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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. "
The Elements of Solid Geometry - Page 46
by William C. Bartol - 1893 - 95 pages
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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - Mathematics - 1872 - 602 pages
...01 as the radii of their bases. The volumes of similar cylinders are to each other as the cubes *f their altitudes, or as the cubes of the radii of their bases. CYLINDRICAL SURFACE or CYLINDER, in higher geometry, is a surface which may be generated by a straight...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

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...
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Manual of Geometry and Conic Sections: With Applications to Trigonometry and ...

William Guy Peck - Conic sections - 1876 - 376 pages
...equal to one-third the product of its base and altitude, (P. 17, B. 7). Cor. 6. Similar cones are to each other as the cubes of their altitudes, or as the cubes of any two homologous lines, (P. 17, Cor. 2, B. 7). PROPOSITION III. THEOREM. The limit of an inscribed...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 426 pages
...the radius of the base, § 199 QED be a cone of revolution, then B = n -Л2 (§ 381); 666. COR. 2. Similar cones of revolution are to each other as the...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, H and H' their altitudes, V and...
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A Treatise on Special Or Elementary Geometry

Edward Olney - Geometry - 1877 - 272 pages
...of (1) by these equals, we have, PROPOSITION XVI. 499. TJieorem.—The volumes of similar cylinders of revolution are to each other as the cubes of their...altitudes, or as the cubes of the radii of their bases. DEM.—Using the same notation as in the last demonstration, the student should be able to give the...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...similar, we have *L= — • H' R'' V тrR*HR? H № R* and H' That is, the volumes of similar cylinders of revolution are to each other as the cubes of their...altitudes, or as the cubes of the radii of their bases. Ex. 1. Bequired, the entire surface and volume of a cylinder of revolution whose altitude is 30 inches,...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...revolution, and R be the radius of the base, then B = IT 1i2 (§ 381); .'. V= I*&X H. 666. COR. 2. Similar cones of revolution are to each other as the cubes of their altitudes, or as Hie cubes of the radii of their bases. For, let R and R' be the radii of two similar cones of revolution,...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Conic sections - 1877 - 458 pages
...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...
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A Treatise on Special Or Elementary Geometry

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" : AŤ...
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Elements of Geometry, After Legendre, with a Selection of Geometrical ...

Charles Scott Venable - 1881 - 380 pages
...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...
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