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" 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. "
Elements of Plane and Spherical Trigonometry - Page 66
by Edwin Schofield Crawley - 1890 - 159 pages
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A Treatise of Plane and Spherical Trigonometry: In Theory and Practice ...

Francis Nichols - Plane trigonometry - 1811 - 162 pages
...found by Cor. 32. 1. PROP VI. 61. 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. Let ABC be the proposed triangle, whose sides are AC, BC, and base AB. About the centre C, with the...
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An Analytical Treatise on Plane and Spherical Trigonometry, and the Analysis ...

Dionysius Lardner - Plane trigonometry - 1828 - 434 pages
...— b~tan.-^(A. — B)' Hence " the sum of 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." This formula is independent of the absolute magnitudes of the sides, and will be applicable if their...
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Elements of Plane and Spherical Trigonometry: With Its Applications to the ...

John Radford Young - Astronomy - 1833 - 308 pages
...— B j ' that is to say., 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. By help of this rule we may determine the remaining parts of the • triangle, when we know two sides...
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Elements of Plane Trigonometry

William Smyth - Plane trigonometry - 1834 - 94 pages
....enunciate ; the sum of two sides of a triangle is to their difference, as tke tangent of half the turn of the opposite angles is to the tangent of half their difference. 70. Ex.1. Let AC (fig.30) be 52.96 yds, BC 70 yds,and the angle C 45° ; it is required to find the...
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Elements of Trigonometry, Plane and Spherical: Adapted to the Present State ...

Charles William Hackley - Trigonometry - 1838 - 338 pages
...(A — B) That is to say, the sum of two of the 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. This proportion is employed when two sides and the included angle of a triangle are given to find the...
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - Plane trigonometry - 1845 - 498 pages
...question is impossible. 81. Theorem. 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. [B. p. 13.] Proof. We have (fig. 1.) a: 6 = sin. A : sin. В ; whence, by the theory of proportions,...
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - Plane trigonometry - 1845 - 498 pages
...question is impossible. 81. Theorem. 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. [B. p. 13.] Proof. We have (fig. 1.) a : b = sin. A : sin. B ; whence, by the theory of proportions,...
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Key to System of practical mathematics. 2 pt. No.xvii

Scottish school-book assoc - 1845 - 278 pages
...to the angles A and B, the expression proves, that the sum of the sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference, which is the rule. (7.) Let (AD— DC) =d then, с — a : d=p cosec. A — p cosec. C : p cot. A —...
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An Elementary Treatise of Spherical Geometry and Trigonometry

Anthony Dumond Stanley - Geometry - 1848 - 134 pages
...half the sum of any two sides of a spherical triangle is to the tangent of half their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. 38. In the following articles it is proposed to present in proper order the formulae which seem best...
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A Treatise on Trigonometry, Plane and Spherical: With Its Application to ...

Charles William Hackley - Trigonometry - 1851 - 524 pages
...(A — B) That is to say, the sum of two of the 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. 76 This proportion is employed when two sides and the included angle of a triangle are given to find...
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