| Benjamin Greenleaf - Geometry - 1863 - 504 pages
...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 - 1868 - 338 pages
...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
...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... | |
| William Chauvenet - Geometry - 1871 - 380 pages
...rectangles being similar, we have H_R h ~ r' and F. v H h ' IP h3 that is, the volumes of similar cylinders **of revolution are to each other as the cubes of their altitudes, or as the cubes of** their radii. THE CONE. 15. Definition. The area of the convex, or lateral, surface of a cone is called... | |
| Elias Loomis - Geometry - 1871 - 302 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,... | |
| Edward Olney - 1872 - 270 pages
...^bh :: A" : a" : : H " : K\ QED PROPOSITION XII. 531, Theorem.—The volumes of similar cones are to **each other as the cubes of their altitudes, or as the cubes of the radii of their bases.** DEM. R and r being the radii of their bases, and H and h their altitudes, R" : r " :: H' : A' (?),... | |
| Edward Olney - Geometry - 1872 - 472 pages
...these equals, we have, PROPOSITION XТI. 409. Theorem. — The volumes of similar cylinders are to **each other as the cubes of their altitudes, or as the cubes of the radii of their bases.** DEM. — Using the same notation ns in the last demonstration, the student should be able to give the... | |
| William Chauvenet - Geometry - 1872 - 382 pages
...generating rectangles being similar, we have and F v IP h 3 ' that is, the volumes of similar cylinders **of revolution are to each other as the cubes of their altitudes, or as the cubes of** their radii. THE CONE. 15. Definition. The area of the convex, or lateral, surface of a cone is called... | |
| Edward Olney - Geometry - 1872 - 566 pages
...: : A1 : a" : : H1 : h3. QED PROPOSITION XIL 831. Theorem. — Tlie volumes of similar cones are to **each other as the cubes of their altitudes, or as the cubes of the radii of their** DEM. R and r being the radii of their bases, and H and A their altitudes, R* : r* :: H« : A« (?),... | |
| Charles Davies - Geometry - 1872 - 464 pages
...themselves are to each other as the cubes of their homologous edges. Cor. 2. Similar prisms are to **each other as the cubes of their altitudes, or as the cubes of** any other homologous lines. PROPOSITION XX. THEOREM. Similar pyramids are to each other as the cubes... | |
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