| HORATIO N. ROBINSON, A. M. - 1853
...point without a circle, by theorem 18, book 3, we have, Hence, . . AB : AE=AF : AG QED PROPOSITION 7. **The sum of any two sides of a triangle, is to their difference, as the tangent of** the half sum of the angles opposite to these sides, to the tangent of half their difference. Let ABC... | |
| Charles Davies - 1854 - 432 páginas
...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, in which the right... | |
| 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),... | |
| Charles Davies - 1854 - 322 páginas
...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 AB+AC... | |
| John Playfair - 1855 - 318 páginas
...difference as the radius to the tangent of the difference between either of them and 45°. PROP. IV. THEOR. **The sum of any two sides of a triangle is to their difference, as the tangent of half the sum** oft/te angles opposite to those sides, to the tangent ofhalft\tw difference. Let ABC be any plane triangle... | |
| Charles Davies - 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+£)... | |
| 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 - 216 páginas
...BD) Whence, AD + BD:AC + 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 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... | |
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