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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. "
A Practical Application of the Principles of Geometry to the Mensuration of ... - Page 105
de Jeremiah Day - 1815 - 96 pages
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - 1836 - 382 pages
...c=2p — 2c, a+c — 6=2p — 26; hence THEOREM V. In every rectilineal triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides, to the tangent of half their difference. For. AB : BC : : sin C : sin...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 332 pages
...difference as the radius to the tangent of the difference between either of them and 45°. PROP. IV. THEOR. 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. Let ABC be any plane triangle...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 410 pages
...to the definitions of this book, the sine of a right angle is equal to the radius. PROP. III. THEOR. 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, is to the tangent of half their difference. Let ABC be a triangle,...
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Elements of Plane Geometry According to Euclid

Andrew Bell, Robert Simson - 1837 - 290 pages
...same manner, it may be demonstrated that AB : BC = sin C : sin A. PROPOSITION VI. THEOREM. The sum of two sides of a triangle is to their difference as the tangent of half the sum of me 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 Surveying: Including a Description of the Instruments and the ...

Charles Davies - 1837 - 338 pages
...AC :: sin C : sin B. THEOREM II. In any triangle, the sum of the two sides containing eithet angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference. 58. Let ACB be a triangle : then will AB+AC:...
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Elements of Trigonometry, Plane and Spherical: Adapted to the Present State ...

Charles William Hackley - 1838 - 336 pages
...— b : : tan £ (A -f- B) : tan \ (A — B) That is to say, the sum of two of the 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 proportion is employed when two sides and the included...
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A Course of Mathematics: Containing the Principles of Plane ..., Volumes 1 à 3

Jeremiah Day - 1838 - 412 pages
...THE OPPOSITE ANGLES ; To THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, (Fig. 25.) is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half their difference. Demonstration . Extend CA to G, making...
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A Course of Mathematics: Containing the Principles of Plane ..., Volumes 1 à 3

Jeremiah Day - 1839 - 432 pages
...THE OPPOSITE ANGLES J To THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, (Fig. 25.) is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half their difference. Demonstration. Extend CA to G, making...
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Elements of Surveying: With a Description of the Instruments and the ...

Charles Davies - 1839 - 370 pages
...AC :: sin C : 'sin B. THEOREM II. In any triangle, the sum of the two sides containing eithei angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference. 53. Let ACB be a triangle : then will AB+AC:...
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Elements of Surveying: With a Description of the Instruments and the ...

Charles Davies - 1839 - 382 pages
...AC :: sin C : sin B. THEOREM II. In any triangle, the sum of the two sides containing eithei angk, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of haJ/ their difference. 58. Let ACB be a triangle : then will AB+AC:...
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