 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...pyramid S.AB CDE : pyramid S.abcde : : AB3 • ab" ; wluch was to be proved. Cor. Similar pyramids are to each other as the cubes of their altitudes, or as the cubes of any other homologous lines. GENERAL FORMULAS. If we denote the volume of any prism by V, its base by... | |
 | 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... | |
 | 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...bases are as the squares of their diameters ; and, since the cylinders are similar, the diameters of their bases are as their altitudes (Def. 6). Therefore... | |
 | 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... | |
 | 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'... | |
 | 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 cylinders... | |
 | 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... | |
 | 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
...squares of their altitudes, or as the squares of the radii of their bases; and their volumes are to each other as the cubes of their altitudes, or as the cubes of the radii of their bases. PROPOSITION IV. THEOREM. 714. The lateral area nf a cone of revolution is equal... | |
 | 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... | |
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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. 
