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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.
An Easy Introduction to the Mathematics: In which the Theory and Practice ... - Page 405
by Charles Butler - 1814

A Treatise on Special Or Elementary Geometry, Volumes 1-2

Edward Olney - Geometry - 1872 - 566 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 any two...

A Treatise on Special, Or Elementary Geometry

Edward Olney - Geometry - 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 any two sides...

Elements of Trigonometry, Plane and Spherical

Edward Olney - Trigonometry - 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 any two sides...

Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 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 found...

Annual Report of the School Committee of the City of Boston

Boston (Mass.). School Committee - Boston (Mass.) - 1873 - 454 pages
...sides are proportional 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. "...

Documents of the Assembly of the State of New York, Issues 10-27

New York (State). Legislature. Assembly - Government publications - 1873 - 820 pages
...(CB); whence 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...

Annual Report, Volume 43

Cincinnati (Ohio). Board of Education - Cincinnati (Ohio) - 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...

Surveying and Navigation, with a Preliminary Treatise on Trigonometry and ...

Aaron Schuyler - Measurement - 1873 - 520 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...