| Charles Davies, William Guy Peck - Mathematics - 1872 - 602 pages
...01 as the radii of their bases. The volumes of similar cylinders are to each other as the cubes *f **their altitudes, or as the cubes of the radii of their bases.** CYLINDRICAL SURFACE or CYLINDER, in higher geometry, is a surface which may be generated by a straight... | |
| Adrien Marie Legendre - Geometry - 1874 - 500 pages
...pyramid S.AB CDE : pyramid S.abcde : : AB3 • ab" ; wluch was to be proved. Cor. Similar pyramids are to **each other as the cubes of their altitudes, or as the cubes of** any other homologous lines. GENERAL FORMULAS. If we denote the volume of any prism by V, its base by... | |
| William Guy Peck - Conic sections - 1876 - 376 pages
...equal to one-third the product of its base and altitude, (P. 17, B. 7). Cor. 6. Similar cones are to **each other as the cubes of their altitudes, or as the cubes of** any two homologous lines, (P. 17, Cor. 2, B. 7). PROPOSITION III. THEOREM. The limit of an inscribed... | |
| George Albert Wentworth - Geometry - 1877 - 426 pages
...the radius of the base, § 199 QED be a cone of revolution, then B = n -Л2 (§ 381); 666. COR. 2. **Similar cones of revolution are to each other as the...altitudes, or as the cubes of the radii of their bases.** For, let R and R' be the radii of two similar cones of revolution, H and H' their altitudes, V and... | |
| Edward Olney - Geometry - 1877 - 272 pages
...of (1) by these equals, we have, PROPOSITION XVI. 499. TJieorem.—The volumes of similar cylinders **of revolution are to each other as the cubes of their...altitudes, or as the cubes of the radii of their bases.** DEM.—Using the same notation as in the last demonstration, the student should be able to give the... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...similar, we have *L= — • H' R'' V тrR*HR? H № R* and H' That is, the volumes of similar cylinders **of revolution are to each other as the cubes of their...altitudes, or as the cubes of the radii of their bases.** Ex. 1. Bequired, the entire surface and volume of a cylinder of revolution whose altitude is 30 inches,... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...revolution, and R be the radius of the base, then B = IT 1i2 (§ 381); .'. V= I*&X H. 666. COR. 2. **Similar cones of revolution are to each other as the cubes of their altitudes, or as** Hie cubes of the radii of their bases. For, let R and R' be the radii of two similar cones of revolution,... | |
| Elias Loomis - Conic sections - 1877 - 458 pages
...and cylinders of the same base are to each other as their altitudes. Cor. 3. Similar cylinders are to **each other as the cubes of their altitudes, or as the cubes of the** diameters of their bases. For the bases are as the squares of their diameters ; and, since the cylinders... | |
| Edward Olney - 1879 - 278 pages
...: : A' : a" : : H" : A3, QED PROPOSITION xn. 531, Theorem. — The volumes of similar cones are to **each other as the cubes of their altitudes, or as the cubes of the radii of their** base*. DEM. R and r being the radii of their bases, and H and A their altitudes, R" : 1s :: H" : AŤ... | |
| Charles Scott Venable - 1881 - 380 pages
...are to each other as the products of their bases and altitudes. • COR. 2. S1mtlar cylinders are to **each other as the cubes of their altitudes, or as the cubes of the** diameters rf their bases. For, the bases being as the squares of the diameters, in the case of similar... | |
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