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Llibres Llibres 91 - 100 de 195 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 Plane and Spherical Trigonometry: With Their Applications to ...

Elias Loomis - 1855 - 178 pągines
...i(A+B) . sin. A-sin. B~sin. i(AB) cos. i(A+B)~tang. i(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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A Treatise on Land-surveying: Comprising the Theory Developed from Five ...

William Mitchell Gillespie - 1856 - 464 pągines
...triangle, the sines of the angles are to each other a* 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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PLANE AND SOLID GEOMETRY

GEORGE R. PERKINS - 1856
...B. . . (2.) In the same way it may be shown that THEOREM II. 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. By Theorem I., we have 5 : c : : sin. B...
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Practical carpentry, joinery, and cabinet-making [by P. Nicholson. by P ...

Peter Nicholson - 1856
...+ BC :: AC-BC : AD — BD. TRIGONOMETRY. — THEOREM 2. 151. The sum of the two sides of a triangle 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. Let ABC be a triangle 4 then, of the two sides,...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - 1856 - 318 pągines
...FG, CE : CF : : BE : BG, (2. 6.) that is, the sum of the two sides of the triangle ABC is t'j the tr difference as the tangent of half the sum of the angles opposite U, there sides to the tangent of half their difference. PROP. V. THEOR. If a perpendicular be drawn...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - 1857 - 448 pągines
...90. We 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,...
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A treatise on land-surveying: comprising the theory developed from five ...

William Mitchell Gillespie - 1857 - 524 pągines
...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 triangle, the...
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A Treatise on Land-surveying: Comprising the Theory Developed from Five ...

William Mitchell Gillespie - 1859 - 418 pągines
...the angles are to each other at the opposite sides. THEOREM II — In every plane triangle, the turn of two sides 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 triangle, t/m...
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A Treatise on Plane and Spherical Trigonometry

1863 - 256 pągines
...proposition is therefore general in its application.* 118. The »urn of any two side» of a plane triangle ie 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 Plane Trigonometry: And Their Application to the Measurement of ...

1864
...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 half the sum of the opposite angles is to the tangent of half their difference. By Theorem II. we have a : b : : sin. A...
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