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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... "
An Elementary Treatise on Plane & Spherical Trigonometry: With Their ... - Page 193
by Benjamin Peirce - 1845 - 449 pages
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A Treatise of Plane and Spherical Trigonometry: In Theory and Practice ...

Francis Nichols - Plane trigonometry - 1811 - 128 pages
...PROP. XVIII. . 76. In any spherical triangle the sine of half the sum of any two sides 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. Let the two sides AC, BC, and the included angle C be proposed;...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 pages
...difference of th angles opposite to them : ;UM! 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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Mathematical and Astronomical Tables: For the Use of Students of Mathematics ...

William Galbraith - Astronomy - 1827 - 322 pages
...half the difference of the angles opposite to them : And the cosine of half the sum of these sides is to the cosine of half their difference, as the cotangent of half tne angle contained between them, is to the tangent of half the sum of the angles opposite to them,t...
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Mathematical and Astronomical Tables: For the Use of Students in Mathematics ...

William Galbraith - Astronomy - 1834 - 428 pages
...half the difference of the angles opposite to them : And 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 is to the tangent of half the sum of the angles opposite to them, t or...
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First Part of an Elementary Treatise on Spherical Trigonometry

Benjamin Peirce - Spherical trigonometry - 1836 - 71 pages
...substituted in (847), gives t sin. % (a -\- c) cotan. B (8M) M.~j (a — с) ~ tang. (Л — C)' 77. Theorem. The cosine of half the sum of two sides of...difference, as the cotangent of half the included angle (852) is to the tangent of half the sum of the other two angles, or in (figs. 4. and 5.), cos. (a...
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First Part of an Elementary Treatise on Spherical Trigonometry

Benjamin Peirce - Spherical trigonometry - 1836 - 71 pages
...gives sin. J (a -\- c) cotan. В sin. (a — c) = tang. J (A^~C)J which is the same as (845). 77. Theorem. The cosine of half the sum of two sides of...cosine of half their difference, as the cotangent of hit If the included angle (852) is to the tangent of half the sum of the other two angles, or in (figs....
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Geometry - 1837 - 318 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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 317 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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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - Plane trigonometry - 1845 - 449 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 - 317 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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