 | John Dougall - 1810 - 734 Seiten
...multiply the circumference by the whole diameter, it follows that the superficial area of a sphere is equal to four times the area of one" of its great circles. From the foregoing demonstrations it tyill also follow, that in order to obtain the superficial area... | |
 | Edward Augustus Kendall - 1811 - 462 Seiten
...an axis. All spheres are to one another as the cubes of their diameten. The surface of a sphere is equal to four times the area of one of its great circles, hence to find the superficies of any sphere, find the area of the great circle, and multiply it by... | |
 | John Bonnycastle - 1818 - 488 Seiten
...: : surface of the sphere : the area of the lune AB c AQED COR. Since the surface of the sphere is equal to four times the area of one of its great circles, if d be put = diameter, c = circumference, and a — length of the arc B m, by the last mentioned proposition,... | |
 | William Nicholson - 1821 - 384 Seiten
...oftlte. \. AH spheres are to one another as the cubes of their diameters. 2. The surface of a sphere is equal to four times the area of one of its great circles, as is demonstrated by Archimedes in bis book of the Sphere and Cylinder, lib. i. prop. 37. Hence, to... | |
 | William Nicholson - 1821 - 382 Seiten
...the. 1. All spheres are to one another as the cubes of their diameters. 2. The surface of a sphere is equal to four times the area of one of its great circles, as is demonstrated by Archimedes in his book of the Sphere and Cylinder, lib. i. prop. 37. Hence, to... | |
 | Thomas Keith - 1826 - 504 Seiten
...180°xm=s X(A + B + C— 180°). SX(A + B + C-180°) S '* -- -- But the whole surface of the sphere is equal to four times the area of one of its great circles*, and the area of a great circle=£ circumference x radius =1 80° x radius, if therefore radius=l, the... | |
 | Dionysius Lardner - 1828 - 434 Seiten
...bears to the surface s the ratio oi : 860°. If L be the lune The surface of a sphere is proved to be equal to four times the area of one of its great circles *. Hence s = 4r-7r, v L = 2r2w. (172.) Cor. 1. Lunes of the same sphere are as their angles. (173.)... | |
 | Euclid, Dionysius Lardner - 1828 - 542 Seiten
...therefore, when multiplied by the diameter, is four times the area. Hence ' the surface of a sphere is equal to four times the area of one of its great circles.' (235) COR. 2. — Hence the surfaces of spheres are as the squares of their radii or diameters. PROPOSITION... | |
 | John Radford Young - 1831 - 340 Seiten
...C. Between the limits x = 0, .r = r, this is 2wr5; hence the surface of the whole sphere is which is equal to four times the area of one of its great circles. 2. To determine the surface of a spheroid. The equation of the generating ellipse is from which we... | |
 | James Bell - 1832 - 736 Seiten
...deduced from the circumference is equal to 7,912.2 miles. The superficial contents of a globe being equal to four times the area of one of its great circles, the surface of the earth will contain 4X 12,428.5X3,956.1=196,673,555.4 square miles. The solid contents... | |
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The surface of a sphere Is equal to four times the area of one... 
