 | Timothy Walker - 1829 - 138 pàgines
...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 —... | |
 | Thomas Dick - 1850 - 586 pàgines
...MIlKIl OF COMETS. helion distance is lees than the radius of the orbit of Mercury, amounts to thirty. This radius, and that of the orbit of Uranus, are...ratio of 1 to 49 ; and the volumes of two spheres arc to each other as the cubes of their radii. If, therefore, we adopt the hypothesis of the equal... | |
 | Charles Davies, William Guy Peck - 1855 - 628 pàgines
...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... | |
 | James Stewart Eaton - 1857 - 376 pàgines
...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... | |
 | Elias Loomis - 1857 - 242 pàgines
...have S=4rrR' or rrD' (Prop. VII., Cor. 5). Also, V_ = £RXS = AdR' or jrrD' ; hence the solidities of spheres are to each other as the cubes of their radii If we put A to represent the altitude of the zone which forms the base of a sector, then the solidity... | |
 | Elias Loomis - 1858 - 256 pàgines
...shall have S=4TrR' or wD' (Prop. VII., Cor. 5). Also, V=|RxS=iTrR' or irrD"; hence the solidities of spheres are to each other as the cubes of their radii If we put A to represent the altitude of the zone which forms the base of a sector, then the solidity... | |
 | James Stewart Eaton - 1868 - 356 pàgines
...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 - 1870 - 510 pàgines
...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 can... | |
 | William Chauvenet - 1871 - 380 pàgines
...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... | |
 | William Chauvenet - 1872 - 382 pàgines
...R, we have (42) Or, if D is the diameter of the sphere, whence D* — (2R)5 = 8R", 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. 
