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" C' (89) (90) (91) (92) (93) 112. 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. "
The Theory and Practice of Surveying: Containing All the Instructions ... - Page 106
by Robert Gibson - 1811 - 508 pages
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1872 - 455 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 found by...
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A Treatise on Special, Or Elementary Geometry

Edward Olney - Geometry - 1872 - 239 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 any...
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An Elementary Geometry and Trigonometry

William Frothingham Bradbury - Geometry - 1872 - 238 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 - Trigonometry - 1872 - 201 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 any...
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A Treatise on Special Or Elementary Geometry, Volumes 1-2

Edward Olney - Geometry - 1872
...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 any...
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Annual Report of the School Committee of the City of Boston

Boston (Mass.). School Committee - Boston (Mass.) - 1873
...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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Documents of the Assembly of the State of New York, Issues 10-27

New York (State). Legislature. Assembly - Government publications - 1873
...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 problem...
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Surveying and Navigation, with a Preliminary Treatise on Trigonometry and ...

Aaron Schuyler - Measurement - 1873 - 490 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 equation...
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Annual Report, Volume 43

Cincinnati (Ohio). Board of Education - Cincinnati (Ohio) - 1873
...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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Catalogue - Harvard University

Harvard University - 1873
...proportional to the sines of the opposite angles. (4.) The sum of any two sides of a plane triangle ia to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. 4. Two sides of a plane oblique triangle...
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