| Charles Davies - Navigation - 1837 - 336 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:... | |
| 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 - 416 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 William Hackley - Trigonometry - 1838 - 336 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 - 498 pages
...of triangles are to each other as the chords of double their opposite angles. PROPOSITION IV. (115) **In any plane triangle, the sum of any two sides is...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 - 432 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 - 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 AB+AC:... | |
| Charles Davies - Surveying - 1839 - 380 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:... | |
| Adrien Marie Legendre - Geometry - 1839 - 372 pages
...— 6=2p — 2b; hence THEOREM V. fit every rectilineal triangle, the sum of two sides is to tlieir **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 A (Theorem III.).... | |
| Roswell Park - Best books - 1841 - 626 pages
...an 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,... | |
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