 | Euclid - Geometry - 1776 - 326 pages
...PROP. XXIH. TN every* fpherical triangle, the cotangent of half thefum of the * angles at the bafe, is to the tangent of half their difference ; as the tangent of half the vertical angle to the tangent of the angle that the perpendicular makes tuith the line bifecling the... | |
 | John Bonnycastle - Trigonometry - 1806 - 464 pages
...according to the conditions of the data ; which circumstance may be readily known, by considering that half the sum of any two sides of a spherical triangle is of the same kind as half the sum of their opposite angles, and taking the triangle accordingly. 78... | |
 | Thomas Keith - Navigation - 1810 - 478 pages
...(K. 94), aad therefore tang £• (A + B) and cos •£ (a + 6) must be both positive; consequently, half the sum of any two sides of a spherical triangle is of the same species as half the sum of their opposite angles. This rule has been applied in the practical... | |
 | John Playfair - Circle-squaring - 1819 - 350 pages
...of an arch is the same with the' cotangent of half the arch itself ; it will fellow, that the sine of half the sum of any two sides of a spherical triangle, is to the sine of half their difference as the cotangent of half the angle contained between them, to the tangent... | |
 | Rev. John Allen - Astronomy - 1822 - 508 pages
...substituting the latter ratios for the former, the cotangent of the hull' sum of t!ie angles A and ABC is to the tangent of half their difference, as the tangent of the half sum of the angles ACD and BCD is to the tangent of half their difference; and, forming rectangles... | |
 | Thomas Keith - Navigation - 1826 - 504 pages
...positive (K. 100.), and therefore tang ¿ (A + B) and cos í (a + b) must be both positive ; consequently, half the sum of any two sides of a spherical triangle is of the same species as half the sum of their opposite angles. This rule is applied in the practical... | |
 | Alexander Ingram - Mathematics - 1830 - 458 pages
...quadrant, each of the angles will, accordingly, be right, obtuse, or acute ; and conversely. Cor. 2. Half the sum of any two sides of a spherical triangle is of the same affection as half the sum of their opposite angles. PROP. XII. If from the angular points... | |
 | William Galbraith - Astronomy - 1834 - 454 pages
...180°, each of the angles will, accordingly, be right, obtuse, or acute, and conversely. Cor. 2 .— Half the sum of any two sides of a spherical triangle is of the same kind as half the sum of their opposite angles. PROPOSITION XX. 41. In any right-angled... | |
 | Benjamin Peirce - Spherical trigonometry - 1836 - 84 pages
...±(A' + B') _ tang. ¿ (A1 — B') ~~ cotau. %(A'—B') ~ ~ К 76. Theorem. The sine of half the sum of two sides of a spherical triangle is to the tangent of half С844) their difference, as the cotangent of half the included 4 angle is to the ta,ngent of half the... | |
 | Benjamin Peirce - Spherical trigonometry - 1836 - 92 pages
...(841) = lang, i (Л' + В') tatig. ¿ (Л' — В') (ащ 76. Theorem. The sine of half the sum of two sides of a spherical triangle is to the tangent of half (844) their difference, as the cotangent of half the included angle is to the tangent of half the difference... | |
| |
... that the sine of half the sum of any two sides of a spherical triangle, is to the sine of half their difference as the cotangent of half the angle contained between them, to the tangent of half the difference of the angles opposite to them : and also... 
