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" The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference. "
A Practical Application of the Principles of Geometry to the Mensuration of ... - Page 105
de Jeremiah Day - 1815 - 96 pages
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New American Practical Navigator

1880 - 880 pages
...triangle (supposing an;/ side to be the base, and calling the other two the sides, the sum of the sides is to their difference as the. tangent of half the sum of the angles at tht base is to the tangent of half the difference of the same angles. Thus, in the triangle...
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A Treatise on Trigonometry by Profs. Oliver, Wait and Jones

Cornell University. Department of Mathematics - 1881 - 120 pages
...negative direction from the origin used. Тнм. 2. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the two opposite angles is to the tangent of half their difference : 106] ie, (a + b) : (a~b) = tan ¿(A...
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A Treatise on Trigonometry

James Edward Oliver - 1881 - 120 pages
...negative direction from the origin used. Tнм. 2. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the two opposite angles is to the tangent of half their difference : 106] ie, (a + b) : (a~&) = tan¿(A...
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The Ohio Educational Monthly and the National Teacher: A Journal ..., Volume 32

1883 - 748 pages
...logarithm of a number having four places. 5. Show that in any plane 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. GENERAL HISTORY. 2. What colonies were established by the...
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A Practical Text-book on Plane and Spherical Trigonometry

Webster Wells - 1883 - 298 pages
...c = sin A : sтБ : sin С abc or, sin A sin Б sin Q 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 Л : sin B Whence, by the theory...
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Text Book of Military Topography ...

William Hamilton Richards - 1883 - 256 pages
...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...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - 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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Examination Papers for Science Schools and Classes

Great Britain. Education Department. Department of Science and Art - 1886 - 648 pages
...value of c, having given A = 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, and C = 120°, find...
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Elements of Plane and Spherical Trigonometry: With Their Applications to ...

Elias Loomis - 1886 - 434 pages
...sin. A : sin. B : sin. C = a : b : c. THEOREM II. 58. In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite anyles is to tJie tangent of half their difference. Let ABC be any triangle; then will AB CB + CA :...
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Plane Trigonometry

Webster Wells - 1887 - 160 pages
...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 the form a: b =...
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