| Nathan Scholfield - 1845
...other as their bases ; and cylinders of the same base arc to each other is 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 basest For the bases are as the squares of their diameters ; and the cylinders being... | |
| George Roberts Perkins - Geometry - 1847 - 308 pages
...other as their bases ; 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... | |
| Charles William Hackley - Geometry - 1847 - 103 pages
...whole length of the element, which if called the element of contact. PROP. VII. Similar prisms and **cylinders are to each other as the cubes of their altitudes, or** of any other like linear dimensions. Let ABCD, EFGH be two similar prisms ; then will the Dprism CD... | |
| Charles Davies - Trigonometry - 1849 - 359 pages
...other as their bases ; 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... | |
| Elias Loomis - Conic sections - 1849 - 226 pages
...other as their bases; 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... | |
| George Roberts Perkins - Geometry - 1850 - 320 pages
...other as their bases ; 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... | |
| Frederick Overman - Machine design - 1851 - 420 pages
...cut by a plane parallel to its base, the section will be equal, and like the base. Similar prisms and **cylinders are to each other as the cubes of their altitudes, or** of any like their linear dimensions. In any pyramid, a section parallel to the base is similar to the... | |
| A. M. LEGENDRE - 1852
...each other as their bases ; and cylinders of equal bases are to each other as their altitudes. Cor. 2. **Similar cylinders are to each other as the cubes of...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 - 432 pages
...each other as their bases; and cylinders of equal bases are to each other as their altitudes. Cor. 2. **Similar cylinders are to each other as the cubes of...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,... | |
| GEORGE R. PERKINS - 1856
...other as their bases ; and 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... | |
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