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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... "
Elements of Trigonometry, Plane and Spherical - Pāgina 43
per Lefébure de Fourcy (M., Louis Etienne) - 1868 - 288 pāgines
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Elements of Trigonometry: Plane and Spherical

Edward Olney - 1877 - 201 pāgines
...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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Annual Report, Volum 47

Cincinnati (Ohio). Board of Education - 1877
...from a given point, find the distance of each from the given point. 2. In a plane triangle, prove that the sum of two sides is to their difference, as the tangent of J the sum of the angles opposite them is to the tangent of J their difference. 3. Prove: tan. a=- sln...
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Annual Report

1878
...rest ? TRIGONOMETRY. Scientific Clatt. 1. Demonstrate, that in any plane triangle, the sure 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. 2. Give the limiting values of the circular...
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A Treatise on Land-surveying: Comprising the Theory Developed from Five ...

1878 - 508 pāgines
...to each other at the opposite sides. THEOREM IL—In every plane triangle, the sum of two tides it to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of kalf their difference. THEOKEJI III.—In every plane triangle, the...
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The Elements of Plane Trigonometry

Eugene Lamb Richards - 1878 - 112 pāgines
...since C is a right angle, its sine is 1 (Art. 35). Also 49. In any triangle, the SUM of any TWO RIDES is to their DIFFERENCE as the TANGENT of HALF the sum of the OPPOSITE ANGLES 18 to the TANGENT of HALF their DIFFERENCE. Let A CB be any triangle. Then EC+CA _...
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The Elements of Plane and Spherical Trigonometry

Eugene Lamb Richards - 1879 - 300 pāgines
...C~AB' For, since C is a right angle, its sine is 1 (Art. 35). Also 49. In any 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. Let ACB be any triangle. Then BC+CA _ tan....
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The Civil-engineer & Surveyor's Manual: Comprising Surveying, Engineering ...

Michael McDermott - 1879 - 586 pāgines
...two Sida and their contained Angle given to Find the other Side and Angles. 203. Rule. The sum of the 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 ; ŋ Ģ., a -f Ъ : a — b : : tan. J (A...
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American Practical Navigator

1880
...any triangle (supposing an;/ side to be the base, and calling the other two the sides, the sum of the sides is to their difference as the. tangent of half the sum of the angles at tht base is to the tangent of half the difference of the same angles. Thus, in the triangle ABC,...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - 1880 - 443 pāgines
...13. Therefore sin. ABC : sin. C : : AC : AB. THEOREM II. 54. 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. Let ABC be any triangle ; then will CB...
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A Treatise on Trigonometry

James Edward Oliver - 1881 - 102 pāgines
...positive or negative direction from the origin used. Tнм. 2. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the two opposite angles is to the tangent of half their difference : 106] ie, (a + b) : (a~&) = tanŋ(A...
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