| Nathaniel Bowditch - Nautical astronomy - 1826 - 732 pages
...THEOREM HI. . In every plane triangle, it will be, as the sum of any two sides is to their difference, su is the tangent of half the sum of the two opposite angles to the tangent 'tif half their difference (by art. u'J, Geom.) THEOREM IV. As the base of any plane triangle is 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,... | |
| William Galbraith - Astronomy - 1827 - 412 pages
...45. In a plane triangle when the two sides and contained angle are given. I. As the sum of the given sides, Is to their difference ; So is the tangent of half the sum of the opposite angles, To the tangent of half their difference. Half the difference added to half the sum... | |
| Alexander Ingram - Mathematics - 1830 - 458 pages
...180°, and take half the remainder, to get half the sum of the unknown angles. Then as the sura of the sides is to their difference, so is the tangent of half the sum of the unknown angles to the tangent of half their difference. Having thus found the half difference, add... | |
| Jeremiah Day - Measurement - 1831 - 520 pages
...other radius. (Art. 1 19.) THEOREM II. 144. In a plane triangle, AS THE SUM OF ANY TWO OF THE SIDES, To THEIR DIFFERENCE ; - So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES; To THE TANGENT OF HALF THEIR DIFFERENCE. Thus the sum of AB and AC (Fig. 25.) is to... | |
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