 | William Guy Peck - Conic sections - 1876 - 376 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 - 272 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 - 416 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 - Conic sections - 1877 - 458 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 - 278 pages
...: : 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 - 1881 - 380 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 - 352 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 - 538 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 - 392 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... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...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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Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases. 
