| Edward Olney - Geometry - 1883 - 352 pages
...Whence, by substitution, we have H* PROPOSITION XVIII. 606. Theorem.—The volumes of similar cylinders **of revolution are to each other as the cubes of their...altitudes, or as the cubes of the radii of their bases.** DEMONSTRATION. For, by (595), V = v and v = irhr*. 1 nce ' 7" ~ ~rfvr• ~ ~W ' V _ irHR' _ HR' and,... | |
| Edward Olney - Geometry - 1883 - 352 pages
...iff _ A _ H IJT - a - T( . ED PROPOSITION XII. 641. 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.** SYNOPSIS OF DEMONSTRATION. Let R and r be the radii of their bases, and /land h their altitudes. Tfi... | |
| Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 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... | |
| Webster Wells - Geometry - 1886 - 392 pages
...altitudes, or as the squares of the radii of their bases; and their volumes are to each other as tlie **cubes of their altitudes, or as the cubes of the radii of their** . J*.. J3. jrustum of a circular cone is equivalent to the sum f three cones, having for their common... | |
| William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...its altitude. Corollary I. For a cone of revolution this proposition may be formulated, Corollary II. **Similar cones of revolution are to each other as the...their altitudes, or as the cubes of the radii of their** PBOPOSITION VIII. The area of the surface generated by a straight line revolving about an axis in its... | |
| William Chauvenet, William Elwood Byerly - Geometry - 1887 - 342 pages
...revolution, the proposition may be formulated, V = Jrr.K ! . H. 30. COROLLARY II. Similar cones of -so **revolution are to each other as the cubes of their...altitudes, or as the cubes of the radii of their bases.** EXERCISE. Theorem..—A frustum of any cone is equivalent to the sum of three cones whose common altitude... | |
| William Chauvenet - Geometry - 1887 - 336 pages
...Proposition IX., CoroM lary.) 13. COROLLARY II. The volumes of similar cylinders of revoJ lution are to **each other as the cubes of their altitudes, or as the cubes of** their radii. THE CONE. 14. Definition. The area of the convex, or lateral, surface of a cone is called... | |
| Edward Albert Bowser - Geometry - 1890 - 414 pages
...revolution, whose altitude is H and radius of the base is R, we have . (439) 780. COR. 2. The volumes of **similar cones of revolution are to each other as the...their altitudes, or as the cubes of the radii of their** boses. (759) EXERCISES. 1. Eequired the lateral area and volume of a right circular cone whose altitude... | |
| 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.... | |
| Edward Albert Bowser - Geometry - 1891 - 424 pages
...is R, we have V = ^7rR•H. (439) 780. COR. 2. The volumes of•similar cones of'revolution are to **each other as the cubes of their altitudes, or as the cubes of the radii of their bases.** (759) EXERCISES. 1. Required the lateral area and volume of a right circular cone whose altitude is... | |
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