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" 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... "
Higher Geometry and Trigonometry: Being the Third Part of a Series on ... - Page 68
by Nathan Scholfield - 1845 - 232 pages
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Catalogue - Harvard University

Harvard University - 1873 - 732 pages
...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

Adrien Marie Legendre - Geometry - 1874 - 512 pages
...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 - 216 pages
...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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Cornell University Register and Catalogue

Cornell University - 1875 - 1012 pages
...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 - Measurement - 1875 - 276 pages
...(Л + ) : 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 - Trigonometry - 1876 - 208 pages
...the results would have been the same. The proposition, therefore, applies in every case. BOOK Ш. 2. In any plane triangle, the sum of any two sides is...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 - Trigonometry - 1876 - 254 pages
...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

Henry Nathan Wheeler - Plane trigonometry - 1876 - 130 pages
...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 - Geometry - 1877 - 458 pages
...of ABC, their sines are equal, Art. 13. Therefore sin. ABC : sin. C : : AC : AB. THEOREM II. . . 54. In any plane triangle, the sum of any two sides is to their differenee as the tangent of half the sum of the opposite angles is to the tangent of half their difference....
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Elements of Trigonometry: Plane and Spherical

Edward Olney - Trigonometry - 1877 - 220 pages
...horizontal parallax. PLANE TR1GONOMETRY. 86. Prop.— The sum of any two sides of aplane triangle 's to their difference, as the tangent of half the sum of the angles oppos'te is to the tangent of half their difference. DEM. — Letting a and b represent any two sides...
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