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

Francis Nichols - Plane trigonometry - 1811 - 128 pages
...tangent of half the difference of the other two sides: also, the cosine of half the sum of any two angles 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. Fig. page 80. Let the angles...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1819 - 333 pages
...half the difference of t,he sides opposite to them; and the cosine of half the sum of the same angles is to the cosine of half their difference, as the tangent of half the side adjacent to them, to the tangent of half the suai of the sides opposite. LetC+B=2S, CB=2D, the base...
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First Part of an Elementary Treatise on Spherical Trigonometry

Benjamin Peirce - Spherical trigonometry - 1836 - 92 pages
...(M-\-N) : cos. (M — N) : : y — x : y+x; which may be written as in (744). 60. Theorem. 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 side to (749) which they are both adjacent...
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Elements of Trigonometry, Plane and Spherical: Adapted to the Present State ...

Charles William Hackley - Trigonometry - 1838 - 307 pages
...: : tan \ c : tan ^ (a — 6) The last one may be translated into ordinary language thus: The sine of half the sum of two angles of a spherical triangle is to the sine of half their difference as tfc.e tangent of half the interjacent side is to the tangent of half...
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Elements of Trigonometry, Plane and Spherical: Adapted to the Present State ...

Charles William Hackley - Trigonometry - 1838 - 307 pages
...(a — 6) : : 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...
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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 sides opposite to them; and the cosine of half the sum of the same angles is to the cosine of half their difference, as the tangent of half the side adjacent to them, to the tangent of half the sum of the sides opposite. LetC+B=2S, C— B=2D, the base...
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - Plane trigonometry - 1845 - 498 pages
...TV) : cos. (M — TV) z= y — x : y -f- ж ; which may be written as in (349). 79. Theorem. 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 side to which Napier's Analogies. they are...
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - Plane trigonometry - 1845 - 449 pages
...-{- N) : cos. (M — N) = y — x : y -\-x ; which may be written as in (349). 79. Theorem. 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 side to which Napier's Analogies. they are...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1846 - 332 pages
...half the difference of the sides opposite to them ; and the cosine of half the sum of the same angles is to the cosine of half their difference, as the tangent of half the side adjacent to them, to the tangent of half the sum of the sides opposite. 260 the segments of the base,...
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A Treatise on Trigonometry, Plane and Spherical: With Its Application to ...

Charles William Hackley - Trigonometry - 1851 - 542 pages
...difference of the other two angles. The third may be translated into ordinary language thus : The sine of half the sum of two angles of a spherical triangle is to the •ine of half their difference as the tangent of half the interjacent side is to the tangent of half...
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