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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. "
Mathematical Dictionary and Cyclopedia of Mathematical Science Comprising ... - Page 146
by Charles Davies, William Guy Peck - 1859 - 592 pages
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Manual of Geometry and Conic Sections: With Applications to Trigonometry and ...

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...
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A Treatise on Special Or Elementary Geometry

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* (?),...
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Elements of Plane and Solid Geometry

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...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

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...
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A Treatise on Special Or Elementary Geometry

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...
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Elements of Geometry, After Legendre: With a Selection of ..., Part 2

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...
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Elementary Geometry: Including Plane, Solid, and Spherical Geometry, with ...

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...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

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...
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The Elements of Geometry

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...
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CHAUVENETS TREATISE ON ELEMENTARY GEOMETRY

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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