 The lateral areas, or the total areas, of two 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...  Plane and Solid Geometry, Suggestive Method - Page 388by George Clinton Shutts - 1913 - 476 pagesFull view - About this book
 | Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...other as the squares of their homologous sides ; hence, the convex surfaces of similar cones are to each other as the squares of their altitudes, or as the squares of the radii of their bases. If the cones arc conjugate, the areas of their generating triangles are equal... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...+ r IT h* That is, 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 the radii of their bases. PROPOSITION III.— PROBLEM. 12. The volume of a cylinder is equal to the... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...r R IP A' That is, 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 the radii of their bases. PROPOSITION III.— PROBLEM. 12. The volume of a cylinder is equal to the... | |
 | Charles Scott Venable - 1881 - 380 pages
...same, are to each other as the altitudes divided by the radii of the bases. 4. The convex surfaces of two similar cylinders are to each other as the squares of their altitudes, or the squares of the diameters of their bases. 5. The convex surface of a cone whose angle at the vertex... | |
 | George Albert Wentworth - Geometry - 1882 - 442 pages
...\Jj' + R' That is, 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 the radii of their bases. 334 GEOMETRY BOOK VII. PROPOSITION XXX. THEOREM. 623. The volume of a cylinder... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...altitude. This may be formulated, Corollary II. The lateral areas of similar cylinders of revolution are to each other as the squares of their altitudes, or as the squares of the radii of their bases. PROPOSITION III. The volume of a cylinder is equal to the product of its... | |
 | Edward Albert Bowser - Geometry - 1890 - 414 pages
...:R"' Therefore, the lateral areas, or the total areas, of two similar cylinders of revolution are to each other as the squares of their altitudes, or as the squares of the radii of their bases. EXERCISES. 1. Required the lateral area, and also the total area, of a cylinder... | |
 | William C. Bartol - Geometry, Solid - 1893 - 106 pages
...their bases. 152. THEOREM. The surfaces, Lateral or total, of two similar cones of revolution are to each other as the squares of their altitudes, or as the squares of the radii of their bases. Use diagram of (151). 153. DEFINITION. Similar pyramids are such as have... | |
 | William Chauvenet - 1893 - 340 pages
...base and H the altitude. 10. COROLLARY II. The lateral areas of similar cylinders of revolution are to each other as the squares of their altitudes, or as the squares of the radii of their bases. Suggestion. = "' s EE If H' . EH -.-=_ = _ since - = - , T hr* h * rh PROPOSITION... | |
 | John Macnie - Geometry - 1895 - 386 pages
...as axes. 687. COB. 2. The lateral areas, or the total areas, of similar cones of revolution, are to each other as the squares of their altitudes, or as the squares of their radii. This may be proved as was Cor. 3 of Prop. I. 688. DEFINITION. A truncated cone is the portion of a... | |
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