| 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... | |
| 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... | |
| 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,... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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