 | Elias Loomis - Conic sections - 1858 - 256 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... | |
 | George Roberts Perkins - Geometry - 1860 - 472 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... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 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... | |
 | Benjamin Greenleaf - Geometry - 1861 - 638 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... | |
 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...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... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 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... | |
 | 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... | |
 | 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... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 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... | |
 | Benjamin Greenleaf - 1869 - 516 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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Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases. 
