| Robert Gibson - Surveying - 1814 - 558 pages
...as their halves, that is, AH : IH: : CE : ED, that is as the sum 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 G, to the tangent of half their difference. QED THEO. III. Fig. 12. In any right... | |
| John Gummere - Surveying - 1814 - 398 pages
...of the two unknown angles. Then ; • * * * * • * As the sum of the two given sides, „• Is to **their difference ; ,. % So is the tangent -of half the sum of the two** uuknown angles, To the tangent of half their difference.* This half difference of the two unknown angles,... | |
| Jeremiah Day - Measurement - 1815 - 388 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, !Ło the tangent of half their difference. Thus the sum of AB and AC (Fig. 25.) is... | |
| Jeremiah Day - Logarithms - 1815 - 172 pages
...radius. (Art. 11 9.) THEOREM II. ..* 144. In a plane triangle, Jl 3 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... | |
| Olinthus Gregory - Plane trigonometry - 1816 - 278 pages
...•. 15. In any plane triangle it will be, as the sum of the sides about the vertical angle, is to **their difference, so is the tangent of half the sum of the** angles at the base, to the tangent of half their difference. By the preceding prop. AC : BC :: sin... | |
| Robert Gibson - Surveying - 1818 - 502 pages
...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... | |
| William Nicholson - Natural history - 1821 - 356 pages
...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 makes with the line CF, bisecting... | |
| William Nicholson - Natural history - 1821 - 356 pages
...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 tangent of the angle which the perpendicular CD makes with the line CF, bisecting... | |
| Nautical astronomy - 1821 - 706 pages
...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,... | |
| Abel Flint - Surveying - 1825 - 252 pages
...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 half... | |
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