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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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A Treatise of Plane and Spherical Trigonometry: In Theory and Practice ...

Francis Nichols - Plane trigonometry - 1811 - 128 pages
...| C : tan. | (A+ B), that 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....
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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 - 448 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 - 84 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...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 - 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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Elements of Trigonometry, Plane and Spherical: Adapted to the Present State ...

Charles William Hackley - Trigonometry - 1838 - 307 pages
...cot \ c : tan \ (A — B) . . . (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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

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

Benjamin Peirce - Plane trigonometry - 1845 - 498 pages
...Napier's Analogies. Proof. This theorem is at once obtained by applying 79 to the polar triangle. 91. Theorem. The cosine of half the sum of two sides of...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)...
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - Plane trigonometry - 1845 - 449 pages
...Napier's Analogies. Proof. This theorem is at once obtained by applying 79 to the polar triangle. 91. Theorem. The cosine of half the sum of two sides of...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)...
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