| James Bates Thomson - Geometry - 1844 - 237 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...cylinders being similar, the diameters of their bases** are to each other as the altitudes; (Def. 4. 8;) hence the bases are as the squares of the altitudes... | |
| Nathan Scholfield - 1845 - 896 pages
...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...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 similar, the diameters... | |
| Charles William Hackley - Geometry - 1847 - 248 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 - 384 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...cylinders being similar, the diameters of their bases** are to each other as the altitudes (Def. 4.) ; hence the bases are as the squares of the altitudes... | |
| Elias Loomis - Conic sections - 1849 - 252 pages
...other as their bases; cones of equal bases are to each other as their altitudes; and similar cones are **as the cubes of their altitudes, or as the cubes of the diameters of their bases.** Cor. 2. If A represent the altitude of a cone, and R the radius of its base, the solidity of the cone... | |
| Frederick Overman - Building - 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... | |
| Adrien Marie Legendre - Geometry - 1852 - 436 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 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... | |
| Charles Davies - Geometry - 1854 - 436 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 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... | |
| Charles Davies, William Guy Peck - Electronic book - 1855 - 592 pages
...volumes of conjugate 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. CīLiNnRiCAL SURFACE or CYLIXDKR, in higher geometry, is a surface which may... | |
| George Roberts Perkins - Geometry - 1856 - 460 pages
...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...cylinders being similar, the diameters of their bases** (D. IV.) are to each other as the altitudes : hence the bases are as the squares of the altitudes ;... | |
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