 | Horatio Nelson Robinson - 1853 - 334 páginas
...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 - 436 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... | |
 | Charles Davies - 1854 - 446 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... | |
 | Allan Menzies - 1854 - 520 páginas
...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),... | |
 | John Playfair - 1855 - 334 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 - 340 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 Mitchell Gillespie - 1855 - 436 páginas
...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 - 192 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 - 518 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 - 478 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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The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference. 
