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" In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of... "
Higher Geometry and Trigonometry: Being the Third Part of a Series on ... - Page 68
by Nathan Scholfield - 1845 - 232 pages
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Ohio Educational Monthly, Volume 32

Education - 1883 - 642 pages
...of 45░. 4. Give directions for finding the logarithm of a number having four places. 5. Show that in any plane triangle the sum of any two sides is...their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. GENERAL HISTORY. 1. Before the Greeks,...
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A Practical Text-book on Plane and Spherical Trigonometry

Webster Wells - Trigonometry - 1883 - 234 pages
...more compactly as follows : a : b : с = sin A : sin В : sin С ab с sin A sin В sin O 145. In any triangle the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Art. 144, a : b = sin A : sinB Whence,...
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Text book of military topography

William Hamilton Richards - Military topography - 1883 - 256 pages
...in which two sides and the contained angle are known, and the third side is required. The sum of the two sides is to their difference, as the tangent of half the sum of the angles at the base, to the tangent of half their difference. Let the known sides be / 1076-53 and e 2846-39,...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...principle, now to be demonstrated, viz. : In any plane triangle, the sum of the sides including any angle, is to their difference, as the tangent of half the sum of the two other angles, is to the tangent of half their difference. Let ABC represent any plane triangle,...
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Trigonometry: Analytical, Plane and Spherical: With Logarithmic Tables

De Volson Wood - Trigonometry - 1885 - 334 pages
...This reduced by (66) gives (A + B) . " that is, Tfe SMWI o/" two sides of a plane triangle is to thcir difference, as the tangent of half the sum of the angles opposite is to the tangent of half their difference. To find A + B we. have A + B = 180░ - 0. (78) To find...
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Examination Papers for Science Schools and Classes

Great Britain. Education Department. Department of Science and Art - 1886 - 642 pages
...10░, a = 23087, b = 7903.2. (25.) 37. Prove geometrically that the sum of two sides of a triangle is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. In a triangle ABC, given a = 3, b = 5,...
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Plane Trigonometry

Webster Wells - Plane trigonometry - 1887 - 150 pages
...The above results may be expressed more compactly as follows: ab с sin , I sin Б sin С 114. In any triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. Formula (45) of Art. 113 may be put in...
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The Essentials of Plane and Spherical Trigonometry

Webster Wells - Trigonometry - 1887 - 200 pages
...A a The above results may be expressed more compactly as follows : , sin A sin B sin G 114. In any triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. Formula (45) of Art. 113 may be put in...
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Trigonometry, Analytical, Plane and Spherical, with Logarithmic Tables

De Volson Wood - 1887 - 264 pages
...'-ftThis reduced by (66) gives __ 0-6 tan | (1-5)' that is, The sum of two sides of a plane triangle is to their difference, as the tangent of half the sum of the angles opposite is to the tangent of half their difference. To▀nd A + Б we "have A + Б = 180░ - G. (78) To▀nd...
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A Treatise on Mine-surveying

Bennett Hooper Brough - Mine surveying - 1888 - 366 pages
...known, and it is required to find the two other angles, and the third side. In this case, the sum of the two sides is to their difference, as the tangent of half the sum of the two unknown angles is to the tangent of half their difference. Half their difference thus found, added...
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