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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. "
A Course of Mathematics: In Three Volumes : Composed for the Use of the ... - Page 63
by Charles Hutton - 1811
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A Treatise on Special Or Elementary Geometry

Edward Olney - 1872 - 472 pages
...horizontal parallax. PLANE TRIGONOMETRY. 80. Ргор.— The sum of any 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. ( DEM. — Letting a and b represent...
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An Elementary Geometry and Trigonometry

William Frothingham Bradbury - 1872 - 262 pages
...same sine, and BD = a sin. BCD = a sin. C (41) B 102. 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. Let ABC (Art. 103) be a plane triangle...
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Elements of Trigonometry, Plane and Spherical

Edward Olney - 1872 - 216 pages
...horizontal parallax. PLANE TRIGONOMETRY. 86. Prop.— Tlie sum of any 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. DEM. — Letting a and b represent...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - 1872 - 464 pages
...have the following principle : In any plane triangle, the sum of the sides including either 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. The half sum of the angles may be...
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A Treatise on Special Or Elementary Geometry, Volumes 1-2

Edward Olney - 1872 - 562 pages
...horizontal parallax. PLANE TRIGONOMETRY. 86. Prop.— TJie sum of any 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. 1 >K\r. — Letting a and b represent...
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Documents of the Assembly of the State of New York, Volume 96, Issue 2

New York (State). Legislature. Assembly - 1873 - 818 pages
...we have the principle. When two sides and their included angles are given : The sum of the two sides is to their difference as the tangent of half the sum of the other two angles is to. the tangent of half their difference. This young man also worked out a...
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Annual Report of the School Committee of the City of Boston

Boston (Mass.). School Committee - 1873 - 454 pages
...to the sines of the opposite angles. III. Prove 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. IV. In a triangle the side AB = 532....
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Annual Report, Volume 43

Cincinnati (Ohio). Board of Education - 1873 - 352 pages
...the other two sides. Prove it. 5. Prove that in a plain triangle the sum of two sides about an angle is to their difference as the tangent of half the sum of the other two angles is to the tangent of half their diff.rence. 6. One point is accessible and another...
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Surveying and Navigation, with a Preliminary Treatise on Trigonometry and ...

Aaron Schuyler - 1873 - 508 pages
...tan \(A + B) : tan \(A — B). Hence, In any plane triangle, the sum of the sides including an angle is to their difference as the tangent of half the sum of the other tiuo angles is to the tangent of half their difference. We find from the proportion, the...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - 1874 - 500 pages
...have tl1e following principle : In any plane triangle, the sum of the sides including either 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. The half sum of the angles may he...
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