 | Charles Davies - 1855 - عدد الصفحات: 340
...sin A : sin BTheorems.THEOREM IIIn any triangle, the sum of the two sides contain1ng either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their differenceLet ACB be a triangle: then will AB + AC:AB-AC::t1M)(C+£)... | |
 | Elias Loomis - 1855 - عدد الصفحات: 192
...i(A+B) . sin. A-sin. B~sin. i(AB) cos. i(A+B)~tang. i(AB) ' that is, The sum of the sines of two arcs is to their difference, as the tangent of half the sum of those arcs is to the tangent of half their difference. Dividing formula (3) by (4), and considering... | |
 | George Roberts Perkins - 1856 - عدد الصفحات: 460
...B. . . (2.) In the same way it may be shown that THEOREM II. In any plane triangle, the sum of any two sides is to their difference as the tangent of...angles is to the tangent of half their difference. By Theorem I., we have 5 : c : : sin. B : sin. 0 ; hence, by composition and division, we have I +... | |
 | William Mitchell Gillespie - 1856 - عدد الصفحات: 478
...angles are to each other a* the opposite sides. THEOREM II. — In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. THEOREM III. — In every plane... | |
 | Peter Nicholson - 1856 - عدد الصفحات: 518
...+ BC :: AC-BC : AD — BD. TRIGONOMETRY. — THEOREM 2. 151. The sum of the two sides of a triangle is to their difference as the tangent of half the sum of the angles at the base is to the tangent of half their difference. Let ABC be a triangle 4 then, of the... | |
 | William Somerville Orr - 1856 - عدد الصفحات: 622
...that in any plane triangle, the sum of two tides i> to their difference, at the tangent of half the mm of the opposite angles is to the tangent of half their difference. The following, therefore, is the rule :— ROLE. — As the sum of the two given sidee Is to their... | |
 | Adrien Marie Legendre, Charles Davies - 1857 - عدد الصفحات: 442
...AC :: sin C : sin B, THEOREM II. In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference. 22. Let A CB be a triangle : then will AB... | |
 | Boston (Mass.). City Council - 1869 - عدد الصفحات: 1192
...and cosecant. 2. Demonstrate that, in any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference. 8. Given two sides and an opposite angle,... | |
 | William Mitchell Gillespie - 1869 - عدد الصفحات: 550
...to each other at the opposite sides. THEOREM EL — In every plane triangle, the turn of two tides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. THEOREM III. — In every plane... | |
 | Charles Davies - 1870 - عدد الصفحات: 392
...0 : sin B. Theorems. THEOREM II. In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference. Let ACB be a triangle: then will AB + AC:... | |
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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. 
