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" 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 of half their difference. "
Geometry: Plane Trigonometry. Chain Surveying. Compass Surveying. Transit ... - Página 18
por International Correspondence Schools - 1906
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - 1857 - 448 páginas
...also have (Art. 22), a + b : a - b : : tan %(A + B) : tan %(A - B) : that 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 thtir difference. 91. In case of a right•angled triangle, in which the right...
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A Treatise on Land-surveying: Comprising the Theory Developed from Five ...

William Mitchell Gillespie - 1857 - 524 páginas
...to each other at the opposite sides. THEOREM II.— In every plane triangle, the turn of two tides is to their difference as 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...
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A Treatise on Surveying and Navigation: Uniting the Theoretical, Practical ...

Horatio Nelson Robinson - 1858 - 347 páginas
...point without a circle, by theorem 1 8, book 3, we have, Hence, . . AB : AE=AF : AO 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 AB...
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ELEMENTS OF PLANE AND SPHERICAL TRIGONOMETRY

ELIAS LOOMIS, LL.D. - 1859
...|(A+B) ^ sin. A~sin. B~sin. i(AB) cos. J(A+B)~tang. J(AB) ' that is, The sum of the sines of two arcs is to their difference, as the tangent of half the sum of those arcs is to the tangent of half their difference. .Dividing formula (3) "by (4), and considering...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860
...same manner it may be demonstrated that AB : BC = sin. C : sin. A. PROPOSITIOK VI. THEOREM. The sum of two sides of a triangle is to their difference as the tangent of half the sum of the angles at the base to the tangent of half their difference. Let ABC be any triangle, then if B and...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1860 - 317 páginas
...it may be shewn that cos. AB+cos. AC : sin. AC—sin. AB : : R : tan. j(AC—AB). PROP. IV. THEOR. The sum of any two sides of a triangle is to their difference, as the tangent of naif the sum of the angles opposite to those sides, to the tangent ofhalft\tv difference. CA+AB : CA—AB...
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Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - 1860 - 453 páginas
...by Cor. Th. 18, B. HI, we have AE x AF — AB x Aa Hence, AB : AE = AF : Ad. t PROPOSITION VII. Tlie sum of any two sides of a triangle is to their difference, as the tangent of one half the sum of the angles opposite to these sides, is to the tangent of one half their difference....
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - 1860 - 443 páginas
...it may be shown that §«.] TRIGONOMETRY. THEOREM It In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the op? posite angles is to the tangent of half their difference. By Theorem I., we have o : c : : sin....
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1861 - 12 páginas
...what angle is the sine of the supplement equal to the sine of the complement. Find sin 15°. Prove 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 these sides, is to the tangent of half their difference. 3. What is the angle of...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1862 - 490 páginas
...^ (A — B) f(\7\ sin A — sin B ~ wt~i (A + B) ; ( ' that is, The sum of the sines of two angles is to their difference as the tangent of half the sum of the angles is to the tangent of half their difference, or as the cotangent of half their difference is...
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