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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. "
Elements of Geometry and Trigonometry: With Notes - Page 187
by Adrien Marie Legendre - 1822 - 367 pages
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Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson - Geometry - 1844 - 237 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...cylinders being similar, the diameters of their bases are to each other as the altitudes; (Def. 4. 8;) hence the bases are as the squares of the altitudes...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 896 pages
...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...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 similar, the diameters...
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Elementary Course of Geometry ...

Charles William Hackley - Geometry - 1847 - 248 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 - 384 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...cylinders being similar, the diameters of their bases are to each other as the altitudes (Def. 4.) ; hence the bases are as the squares of the altitudes...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...other as their bases; cones of equal bases are to each other as their altitudes; and similar cones are as the cubes of their altitudes, or as the cubes of the diameters of their bases. Cor. 2. If A represent the altitude of a cone, and R the radius of its base, the solidity of the cone...
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Mechanics for the Millwright, Machinist, Engineer, Civil Engineer, Architect ...

Frederick Overman - Building - 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

Adrien Marie Legendre - Geometry - 1852 - 436 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 their 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...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 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 their 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...
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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - Electronic book - 1855 - 592 pages
...volumes of conjugate cylinders are as their altitudes, or as the radii of their bases. The volumes of similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the radii of their bases. CīLiNnRiCAL SURFACE or CYLIXDKR, in higher geometry, is a surface which may...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1856 - 460 pages
...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...cylinders being similar, the diameters of their bases (D. IV.) are to each other as the altitudes : hence the bases are as the squares of the altitudes ;...
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