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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 angle is to the tangent of half the difference of the other two angles.
First Part of an Elementary Treatise on Spherical Trigonometry - Page 62
by Benjamin Peirce - 1836 - 71 pages
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A Treatise of Plane and Spherical Trigonometry: In Theory and Practice ...

Francis Nichols - Plane trigonometry - 1811 - 162 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...
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First Part of an Elementary Treatise on Spherical Trigonometry

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)...
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Elements of Trigonometry, Plane and Spherical: Adapted to the Present State ...

Charles William Hackley - Trigonometry - 1838 - 338 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...
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

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....
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

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), cos.£(a— c) : cos.|(a— c)=cotan.£J5 : tang....
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A Treatise on Trigonometry, Plane and Spherical: With Its Application to ...

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...
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A Treatise on Trigonometry, Plane and Spherical: With Its Application to ...

Charles William Hackley - Trigonometry - 1851 - 540 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...
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Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

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...
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An Elementary Treatise on Plane and Spherical Trigonometry: With Their ...

Benjamin Peirce - Trigonometry - 1861 - 396 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...
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An Elementary Treatise on Plane and Spherical Trigonometry: With Their ...

Benjamin Peirce - Plane trigonometry - 1861 - 394 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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