 | 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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Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases. 
