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Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases.
Elements of Geometry and Trigonometry: With Notes - Page 187
by Adrien Marie Legendre - 1822 - 367 pages

Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 512 pages
...pyramid S.AB CDE : pyramid S.abcde : : AB3 • ab" ; wluch was to be proved. Cor. Similar pyramids are to each other as the cubes of their altitudes, or as the cubes of any other homologous lines. GENERAL FORMULAS. If we denote the volume of any prism by V, its base by...

Manual of Geometry and Conic Sections: With Applications to Trigonometry and ...

William Guy Peck - Conic sections - 1876 - 376 pages
...7). Hence, any two cylinders are to each other as the products of their bases and altitudes. Cor. 4. Similar cylinders are to each other as the cubes of their altitudes, or as the cube of any two homologous lines, (P. 14, Cor. 2, B. 7). PROPOSITION II. THEOREM. The limit of an inscribed...

Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1877 - 458 pages
...other as their bases, and cylinders of the same base are to each other as their altitudes. Cor. 3. Similar cylinders are to each other as the cubes of...bases are as the squares of their diameters ; and, since the cylinders are similar, the diameters of their bases are as their altitudes (Def. 6). Therefore...

Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...the base, then B — тr A.3 (§381); .-. V=^B2X H. 66C. COR. 2. Similar cones of revolution are to each other as the cubes of their altitudes, or as the cubes of the radii of their bases. For, let R and R be the radii of two similar cones of revolution, // and ff their...

A Treatise on Special Or Elementary Geometry

Edward Olney - Geometry - 1877 - 272 pages
...£JA:: A' : a" : : H' : h 3 . QED PROPOSITION XII. 531, 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. DEM. R and r being the radii of their bases, and H and h their altitudes, R'...

Elements of Geometry, After Legendre, with a Selection of Geometrical ...

Charles Scott Venable - 1881 - 382 pages
...Any two cylinders are to each other as the products of their bases and altitudes. • COR. 2. S1mtlar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters rf their bases. For, the bases being as the squares of the diameters, in the case of similar cylinders...

Elementary Geometry: Including Plane, Solid, and Spherical Geometry, with ...

Edward Olney - Geometry - 1883 - 354 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...

Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Adrien Marie Legendre, Charles Davies - Geometry - 1885 - 540 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...