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Llibres Llibres 121 - 130 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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Annual Report, Volum 43

Cincinnati (Ohio). Board of Education - 1873
...the other two sides. Prove it. 5. Prove that in a plain triangle the sum of two sides about an angle is to their difference as the tangent of half the sum of the other two angles is to the tangent of half their diff.rence. 6. One point is accessible and another...
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Catalogue - Harvard University

Harvard University - 1873
...proportional to the sines of the opposite angles. (4.) The sum of any two sides of a plane triangle ia to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. 4. Two sides of a plane oblique triangle...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

1874 - 455 pągines
...have tl1e following principle : In any plane triangle, the sum of the sides including either angle, is to their difference, as the tangent of half the sum of the two other angles, is to the tangent of half their difference. The half sum of the angles may he found...
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Military surveying and field sketching

William Hamilton Richards - 1875
...given angle from 180°, E + F = 180° 150° T — 29° 3'. and \ (E + F) = 14° 31' 30". The sum of the two sides is to their difference, as the tangent of half the sum of the angles at the base, to the tangent of half their difference. Ar. co. Log. (e + /) 3922'92 = 6'406347 Log....
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The Register, Cornell University

1875
...cos'^r — sin'.r=:2cosa;r — 1 = I — 2sinV. 4. Prove that in any plane triangle the sum of cither two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of hall' their difference. 5. Given two sides of a triangle equal...
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Plane and Spherical Trigonometry and Mensuration

Aaron Schuyler - 1875 - 184 pągines
...£(Л + ß) : tan £(Л — B). Hence, In any plane triangle, the sum of the sides inchuling an angle is to their difference as the tangent of half the sum of the other two angles is to the tangent of half their difference. We find from the proportion, the equation...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - 1876 - 170 pągines
...The proposition, therefore, applies in every case. BOOK Ш. 2. 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. For, by (90), a : 6 : : sin A : sin B;...
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Plane and Spherical Trigonometry

Henry Nathan Wheeler - 1876 - 208 pągines
...sides of any triangle are proportional to the sines of { 72. The surn of any 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 . . 78 § 73. The square of any side of...
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The Elements of Plane Trigonometry

1876 - 109 pągines
...that sin B is equal to the sine of its supplement CBP. § 72. The sum of any two sides of a triangle is to their difference as the tangent of half the sum of tlie opposite angles is to the tangent of half their difference. From [67] we get, by the theory of...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - 1877 - 443 pągines
...(Art. 53), it follows, from the preceding theorem, that the sura 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. This is the same as Theorem II., Art. 54,...
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