 | Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...area of the circle, and 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... | |
 | Miles Bland - Astronomy - 1830 - 394 pages
...rectangle, when the segment is diminished without limit. 23. Prove by the method of limits, (1.) that the surface of a sphere is equal to four times the area of a great circle of the sphere; (2.) that the area of the cissoid of Diocles between the vertex and an ordinate to the... | |
 | Pierce Morton - Geometry - 1830 - 584 pages
...greater nor less than the surface of the sphere ; that is, it is equal to it. Therefore, &c. Cor. 1. The surface of a sphere is equal to four times the area of its generating circle. For the area of this circle is equal to half the product of the radius and circumference... | |
 | Jeremiah Day - Measurement - 1831 - 520 pages
...the surface of the segment produced by the revolution of BD about DN is equal to DN Xcirc CP. Cor. 2. The surface of a sphere is equal to four times the area of a circle of the same diameter ; and therefore, the convex surface of a hemisphere is equal to twice the... | |
 | Jeremiah Day - Logarithms - 1831 - 418 pages
...the surface of the segment produced by the revolution of BD about DN is equal to DN Xcirc CP. Cor. 2. The surface of a sphere is equal to four times the area of a circle of the same diameter ; and therefore, the convex surface of a hemisphere is equal to twice the... | |
 | John Radford Young - Astronomy - 1833 - 286 pages
...number 3.14159, &c. It can be proved, although not by the elementary principles of Trigonometry, that the surface of a sphere is equal to four times the area of one of its great circles ;* that is, r being the radius of the sphere S = 4vri, so that the expression... | |
 | Mathematics - 1835 - 684 pages
...greater nor less than the surface of the sphere ; that is, it is equal to it. t Therefore, &c. Cor. 1. The surface of a sphere is equal to four times the area of its generating circle. For the area of this circle is equal to half the product of the radius and circumference... | |
 | William Ritchie - Calculus - 1836 - 198 pages
...hemisphere, and far* = surface of the sphere. But itr2 = area of a circle whose radius is r. Hence the surface of a sphere is equal to four times the area of one of its great circles. COR. 1. Since 2irrx is the expression for the convex surface of a cylinder... | |
 | Jeremiah Day - Geometry - 1838 - 416 pages
...the surface of the segment produced by the revolution of BD about DN is equal to DNxcirc CP. Cor. 2. The surface of a sphere is equal to four times the area of a circle of the same diameter ; and therefore, the convex surface of a hemisphere is equal to twice the... | |
 | John West, Sir John Leslie - Analytic functions - 1838 - 664 pages
...of the generating circle multiplied by the altitude of the segment. Hence, the whole surface of the sphere is equal to four times the area of a great circle. EXAMPLE 5. To find the curve surface of the parabolic conoid. From the equation of the parabola, y' = %ax,... | |
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The surface of a sphere is equal to four times the area of a circle... 
