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" The cosine of half the sum of two angles of a spherical triangle is to the cosine of half their difference as the tangent of half the included side is to the tangent of half the sum of the other two sides. "
First Part of an Elementary Treatise on Spherical Trigonometry - Page 51
by Benjamin Peirce - 1836 - 71 pages
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - Trigonometry - 1852 - 400 pages
...gives sin. J (A + C) _ tang. j. i sin. b(A — C) * tang. J (a — c)' which is the same as (350). 80. Theorem. The cosine of half the sum of two angles...their difference, as the tangent of half the side to which they are both adjacent is to the tangent of half the sum of the other two sides ; that is, in...
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An Elementary Treatise on Plane and Spherical Trigonometry: With Their ...

Benjamin Peirce - Plane trigonometry - 1861 - 394 pages
...sin, j (A + C) _ tang, ft & sin. i(A — C)~ tang. 4 (a — c) ' l' J which is the same as (350). 80. Theorem. The cosine of half the sum of two angles...of half their difference as the tangent of half the interjacent side is to the tangent of half the sum of the opposite sides ; that is, in the spherical...
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - Trigonometry - 1861 - 400 pages
..._ tang. J ft sin. \ (A — C) tang. \ (a. — c) ' which is the same as (350). (353) 80. Tlieorem. The cosine of half the sum of two angles of a spherical...of half their difference as the tangent of half the interjacent side is to the tangent of half the sum of the opposite sides ; that is, in the spherical...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 520 pages
...tangent of half the included side is to the tangent of half the sum of the other two sides. The sine of half the sum of two angles of a spherical triangle is 'to the sine of half their difference as the tangent of half the included side is to the tangent of half the...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 514 pages
...tangent of half the included side is to the tangent of half the sum of the other two sides. The sine of half the sum of two angles of a spherical triangle is to the sine of half their difference as the tangent of half the included side is to the tangent of half the...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1861 - 628 pages
...J (a — 4) : : 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...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 504 pages
...tangent of half the included side is to the tangent of half the sum of the other two sides. The sine of half the sum of two angles of a spherical triangle is to the sine of half their difference as the tangent of half the included side is to the tangent of half the...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - 1867 - 188 pages
...(a-)-6), (188) sin (^ + 5} : sin (A — B) : : tan c : tan (a — i). (189) That is, 7%e cosine of half the sum of two angles of a spherical triangle is to tlte cosine of half their difference as the tangent of half the included side is to the tangent of...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1869 - 516 pages
...-f- 6), (188) sin (A-\-B) : sin ,} (A — B) : : tan c : tan (a — 5). (189) That is, 7%e cosine of half the sum of two angles of a spherical triangle it to the cosine of half their difference as the tangent of half the included side is to the tangent...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Trigonometry - 1876 - 208 pages
...tangent of half the included side is to the tangent of half the sum of the other two sides. The sine of half the sum of two angles of a spherical triangle is to the sine of half their difference as the tangent of half the included side is to the tangent of half the...
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