| Andrew Bell - Euclid's Elements - 1837 - 240 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... | |
| Jeremiah Day - Geometry - 1838
...equal to the sum, and FH to the difference of AC and AB. And by theorem II, (Art. 144.) the sum of the **sides is to their difference ; as the tangent of half the sum of the** opposite angles, to the tangent of half their difference. Therefore, R : tan (ACH— 45°) : : tan... | |
| Charles William Hackley - Trigonometry - 1838 - 307 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 sides... | |
| Thomas Keith - 1839
...other as the chords of 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... | |
| Jeremiah Day - Geometry - 1839 - 370 pages
...equal to the sum, and FH to the difference of AC and AB. And by theorem II, (Art. 144.) the sum of the **sides is to their difference ; as the tangent of half the sum of the** opposite angles, to the tangent of half their difference. Therefore, R : tan (ACH— 45°) : : tan... | |
| Charles Davies - Surveying - 1839 - 261 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:... | |
| Roswell Park - Best books - 1841 - 587 pages
...oblique angled triangle, the sides are proportional to the sines of the opposite angles : also, the **sum of any two sides is to their difference, as the tangent of** the half sum of the two opposite angles, is to the tangent of their half difference : and finally,... | |
| John Playfair - Euclid's Elements - 1842 - 317 pages
...difference between either of them and 45°. PROP. IV. THE OR. 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 ofhalftlteir difference. Let ABC be any plane triangle... | |
| Enoch Lewis - Conic sections - 1844 - 228 pages
...sines being suited to any radius whatever (Art. 27). QED ART. 30. In any right lined triangle, the **sum of any two sides 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 the triangle; AC, AB,... | |
| 1845
...sin. A' a ~b a c b sin. B sin. A sin. C sin. B sin. C. 68 PROFOSITION in. In any plane triangle, the **sum of any two sides, is to their difference, as the tangent of half the sum of the angles** opposite to them, is to the tangent of half their difference. Let ABC be any plane triangle, then,... | |
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