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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. "
A Treatise of Plane Trigonometry: To which is Prefixed, a Summary View of ... - Pągina 68
per Jeremiah Day - 1815 - 126 pągines
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - 1872 - 464 pągines
...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...
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An Elementary Geometry and Trigonometry

William Frothingham Bradbury - 1872 - 262 pągines
...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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Documents of the Assembly of the State of New York, Volum 96,Edició 2

New York (State). Legislature. Assembly - 1873 - 818 pągines
...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 - 1873 - 508 pągines
...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 of the School Committee of the City of Boston

Boston (Mass.). School Committee - 1873 - 454 pągines
...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, Volum 43

Cincinnati (Ohio). Board of Education - 1873 - 352 pągines
...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 - 732 pągines
...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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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - 1874 - 500 pągines
...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 found...
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Military Surveying and Field Sketching ...

William Hamilton Richards - 1875 - 216 pągines
...from 180°, E + F = 180° 150° T — 29° 3'. and \ (E + F) = 14° 31' 30". 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. Ar. co. Log. (e + /) 3922'92 = 6'406347 Log....
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Plane and Spherical Trigonometry and Mensuration

Aaron Schuyler - 1875 - 284 pągines
...£(Л + ß) : tan £(Л — B). Hence, In any plane triangle, the sum of the sides inchuling 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 difference. We find from the proportion, the equation...
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