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Llibres Llibres 81 - 90 de 194 sobre In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions....
" In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of... "
Elements of Trigonometry: Plane and Spherical - Pągina 45
per Lefébure de Fourcy (M., Louis Etienne) - 1868 - 288 pągines
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - 1886 - 324 pągines
...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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Annual Report of the Trustees, Volums 4-8

College of the City of New York (1866-1926) - 1853
...each other as the sides opposite. 5. Find the value of tang. (a+b). 6. In a plane triangle, show that the sum of two sides is to their difference as the tangent of half the sum is to tangent of half the difference of the angles opposite. 7. Find the sin. \ A, and prove that 1...
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A Course of Mathematics: Containing the Principles of Plane Trigonometry ...

Jeremiah Day - 1853 - 5 pągines
...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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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - 1854 - 432 pągines
...sides. 90. We 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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Report of twenty-one years' experience of the Dick bequest for elevating the ...

Allan Menzies - 1854
...Suppose AC, CB, and angle C to be given, then rule is, — Sum of the two sides (containing given angle) is to their difference as the tangent of half the sum of the angles at the base is to the tangent of half their difference ; half the sum = ^ (180 — angle C), then having...
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Elements of Surveying, and Navigation: With Descriptions of the Instruments ...

Charles Davies - 1854 - 322 pągines
...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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A Treatise on Land-Surveying Comprising The Theory Developed from Five ...

W.M. Gillespie, A.M., Civ. Eng - 1855
...triangle, the sines of the angles are to each other as the opposite sides. THEOREM II. — In every plane triangle, the sum of two sides is to their difference...the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. THEOREM III. — In every plane triangle, the...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - 1855 - 318 pągines
...parallel to FG, CE : CF : : BE : BG, (2. 6.) that is, the sum of the two sides of the triangle ABC is to their difference as the tangent of half the sum of the angles opposite to there sides to the tangent of half their difference. PROP. V. THEOR. If a perpendicular be drawn from...
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Elements of geometry and trigonometry: with applications in mensuration

1855 - 324 pągines
...sin A : sin BTheorems.THEOREM IIIn any triangle, the sum of the two sides contain1ng either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their differenceLet ACB be a triangle: then will AB + AC:AB-AC::t1M)(C+£)...
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Elements of Plane Trigonometry, Surveying and Navigation

William Smyth - 1855 - 223 pągines
...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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