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" 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 sine of half the sum of two sides of a... "
A Treatise of Plane and Spherical Trigonometry: In Theory and Practice ... - Page 87
by Francis Nichols - 1811 - 128 pages
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...half the difference of the angles opposite to them : and also that the cosine of half the sum of these sides, is to the cosine of half their difference, as the cotangent of half the angle contained between them, to the tangent of half the sum of the angles opposite to them. COR. 2....
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - Plane trigonometry - 1845 - 498 pages
...53° 8'. 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 angle is to the tangent of half the difference of the other two angles, that is, in ABC (figs. 32 and 33), sin.£(a+ c) :sin. |(a— c)=cotan....
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - Plane trigonometry - 1845 - 498 pages
...53° 8'. 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 angle is to the tangent of half the difference of the other two angles, that is, in ABC (figs. 32 and 33), sin.¿(ajc) :sin.i(a— c)=cotan....
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...half the difference of the angles opposite to them : and also that the cosine of half the sum of these sides, is to the cosine of half their difference, as the cotangent of half the angle contained between them, to the tangent of half the sum of the angles opposite to them. COR. 2....
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A Treatise on Trigonometry, Plane and Spherical: With Its Application to ...

Charles William Hackley - Trigonometry - 1851 - 524 pages
...: tan i (6 — c) . . . 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...the tangent of half the sum of the other two angles. The second may be repeated in a similar manner, changing cosine into sine and tangent of the half sum...
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A Treatise on Trigonometry, Plane and Spherical: With Its Application to ...

Charles William Hackley - Trigonometry - 1851 - 540 pages
...a : tan 4 (b — c) . . . 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...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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An Elementary Treatise on Plane and Spherical Trigonometry: With Their ...

Benjamin Peirce - Trigonometry - 1852 - 398 pages
...applying § 79 to the polar triangle. 91. Theorem. The cosine of half the sum of tico sides of a triangle is to the cosine of half their difference, as the...angle is to the tangent of half the sum of the other tico angles, or in (figs. 32 and 33), cos. J (a + c) : cos. J (a — c) = cotan. \ B : tang. J ( A...
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Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - Geometry - 1860 - 468 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 & Spherical Trigonometry: With Their ...

Benjamin Peirce - Trigonometry - 1861 - 396 pages
...to the polar triangle. »• jf 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 tJie included angle is to the tangent of half the sum of the other two angles ; or, in ABO (fig. 32...
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The Projection and Calculation of the Sphere for Young Sea Officers Being a ...

S. M. Saxby - Nautical astronomy - 1861 - 140 pages
...two sides is to the cosine of half their difference, so is the cotangent of half the contained angle to the tangent of half the sum of the other two angles. And half the difference thus found added to half the sum gives the greater angle ; and half the difference...
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