| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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