 | William Chauvenet - Geometry - 1884 - 384 pages
...therefore, RH r'h~ IP h' T t ' R H+R That is, the lateral areas, or the total areas, of similar cylinders oj revolution are to each other as the squares of their altitudes, or as the square* of the radii of their bases. PROPOSITION III.— PROBLEM. 12. The volume of a cylinder is equal... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...(§ 397), we have PROPOSITION III. THEOREM. 709. The lateral or total areas of two similar cylinders of revolution are to each other as the squares of...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... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...the radius of the base and H the altitude. 10. COROLLARY II. The lateral areas of similar cylinders of revolution are to each other as the squares of...altitudes, or as the squares of the radii of their bases. Suggestion. = ^ s Zxr.h R H__R Z __H* . R_H r * A~7~^' r ~~h> by (5). PROPOSITION III.— THEOREM.... | |
 | William Chauvenet - Geometry - 1888 - 826 pages
...— r H h • R} R H+R T t " That is, the lateral areas, or the total areas, of similar cylinders oj 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 product of its base by its... | |
 | Edward Albert Bowser - Geometry - 1890 - 420 pages
...2. By the process that was employed in (756) we may show that the lateral areas, or the total areas, of two similar cones of revolution are to each other as the squares of their radii, or of their slant heights, or of their altitudes. Proposition 6. Theorem. 776. The... | |
 | George Albert Wentworth - Geometry - 1888 - 466 pages
...itR2 X H. PROPOSITION XXXIV. THEOREM. 651. The lateral areas, or the total areas, of similar cylinders of revolution are to each other as the squares of their altitudes, or of their radii; and their volumes are to each other as the cubes of their altitudes, or of their radii.... | |
 | William Chauvenet - 1893 - 340 pages
...its altitude. This may be formulated, S = ZvRH. Corollary II. The lateral areas of similar cylinders of revolution are to each other as the squares of...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 base by its altitude. Corollary... | |
 | George Clinton Shutts - Geometry - 1894 - 412 pages
...base of the cylinder of revolution. 305 581. COROLLARY II. The lateral areas of similar cylinders 0} revolution are to each other as the squares of their...altitudes, or as the squares of the radii of their bases. Let A, H, and R represent, respectively, the area, altitude, and the radius of the base of one cylinder,... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 416 pages
...The truth of the theorem may be expressed by the formula CONES. 503. COROLLARY II. The lateral areas of two similar cones of revolution are to each other as the squares of their slant heights, or the squares of their altitudes, or the squares of the radii of their bases.... | |
 | John Macnie - Geometry - 1895 - 386 pages
...triangles revolving about homologous arms 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... | |
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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... 
