 | William James Milne - Geometry - 1899 - 404 pages
...of the squares of their radii ? Theorem. The lateral areas, or the total areas, of similar cylinders of revolution are to each other as the squares of their altitudes, or as the squares of their radii. Data: Any two similar cylinders of revolution, whose altitudes are H and and radii R and... | |
 | George Albert Wentworth - Geometry - 1899 - 500 pages
...radius R, PROPOSITION XXXV. THEOBEM. 701. The lateral areas, or the total areas, of similar cylinders of revolution are to each 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... | |
 | George Albert Wentworth - Geometry - 1899 - 498 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 ; and their volumes are to... | |
 | George Albert Wentworth - Geometry, Solid - 1899 - 246 pages
....-.V = ^BXH. §284 QED PROPOSITION XLI. THEOBEM. 726. The lateral areas, or the total areas, of tivo 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 ; and their volumes are to... | |
 | Webster Wells - Geometry - 1899 - 180 pages
...and R the radius of the base, of a circular cone, PROP. VI. THEOREM. 656. TJie lateral or 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 of their... | |
 | Civil service - 1899 - 134 pages
...MECHANICS. 6. Assuming the formula for determining the solidity of a cone as proved, show that the volumes of two similar cones of revolution are to each other as the cuhes of their heights. 7. Given two adjacent sides, a and h, of a triangle, and also the included... | |
 | George Albert Wentworth - Geometry, Solid - 1899 - 248 pages
...the base, B = irR\ • § 463 PROPOSITION XLI. THEOREM. 726. The lateral areas, or the total areas, of two similar cones of revolution are to each other as the square* of their altitudes, as the squares of their radii, or as the squares of their slant heights... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...314 and its altitude is 2. PROPOSITION XXXIII. THEOREM 666. T7ie 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 ; and their volumes are to... | |
 | Arthur Schultze - 1901 - 392 pages
...height is 13. SOLID GEOMETRY PROPOSITION XXXIII. THEOREM 666. 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 ; and their volumes are to... | |
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...of two similar cones of revolution are in the same ratio as the squares of their slant heights, or as the squares of their altitudes, or as the squares of the radii of their bases. DEFINITION. Similar cones of revolution, or right circular cones, are generated by similar right triangles... | |
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The lateral areas, or the total -areas, of two similar cones of revolution are to each other as the squares of their altitudes... 
