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" 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. "
A Course of Mathematics: In Three Volumes : Composed for the Use of the ... - Page 63
by Charles Hutton - 1811
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Elements of Surveying: Including a Description of the Instruments and the ...

Charles Davies - 1837 - 342 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...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 290 pages
...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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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 410 pages
...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 Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 332 pages
...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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A Course of Mathematics: Containing the Principles of Plane ..., Volumes 1-3

Jeremiah Day - 1838 - 416 pages
...sin b tan £ (a — b)' ' sin a+sin b : sin a — sin b : : tan $ (a+6) : tan i (a — 6.) That is, The sum of the sines of two arcs or angles, is to the difference of those sines ; as the tangent of half the sum of the arcs or angles, to the tangent...
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Elements of Trigonometry, Plane and Spherical: Adapted to the Present State ...

Charles William Hackley - 1838 - 338 pages
...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...
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Elements of Surveying: With a Description of the Instruments and the ...

Charles Davies - 1839 - 376 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...
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A Course of Mathematics: Containing the Principles of Plane ..., Volumes 1-3

Jeremiah Day - 1839 - 434 pages
...sin b tan $ (a — b). ' sin a+sin b : sin a — sin b : : tan $ (a+6) : tan £ (a — b.) That is, The sum of the sines of two arcs or angles, is to the difference of those sines ; as the tangent of half the sum of the arcs or angles, to the tangent...
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An introduction to the theory ... of plane and spherical trigonometry ...

Thomas Keith - 1839 - 498 pages
...double their opposite angles. PROPOSITION IV. (115) In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of their opposite angles is to the tangent of half their difference, Let ABC be any triangle ; make BE...
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Elements of Surveying: With a Description of the Instruments and the ...

Charles Davies - 1839 - 376 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...
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