 | Charles Astor Bristed - 1874 - 632 pages
...are proportional to the sines of the opposite sides. i7. The area of a spherical triangle varies as the excess of the sum of its angles over two right angles. 15. Given the logarithms of two consecutive whole numbers, p, p -4- 1, investigate a series for the... | |
 | William Guy Peck - Conic sections - 1876 - 376 pages
...180° _ 60^ _ 2 • Hj ~ "~ 90° ~ 90° ~~ 3' 135. The spherical excess of a spherical polygon is equal to the excess of the sum of its angles over two right angles, multiplied by the number of sides of the polygon less two ; for if the polygon is divided into triangles... | |
 | Humanities - 1877 - 626 pages
...difficulties that he could discover. One would like to have his interpretation of the theorem that the area of a spherical triangle is proportional to the excess of its angles above two right angles. If there were no such thing as resistance in the world, it would... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...Edge of an ungula is the edge of its angle. 757. DEF. The Spherical Excess of a spherical triangle is the excess of the sum of its angles over two right angles. C 758. DEF. Three planes which pass through the centre of the sphere, each perpendicular to the other... | |
 | Great Britain. Parliament. House of Commons - Great Britain - 1879 - 632 pages
...finished goods respectively. HIGHER MATHEMATICS. (OPTIONAL.) Time allowed, 3-^ hours. 1. Prove that the area of a spherical triangle is proportional to the excess of the sum of the angles over two right angles. 2. State Napier's rules for the solution of right-angled spherical... | |
 | 1879 - 636 pages
...finished goods respectively. HIGHER MATHEMATICS. (OPTIONAL.) Time allowed, 3£ hours. 1. Prove that the area of a spherical triangle is proportional to the excess of the sum of the angles over two right angles. 2. State Napier's rules for the solution of right-angled spherical... | |
 | William Thomson Baron Kelvin, Peter Guthrie Tait - Calculators - 1879 - 572 pages
...spherical triangle (on a sphere of uuit radius) is known to be equal to the " spherical excess," ie, the excess of the sum of its angles over two right angles, or the excess of four right angles over the sum of its exterior angles. Area of The area of a spherical... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...unit, by A, B, and C, we have, E = A + B + C-2. The spherical excess of any spherical polygon is equal to the excess of the sum of its angles over two right angles taken as many times, less two, as the polygon has sides. If we denote the spherical excess by E, the... | |
 | William Chauvenet - Geometry - 1887 - 346 pages
...the unit of surface the spherical degree. PROPOSITION XXII. The area of a spherical triangle is equal to the excess of the sum of its angles over two right angles. PROPOSITION XXIII. The shortest line that can be drawn on the surface of a sphere iR'tween two points... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...contains degrees of arc. PROPOSITION XXII.—THEOREM. 73, The area of a spherical triangle is equal to the excess of the sum of its angles over two right angles. For, let ABC be a spherical triangle. Complete the great circle ABA'B', and produce the arcs AC and... | |
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The spherical excess of any spherical polygon is equal to the excess of the sum of its angles over two right angles taken as many times as the polygon has sides, less two. 
