 | 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... | |
 | 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... | |
 | Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...intersecting form four volume of any sphere, whose radius is r, and diameter is d, The volumes of any two spheres are to each other as the cubes of their radii, or as the cubes of their diameters ; and in general, as spherical angles at the same point, whose sum... | |
 | Thomas Dick - 1857 - 878 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... | |
 | James Stewart Eaton - Arithmetic - 1857 - 376 pages
...all similar solids are to each other as the cubes of their homologous lines ; thus, the solidities of two spheres are to each other as the cubes of their radii, as the cubes of their diameters, or as the cubes of' their circumferences, etc., etc. ; the solidities... | |
 | James Stewart Eaton - Arithmetic - 1868 - 356 pages
...the volumes of all similar bodies are to each other as the cubes of their homologous lines ; thus, the volumes of two spheres are to each other as the cubes of their radii, as the cubes of their diameters, or as the cubes of their circumferences, etc., etc. ; the volumes... | |
 | Albert Taylor Bledsoe, Sophia M'Ilvaine Bledsoe Herrick - Periodicals - 1870 - 510 pages
...thirty-seven. This radius and that of the orbit of Neptune are in the ratio of one to seventy-eight. But the volumes of two spheres are to each other as the cubes of their radii. If, then, we adopt the hypothesis of an equal distribution of comets in our system, — and no reason... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...V=±xR* X \R = $xR*. Or, if D is the diameter of the sphere, whence D3 = (2R)3 = 8R3, 48. Corollary II. The volumes of two spheres are to each other as the cubes of their radii, or as the cubes of their diameters. PROPOSITION XV.— THEOREM. 49. The solid generated by a circular... | |
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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. 
