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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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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845
...other as their bases ; and cylinders of the same base arc to each other is their altitudes. Cor. 2. Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their basest For the bases are as the squares of their diameters ; and the cylinders being...
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 308 pages
...other as their bases ; and cylinders of the same base are to each other as their altitudes. Cor. 2. 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 the cylinders being...
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Elementary Course of Geometry ...

Charles William Hackley - Geometry - 1847 - 103 pages
...whole length of the element, which if called the element of contact. PROP. VII. Similar prisms and cylinders are to each other as the cubes of their altitudes, or of any other like linear dimensions. Let ABCD, EFGH be two similar prisms ; then will the Dprism CD...
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 359 pages
...other as their bases ; and cylinders of the same base are to each other as their altitudes. Cor. 2. 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 the cylinders being...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 226 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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Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 320 pages
...other as their bases ; and cylinders of the same base are to each other as their altitudes. Cor. 2. 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 the cylinders being...
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Mechanics for the Millwright, Machinist, Engineer, Civil Engineer, Architect ...

Frederick Overman - Machine design - 1851 - 420 pages
...cut by a plane parallel to its base, the section will be equal, and like the base. Similar prisms and cylinders are to each other as the cubes of their altitudes, or of any like their linear dimensions. In any pyramid, a section parallel to the base is similar to the...
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ELEMENTS OF GEOMETRY AND TRIGONOMETRY

A. M. LEGENDRE - 1852
...each other as their bases ; and cylinders of equal bases are to each other as their altitudes. Cor. 2. Similar cylinders are to each other as the cubes of...altitudes, or as the cubes of the radii of their bases. For, the bases are as the squares of their radii (B. v., P. 13) ; and the cylinders being similar,...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 432 pages
...each other as their bases; and cylinders of equal bases are to each other as their altitudes. Cor. 2. Similar cylinders are to each other as the cubes of...altitudes, or as the cubes of the radii of their bases. For, the bases are as the squares of their radii (B. v., P. 13) ; and the cylinders being similar,...
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PLANE AND SOLID GEOMETRY

GEORGE R. PERKINS - 1856
...other as their bases ; and cylinders of the same base are to each other as their altitudes. Cor. II. 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 the cylinders being...
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