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" The volumes of two spheres are to each other as the cubes of their radii, or as the cubes of their diameters. "
Mathematical Dictionary and Cyclopedia of Mathematical Science Comprising ... - Page 520
by Charles Davies, William Guy Peck - 1859 - 592 pages
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 208 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...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 367 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 Ła-.R3....
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 224 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...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 224 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...
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The Edinburgh New Philosophical Journal: Exhibiting a View of the ..., Volume 19

Geology - 1835
...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...
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - Geometry - 1829 - 129 pages
...The surfaces of two spheres are to each, other as the squares of their radii. 4. The solidities of two spheres are to each other as the cubes of their radii. 5. Two similar pnlyedrons are to each other as the cubes of their homologous sides. 6. Two similar...
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The Edinburgh New Philosophical Journal, Volume 19

Science - 1835
...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...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 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...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1837 - 359 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...
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The Family Library (Harper)., Volume 99

Child rearing - 1840
...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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