| George Roberts Perkins - Geometry - 1850 - 332 pages
...and cylinders of the same base are to each other as their altitudes. Cor. 2. 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 the cylinders being... | |
| Adrien Marie Legendre - Geometry - 1852 - 436 pages
...and cylinders of equal bases are to each other as their altitudes. Cor. 2. Similar cylinders are to **each other as the cubes of their altitudes, or as the cubes of the radii of their bases.** For, the bases are as the squares of their radii (B. v., P. 13) ; and the cylinders being similar,... | |
| Charles Davies - Geometry - 1854 - 436 pages
...and cylinders of equal bases are to each other as their altitudes. Cor. 2. Similar cylinders are to **each other as the cubes of their altitudes, or as the cubes of the radii of their bases.** For, the bases are as the squares of their radii (B. v., P. 13) ; and the cylinders being similar,... | |
| Charles Davies, William Guy Peck - Mathematics - 1855 - 630 pages
...cylinders are as their altitudes, or as the radii of their bases. The volumes of similar cylinders are to **each other as the cubes of 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... | |
| George Roberts Perkins - Geometry - 1856 - 460 pages
...cylinders of the same base are to each other as their altitudes. Cor. II. 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 the cylinders being... | |
| Elias Loomis - Conic sections - 1858 - 256 pages
...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... | |
| George Roberts Perkins - Geometry - 1860 - 470 pages
...cylinders of the same base are to each other as their altitudes. Cor. II. 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 the cylinders being... | |
| Benjamin Greenleaf - Geometry - 1861 - 628 pages
...cylinders of equal bases are to each other as their altitudes. 577. Cor. 2. 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 radii (Prop. XIII. Bk. VI.), and... | |
| Benjamin Greenleaf - Geometry - 1862 - 520 pages
...cylinders of equal bases are to each other as their altitudes. 577. Cor. 2. 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 radii (Prop. XIII. Bk. VI.), and... | |
| Adrien Marie Legendre - Geometry - 1863 - 464 pages
...the product of its base and altitude ; ichich was to be proved. 217 Cor. 2. Similar cylinders are to **each other as the cubes of their altitudes, or as the cubes of the radii of their bases.** For, the bases are as the squares of their radii (BV, P. XIII.), and the cylinders being similar, these... | |
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