| William Guy Peck - Conic sections - 1876 - 366 pages
...7). Hence, any two cylinders are to each other as the products of their bases and altitudes. Cor. 4. **Similar cylinders are to each other as the cubes of their altitudes, or as the** cube of any two homologous lines, (P. 14, Cor. 2, B. 7). PROPOSITION II. THEOREM. The limit of an inscribed... | |
| Edward Olney - Geometry - 1877 - 239 pages
...£JA:: A' : a" : : H' : h 3 . QED PROPOSITION XII. 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 bases.** DEM. R and r being the radii of their bases, and H and h their altitudes, R' : r" :: H " : h* (?),... | |
| George Albert Wentworth - Geometry - 1877 - 398 pages
...the base, then B — тr A.3 (§381); .-. V=^B2X H. 66C. COR. 2. Similar cones of revolution are to **each other as the cubes of their 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, // and ff their altitudes, Fand V... | |
| Elias Loomis - Geometry - 1877 - 443 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... | |
| Edward Olney - 1879
...: : 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" : AĞ... | |
| Charles Scott Venable - Geometry - 1881 - 366 pages
...Any two cylinders 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... | |
| Edward Olney - Geometry - 1883 - 333 pages
...iff _ A _ H IJT - a - T( . ED PROPOSITION XII. 641. 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 bases.** SYNOPSIS OF DEMONSTRATION. Let R and r be the radii of their bases, and /land h their altitudes. Tfi... | |
| Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 512 pages
...themselves are to each other as the cubes of their homologous edges. Cor. 2. Similar prisms are to **each other as the cubes of their altitudes, or as the cubes of** any other homologous lines. PROPOSITION XX. THEOREM. Similar pyramids are to each other as the cubes... | |
| Webster Wells - Geometry - 1886 - 371 pages
...altitudes, or as the squares of the radii of their bases; and their volumes are to each other as tlie **cubes of their altitudes, or as the cubes of the radii of their** . J*.. J3. jrustum of a circular cone is equivalent to the sum f three cones, having for their common... | |
| W. E. BYERLY - 1887
...of revolution this proposition may be formulated, Corollary II. Similar cones of revolution are to **each other as the cubes of their altitudes, or as the cubes of the radii of their** PBOPOSITION VIII. The area of the surface generated by a straight line revolving about an axis in its... | |
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