| Adrien Marie Legendre - Geometry - 1874 - 512 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 - Geometry - 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 - 382 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 - 354 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... | |
| Adrien Marie Legendre, Charles Davies - Geometry - 1885 - 540 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 - 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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