| Francis Nichols - Plane trigonometry - 1811 - 128 pages
...is, in any spherical triangle the cosine of half the sum of any two sides is to the cosine of half **their difference, as the cotangent of half the included angle is to the tangent of half the** sum of the other two angles. 78. Remark. From this proposition and cor. we obtain half the sum S, and... | |
| Benjamin Peirce - Spherical trigonometry - 1836 - 84 pages
...is to the sine of half their difference, as the tangent of half the side to they are both adjacent **is to the tangent of half the difference of the other two** sides ; that is, in the spherical triangle ABC (figs. 4. and 5.), sin. J (A + C) : sin. i (A — C)... | |
| Charles William Hackley - Trigonometry - 1838 - 336 pages
...(9) That is, the cosine of half the sum of two sides of a spherical triangle is to the cosine of half **their difference, as the cotangent of half the included angle is to the tangent of half the** sum of the other two angles. The second may be repeated in a similar manner, chang. ing cosine into... | |
| Benjamin Peirce - Plane trigonometry - 1845 - 498 pages
...triangle. 91. Theorem. The cosine of half the sum of two sides of a triangle is to the cosine of half **their difference, as the cotangent of half the included angle is to the tangent of half the** sum of the other two angles, or in (figs. 32 and 33), соз4(а^с) : cos?4(a— c)=:cotan. \B : tang.... | |
| Benjamin Peirce - Plane trigonometry - 1845 - 449 pages
...triangle. 91. Theorem. The cosine of half the sum of two sides of a triangle is to the cosine of half **their difference, as the cotangent of half the included angle is to the tangent of half the** sum of the other two angles, or in (figs. 32 and 33), cos.£(a— c) : cos.|(a— c)=cotan.£J5 : tang.... | |
| Charles William Hackley - Trigonometry - 1851 - 524 pages
.... That is, the cosine of half the sum of two sides of a spherical triangle it to the cosine of half **their difference, as the cotangent of half the included angle is to the tangent of half the** sum of the other two angles. The second may be repeated in a similar manner, changing cosine into sine... | |
| Charles William Hackley - Trigonometry - 1851 - 538 pages
.... That is, the cosine of half the sum of two sides of a spherical triangle is to the cosine of half **their difference, as the cotangent of half the included angle is to the tangent of half** ike sum of the other two angles. The second may be repeated in a similar manner, changing cosine into... | |
| Horatio Nelson Robinson - Geometry - 1860 - 472 pages
...sum of any two sides of a spherical triangle is to the sine of the half difference of the same sides, **as the cotangent of half the included angle is to the tangent of** the half difference of the other two angles. The half sum, and the half difference of two angles of... | |
| Benjamin Peirce - Trigonometry - 1861 - 400 pages
.../ 90. Theorem. The sine of half the sum of two sides of a spherical triangle is to the sine of half **their difference as the cotangent of half the included...difference of the other two angles ; that is, in ABC** (fig. 32 or 33), sin. J (a -fc) : sin. \ (a — c) = cotan. JB : tang. J (A — C). (369) Proof. This... | |
| Benjamin Peirce - Plane trigonometry - 1861 - 396 pages
...55". 90. Theorem. The sine of half the sum of two sides of a spherical triangle is to the sine of half **their difference as the cotangent of half the included...the difference of the other two angles ; that is, in** ABO (fig. 32 or 33), sin. \ (a -fc) : sin. ¿ (a — c) = cotan. £ В : tang. \ (A — C). (369) Proof.... | |
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