| Allan Menzies - 1854
...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 C),... | |
| 1855 - 324 páginas
...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+£)... | |
| William Smyth - 1855 - 223 páginas
...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,... | |
| W.M. Gillespie, A.M., Civ. Eng - 1855
...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 plane... | |
| Elias Loomis - 1855 - 178 páginas
...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... | |
| Peter Nicholson - 1856
...+ 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... | |
| GEORGE R. PERKINS - 1856
...(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. B... | |
| William Mitchell Gillespie - 1856 - 464 páginas
...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... | |
| Adrien Marie Legendre - 1857 - 448 páginas
...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 +... | |
| William Mitchell Gillespie - 1857 - 524 páginas
...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 plane... | |
| |