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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 Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 234 pages
...otner 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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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 443 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 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 Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 490 pages
...other as their bases ; and cylinders of equal bases are to each other as their altitudes. 577. 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 radii (Prop. XIII. Bk. VI.), and...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1861 - 490 pages
...other as their bases ; and cylinders of equal bases are to each other as their altitudes. 577. 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 radii (Prop. XIII. Bk. VI.), and...
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ELEMENTS OF GEOMETRY AND TRIGONOMETRY

CHARLES DAVIES, LL.D. - 1863
...the cylinder is equal to the product of its base and altitude ; ichich was to be proved. 217 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 (BV, P. XIII.), and the cylinders being similar, these...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 320 pages
...other as their bases ; and cylinders of equal bases are to each other as their altitudes. 577. 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 radii (Prop. XIII. Bk. VI.), and...
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Elements of Geometry and Trigonometry

C. Davies - 1867
...each other as their altitudes; cylinders having equal altitudes are to each other as their basesCor 3 Similar cylinders are to each other as the cubes of their altitudes, or of the radii of the bases- Let the pupil prove itTHEOREM III-" \ The convex surface of a cone is equal...
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Elements of Plane and Solid Geometry: And of Plane and Spherical ...

Gerardus Beekman Docharty - Geometry - 1867 - 283 pages
...are the proper numeral measures of their quantities or magnitudes. PROPOSITION VI. 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 prism CD...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1868 - 320 pages
...other as their bases ; and cylinders of equal bases are to each other as their altitudes. 577. 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 radii (Prop. XIII. Bk. VI.), and...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1869 - 382 pages
...other as their bases ; and cylinders of equal bases are to each other as their altitudes. 577. 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 radii (Prop. XIII. Bk. VI.), and...
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