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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... "
First Part of an Elementary Treatise on Spherical Trigonometry - Page 63
by Benjamin Peirce - 1836 - 71 pages
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1846 - 332 pages
...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 - 538 pages
...: : tan 4 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 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...
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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 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...
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - Trigonometry - 1852 - 400 pages
...once obtained by 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 cotangent of half the included, angle is to the tangent of half the sum of the other tico angles, or in (figs. 32 and 33), cos. J (a + c)...
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - Trigonometry - 1861 - 400 pages
...(369) Proof. This theorem is at once obtained by applying (350) to the polar triangle. • jf 91. Theorem. The cosine of half the sum of two sides of...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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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1861 - 628 pages
...cot C : tan (4 — B). (187) 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 sine of half the sum of two sides of...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 520 pages
...: cot JC : tan (4 — #). (187) That is, y^e 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...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 514 pages
...the other two angles. 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 haJf the difference of the other two angles. By applying (186) and (187) to the...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 504 pages
...cot C : tan (4 — B). (187) 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 sine of half the sum of two sides of...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1869 - 516 pages
...: cot i C : tan (^ — 5). (187) 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 sine of half the sum of two sides of...
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