| Allan Menzies - 1854 - 520 pages
...Suppose AC, CB, and angle C to be given, then rule is, — Sum of the two sides (containing given angle) **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 ; half the sum = ^ (180 — angle... | |
| Charles Davies - 1854 - 436 pages
...also have (Art. 22), a + b : ab :: tan $(A + B) : ta.n$(A — B): tha| is, the sum of any two sides **is to their difference, as the tangent of half the sum of** the opposite angles to the tangent of half their difference. 91. In case of a right•angled triangle,... | |
| Charles Davies - 1854 - 446 pages
...AC :: sin G : sin B. THEOREM II. In any triangle, the sum of the two sides containing either *ngle, **is to their difference, as the tangent of half the sum of** the two oilier angles, to the tangent of half their difference. 22. Let ACS be a triangle: then will... | |
| William Mitchell Gillespie - 1855 - 436 pages
...to each other as 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... | |
| William Smyth - 1855 - 234 pages
...tan — ~ ; lU —4 a proportion, which we may thus enunciate ; the sum of two sides of a triangle **is to their difference, as the tangent of half the sum of** the opposite angles is to the tangent of half their difference. Ex. 1. Let AC (fig. 30) be 52. 96 -yds,... | |
| Elias Loomis - 1855 - 192 pages
...BC, or sin. A : sin. B :: BC : AC. THEOREM II. (50.) In any plane triangle, the sum of any tico sides **is to their difference, as the tangent of half the sum of** the opposite angles is to the tangent of half their difference. Let ABC be any triangle; then will... | |
| William Mitchell Gillespie - 1856 - 478 pages
...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... | |
| George Roberts Perkins - 1856 - 460 pages
...(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 half the sum of** the opposite angles is to the tangent of half their difference. By Theorem I., we have 5 : c : : sin.... | |
| Peter Nicholson - 1856 - 518 pages
...+ 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... | |
| William Mitchell Gillespie - 1857 - 538 pages
...to each other at the opposite sides. THEOREM II.— 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... | |
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