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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 and Conic Sections

Elias Loomis - Conic sections - 1857 - 226 pages
...base, are to each other as their altitudes. Cor. 3. Similar cylinders are to each other as the cabes of their altitudes, or as the cubes of the diameters...bases are as the squares of their diameters ; and since the cylinders are similar, the diameters of the bases are as their altitudes (Def. 6). Therefore...
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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - Mathematics - 1857 - 608 pages
...altitudes will be to each other as the radii of their bases ; hence, the solidities of similar cones are to each other as the cubes of their altitudes, or as the cubes of the radii of their bases. If the cones are conjugate, we have the following expressions for their solidities...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 234 pages
...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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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...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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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1861 - 628 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 bases. For the bases are as the squares of their radii (Prop. XIII. Bk. VI.), and the cylinders being similar, the radii of their bases are to each...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 520 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 bases. For the bases are as the squares of their radii (Prop. XIII. Bk. VI.), and the cylinders being similar, the radii of their bases are to each...
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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 bases. For the bases are as the squares of their radii (Prop. XIII. Bk. VI.), and the cylinders being similar, the radii of their bases are to each...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1863 - 464 pages
...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 (BV, P. XIII.), and the cylinders being similar, these radii are to each other as their altitudes...
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Elements of Geometry and Trigonometry

C. Davies - 1867 - 342 pages
...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 - 474 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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