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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 New Practical Builder and Workman's Companion, Containing a Full Display ... - Page 81
by Peter Nicholson - 1823 - 596 pages
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Mathematical Recreations: Containing Solutions of Many Very Difficult and ...

Horatio Nelson Robinson - Mathematics - 1851 - 96 pages
...Demonstrate that radius is to the tangent of the difference between this angle and half a right angle, as the tangent of half the sum of the angles at the base of the triangle, is to the tangent of half their difference, To obtain that certain angle, we must...
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Elements of Plane Trigonometry: With Its Application to Mensuration of ...

William Smyth - Plane trigonometry - 1852 - 198 pages
...AC : : tang — - — - tang ; "•" /^ a proportion, which we may thus enunciate : the sum of tioo 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. parts. Subtracting the angle C 45 from...
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A Treatise on Plane and Spherical Trigonometry

William Chauvenet - 1852 - 268 pages
...The proposition is therefore general in its application.* 118. The sum of any 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. For, by the preceding article, a : b =...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...AC :: sin 0 : sin jR THEOEEM II. In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference. 22. Let ACB be a triangle: then will AJ3...
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1886 - 334 pages
...C : sin B. Theorems. THEOREM 11. In any triangle, the sum of the two sides containing eithe1 angle, is to their difference, as the tangent of half the sum of (he t1eo other angles, to the tangent of half their di/ereMe. Let ACB be a triangle: then will With...
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A Course of Mathematics: Containing the Principles of Plane Trigonometry ...

Jeremiah Day - Mathematics - 1853 - 288 pages
...opposite angles. It follows, therefore, from the preceding proposition, (Alg. 38'.>.) that the sum of any two sides of a. triangle, is to their difference ; as the tangent of half the sum of tin; opposite angles, to the tangent of half their difference. This is the second theorem npplied to...
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A Treatise on Surveying and Navigation: Uniting the Theoretical, Practical ...

Horatio Nelson Robinson - History - 1853 - 334 pages
...circle, by theorem 18, book 3, we have, Hence, . . AB : AE=AF : AG QED PROPOSITION 7. The sum of any two sides of a triangle, is to their difference, as the tangent of the half sum of the angles opposite to these sides, to the tangent of half their difference. Let ABC...
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Elements of Surveying, and Navigation: With Descriptions of the Instruments ...

Charles Davies - Navigation - 1854 - 446 pages
...AC :: sin G : sin B. THEOREM II. In any triangle, the sum of the two sides containing either *ngle, is to their difference, as the tangent of half the sum of the two oilier angles, to the tangent of half their difference. 22. Let ACS be a triangle: then will AB+AC...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...also have (Art. 22), a + b : ab :: tan $(A + B) : ta.n$(A — B): tha| is, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles to the tangent of half their difference. 91. In case of a right•angled triangle,...
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Elements of Plane Trigonometry, Surveying and Navigation

William Smyth - Navigation - 1855 - 236 pages
...— AC : : tan — i— : tan — ~ ; lU —4 a proportion, which we may thus enunciate ; 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. Ex. 1. Let AC (fig. 30) be 52. 96 -yds,...
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