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" In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. "
Elements of Geometry and Trigonometry Translated from the French of A.M ... - Page 241
by Charles Davies - 1849 - 359 pages
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...AC :: sin 0 : sin jR THEOEEM II. In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference. 22. Let ACB be a triangle: then will AJ3...
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A Treatise on Plane and Spherical Trigonometry

William Chauvenet - 1852 - 268 pages
...proposition is therefore general in its application.* 118. The sum of any two sides of a plane triangle is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. For, by the preceding article, a : b =...
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1886 - 340 pages
...C : sin B. Theorems. THEOREM 11. In any triangle, the sum of the two sides containing eithe1 angle, is to their difference, as the tangent of half the sum of (he t1eo other angles, to the tangent of half their di/ereMe. Let ACB be a triangle: then will With...
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Annual Report of the Trustees, Volumes 4-8

1853 - 476 pages
...each other as the sides opposite. 5. Find the value of tang. (a+b). 6. In a plane triangle, show that the sum of two sides is to their difference as the tangent of half the sum is to tangent of half the difference of the angles opposite. 7. Find the sin. \ A, and prove that 1...
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The Computist's Manual of Facts: And Merchant's and Mechanic's Calculator ...

Ezra S. Winslow - Business mathematics - 1853 - 264 pages
...cos A. In every plane triangle, as the sum of any two sides is to their difference, so is the natural tangent of half the sum of the angles opposite those sides to the natural tangent of half their difference ; and half the sum of the two angles, plus half their difference,...
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A Course of Mathematics: Containing the Principles of Plane Trigonometry ...

Jeremiah Day - Mathematics - 1853 - 288 pages
...therefore, from the preceding proposition, (Alg. 38'.>.) that the sum of any two sides of a. triangle, is to their difference ; as the tangent of half the sum of tin; opposite angles, to the tangent of half their difference. This is the second theorem npplied to...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...sides. 90. We also have (Art. 22), a + b : ab :: tan $(A + B) : ta.n$(A — B): tha| is, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles to the tangent of half their difference. 91. In case of a right•angled triangle,...
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Report of twenty-one years' experience of the Dick bequest for elevating the ...

Allan Menzies - 1854 - 520 pages
...Suppose AC, CB, and angle C to be given, then rule is, — Sum of the two sides (containing given angle) is to their difference as the tangent of half the sum of the angles at the base is to the tangent of half their difference ; half the sum = ^ (180 — angle C), then having...
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Elements of Surveying, and Navigation: With Descriptions of the Instruments ...

Charles Davies - Navigation - 1854 - 446 pages
...AC :: sin G : sin B. THEOREM II. In any triangle, the sum of the two sides containing either *ngle, is to their difference, as the tangent of half the sum of the two oilier angles, to the tangent of half their difference. 22. Let ACS be a triangle: then will AB+AC...
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A Treatise on Land Surveying: Comprising the Theory Developed from Five ...

William Mitchell Gillespie - Surveying - 1855 - 436 pages
...triangle, the sines of the angles are to each other as the opposite sides. THEOREM II. — In every plane triangle, the sum of two sides is to their difference...of half the sum of the angles opposite those sides is to the tangent of half their difference. THEOREM III. — In every plane triangle, the cosine of...
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