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Llibres Llibres 61 - 70 de 193 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 - Pāgina 45
per Lefébure de Fourcy (M., Louis Etienne) - 1868 - 288 pāgines
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Elements of Surveying: With a Description of the Instruments and the ...

Charles Davies - 1839 - 334 pāgines
...AC :: sin C : sin B. THEOREM II. In any triangle, the sum of the two sides containing eithei angk, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of haJ/ their difference. 58. Let ACB be a triangle : then will AB+AC:...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - 1839 - 359 pāgines
...— 6=2p — 2b; hence THEOREM V. fit every rectilineal triangle, the sum of two sides is to tlieir difference as the tangent of half the sum of the angles opposite those sides, to the tangent of half their difference. For. AB : BC : : sin C : sin A (Theorem III.)....
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Elements of Surveying, and Navigation, with a Description of the Instruments ...

Charles Davies - 1841 - 359 pāgines
...AC : : sin C : sin B. THEOREM II. In any triangle, the sum of the two sides containing eithei angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference. 58. Let ACB be a triangle : then will AB+AC:...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 pāgines
...difference between either of them and 45°. PROP. IV. THE OR. The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles-opposite to those sides, to the tangent ofhalftlteir difference. Let ABC be any plane triangle...
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A Treatise on Plane and Spherical Trigonometry: Including the Construction ...

Enoch Lewis - 1844 - 228 pāgines
...being suited to any radius whatever (Art. 27). QED ART. 30. In any right lined triangle, the sum of any two sides is, to their difference, as the tangent...half the sum of the angles, opposite to those sides, to the tangent of half their difference. Let ABC be the triangle; AC, AB, the sides. From the centre...
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A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ...

Nathan Scholfield - 1845
...sin. A ' b a sin. B sin. A c sin. C sin. B b PROPOSITION III. In any plane triangle, the sum of any two sides, is to their difference, as the tangent of half the sum of the angles opposite to them, is to the tangent of half their difference. Let ABC be any plane triangle, then, by Proposition...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

1845
...a c b sin. B sin. A sin. C sin. B sin. C. 68 PROFOSITION in. In any plane triangle, the sum of any two sides, is to their difference, as the tangent of half the sum of the angles opposite to them, is to the tangent of half their difference. Let ABC be any plane triangle, then, by Proposition...
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Higher Geometry and Trigonometry: Being the Third Part of a Series on ...

Nathan Scholfield - 1845 - 232 pāgines
...sin. A^ 6 a sin. B sin. A c 6 sin. C sin. B 08 PROPOSITION III. In any plane triangle, the sum of any two sides, is to their difference, as the tangent of half the sum of the angles opposite to them, is to the tangent of half their difference, Let ABC be any plane triangle, then, by Proposition...
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Plane trigonometry and mensuration

1845
...b : a — b :: tan. | (A + в) : tan. ŋ (A — в).* Hence the sum of any two sides of a triangle, is to their difference, as the tangent of half the sum of the angles oppo-* site to those sides, to the tangent of half their difference. SECT. T. EESOLUTION OF TRIANGLES....
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Key to System of practical mathematics. 2 pt, Ediciķ 17

1845
...a — 6 tan. 4(A — B) opposite to the angles A and B, the expression proves, that the sum of the sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference, which is the rule. (7.) Let (AD— DC)...
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