| Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 562 pages
...similar right triangles about homologous sides. 959. COR. III. The lateral areas, or the total areas, **of two similar cones of revolution are to each other as the** squares of their slant heights, or as the squares of their altitudes, or as the squares of the radii... | |
| Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 468 pages
...respective altitudes and r, r' the respective radii. Can you show that the volumes of these cones are to **each other as the cubes of their altitudes, or as the cubes of the radii of their bases,** or as the cubes of the diameters of their bases? Sug. Let V = volume of (I) and v = volume of (2).... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry - 1898 - 324 pages
...i^' Therefore 966. COR. I 967, COR. II. The volumes of two similar cones of revolution are to eacli **other as the cubes of their altitudes, or as the cubes of the radii of their bases.** Hint. — The method of proof is the same as that followed in § 942. 068. Def. — The altitude of... | |
| James Howard Gore - Geometry - 1898 - 232 pages
...themselves are to each other as the cubes of their homologous edges. 432. COR. 2. Similar prisms are to **each other as the cubes of their altitudes, or as the cubes of** any other homologous lines. 433. COR. 3. Since the cylinder is the limit of a prism of infinite number... | |
| Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 468 pages
...proposition. Can you make an arithmetical formula for this proposition ? EXERCISES. 498. The lateral areas **of two similar cones of revolution are to each other as the** squares of their slant height, or the squares of their altitudes, or the squares of the radii of their... | |
| Webster Wells - Geometry - 1899 - 424 pages
...squares of their altitudes, or as the squares of the radii of their bases ; and their volumes are to **each other as the cubes of their altitudes, or as the cubes of the radii of their bases.** Given S and s the lateral areas, T and t the total areas, V and v the volumes, H and h the altitudes,... | |
| Webster Wells - Geometry - 1899 - 450 pages
...squares of their altitudes, or as the squares of the radii of their bases ; and their volumes are to **each other as the cubes of their altitudes, or as the cubes of the radii of their bases.** Given S and s the lateral areas, T and t the total areas, V and v the volumes, H and h the altitudes,... | |
| William James Milne - Geometry - 1899 - 404 pages
...of the cubes of their radii? SOLID GEOMETRY. — BOOK IX. Theorem. The volumes of simitar cylinders **of revolution are to each other as the cubes of their altitudes, or as the cubes of** their radii. Data : Any two similar cylinders of revolution, whose altitudes are H and H', and radii... | |
| George Albert Wentworth - Geometry, Solid - 1899 - 246 pages
...other as the squares of their altitudes, or as the squares of their radii ; and their volumes are to **each other as the cubes of their altitudes, or as the cubes of** their radii. Let S, S' denote the lateral areas, T, T' the total areas, V, V the volumes, H, H' the... | |
| George Albert Wentworth - Geometry - 1899 - 500 pages
...of the base, B = -irR2. § 463 PROPOSITION XLI. THEOREM. 726. The lateral areas, or the total areas, **of two similar cones of revolution are to each other as the** squares of their altitudes, as the squares of their radii, or as the squares of their slant heights... | |
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