 | Benjamin Williamson - Calculus - 1877 - 372 pages
...generated by the polygon becomes a sphere; and we get 471- .R2 for the entire surface of the sphere. Hence, the surface of a sphere is equal to four times the area of one of its great circles. Again, it is easy to find the surface generated by any number of sides of... | |
 | William Guy Peck - Calculus - 1877 - 238 pages
...values of у and dy in (1), and integrating from — r to + r, we have, 8" = 2«rfdx = 4«r* (2) Hence, the area of the surface of a sphere is equal to four great circles, or to two-thirds the surface of the circumscribed cylinder. 2°. To find the surface... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...the surface of a sphere = 4»R2. Coit. 2. The area of a great circle = «R2 (IV., 12, Cor. 3) : hence the surface of a sphere is equal to four times the area of one of its great circles. BOOK VIII.] MEASUREMENT OF SOLIDS. COR. 3. The surfaces of two spheres are... | |
 | James Morton - Circle-squaring - 1881 - 236 pages
...circumscribing cube. To find the surface of a sphere, square its diameter ; multiply said square by. 3183. The surface of a sphere is equal to four times the area of its great circle, or to the area of a circle whose diameter is twice as great as that of the sphere.... | |
 | Samuel Earnshaw - Differential equations, Partial - 1881 - 602 pages
...before Eudoxus) no one had discovered them. In like manner, none before Archimedes had discovered that the surface of a sphere is equal to four times the area of one of its great circles (prop. 35) ; the volume of a sphere to two thirds of the circumscribed cylinder... | |
 | Alexis Claude Clairaut - 1881 - 184 pages
...straight line os and of the arc MN are equal in area. It is also manifest, from the preceding, that the surface of a sphere is equal to four times the area of its great circle ; for the surface of this great circle has for its measure the product of half the... | |
 | Charles Taylor - Mathematics - 1881 - 486 pages
...before Eudoxus) no one had discovered them. In like manner, none before Archimedes had discovered that the surface of a sphere is equal to four times the area of one of its great circles (prop. 35) ; the volume of a sphere to two thirds of the circumscribed cylinder... | |
 | John Ogilvie - 1883 - 830 pages
...two-thirds of its circumscribing cylinder. Spheres are to one another as the cubes of their diameters. The surface of a sphere Is equal to four times the area of one of its great circles, and the solidity is found by multiplying the cube of the diameter by •5230... | |
 | John Ogilvie - Encyclopedias and dictionaries - 1883 - 834 pages
...two-thirds of its circumscribing cylinder. Spheres are to one another as the cubes of their diameters. The surface of a sphere is equal to four times the area of one of its great circles, and the solidity is found by multiplying the cube of the diameter by •5236... | |
 | Benjamin Williamson - Calculus of variations - 1884 - 424 pages
...by the polygon becomes a sphere ; and we get 471- .ft2 for the entire surface of the sphere. Hence, the surface of a sphere is equal to four times the area of one of its great circles. Again, it is easy to find the surface generated by any number of sides of... | |
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The surface of a sphere is equal to four times the area of a circle... 
