 The volumes of two spheres are to each other as the cubes of their radii, or as the cubes of their diameters.  Solid Geometry - Page 319by Walter Burton Ford, Charles Ammerman - 1913 - 107 pagesFull view - About this book
 | Adrien Marie Legendre - Geometry - 1819 - 574 pages
...multiplied by the radii are as the cubes of the radii. Therefore the solidities of two spheres are as the cubes of their radii, or as the cubes of their diameters. 548. Scholium. Let R be the radius of a sphere, its surface will be 4 *• fi3 , and its solidity 4... | |
 | Adrien Marie Legendre - Geometry - 1822 - 394 pages
...the squares of the radii must be as the cubes of the latter. Hence the solidities of two spheres are as the cubes of their radii, or as the cubes of their diameters. Scholium. Let R be the radius of a sphere, its surface will be 4jrR2 ; its solidity 4a-R2x JR, or £a-.R3.... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...multiplied by the radii are as the cubes of the radii. Therefore the solidities of two spheres are as the cubes of their radii, or as the cubes of their diameters. 548. Scholium. Let R be the radius of a sphere, its surface will be 4 nR*, and its solidity tnR* X... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 294 pages
...multiplied by the radii are as the cubes of the radii. Therefore the solidities of two spheres are as the cubes of their radii, or as the cubes of their diameters. 548. Scholium. Let R be the radius of a sphere, its surface will be 4 nR2, and its solidity 4 nR" X... | |
 | Geology - 1835 - 476 pages
...Mercury, amounts to 30. This radius, and that of the orbit of Uranus, are in the ratio of 1 to 49. And the volumes of two spheres are to each other as the cubes of their radii. If, therefore, we adopt the hypothesis of the equal distribution of comets in all the regions of our... | |
 | Timothy Walker - Geometry - 1829 - 138 pages
...surfaces of two spheres are to each other as the squares of their radii — . 4. — The tblidities of two spheres are to each other as the cubes -of their radii — . 5. — Tjoo similar polyedrons are to each other as the cubes of their homologo'is sides —... | |
 | Science - 1835 - 704 pages
...Mercury, amounts to 30. This radius, and that of the orbit of Uranus, are in the ratio of 1 to 49- And the volumes of two spheres are to each other as the cubes of their radii. If, therefore, we adopt the hypothesis of the equal distribution of comets in all the regions of our... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...as their surfaces multiplied by their radii, it follows that the solidities of spheres are to sack other as the cubes of their radii, or as the cubes of their diameters. Scholium 3. Let R be the radius of a sphere ; its surface will be expressed by 4"R3, and its solidity... | |
 | Adrien Marie Legendre - Geometry - 1837 - 376 pages
...their solidities are as their surfaces multiplied by their radii, it follows that the solidities of spheres are to each other as the cubes of their radii, or as the cubes of their diameters. Scholium 3. Let R be the radius of a sphere ; its surface will be expressed by 4«Ra, and its solidity... | |
 | Child rearing - 1840 - 460 pages
...amounts to thirty. This radius, and that of the orbit of Uranus, are in the ratio of 1 to 49 ; and the volumes of two spheres are to each other as the cubes of their radii. If, therefore, we adopt the hypothesis of the equal distribution of comets in all the regions of our... | |
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