| 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... | |
| 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... | |
| 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... | |
| 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 ;... | |
| 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... | |
| 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... | |
| 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... | |
| Adrien Marie Legendre - Geometry - 1863 - 455 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... | |
| 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... | |
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