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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
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Plane and Solid Geometry

George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 500 pages
...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 of their radii. Given two similar cylinders of revolution, / and /' denoting their lateral areas, t and...
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Plane and Solid Geometry, Suggestive Method

George Clinton Shutts - Geometry - 1913 - 498 pages
...radius r by the formula V — 638. COR. II. The volumes of two similar cylinders of revolution are to each other as the cubes of their altitudes or as the cubes of their radii (or their diameters) . Proof. Left to the pupil. See 633. 7. Which generates the greater...
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Solid Geometry

George C. Shutts - 1913 - 212 pages
...Complete the demonstration. 638. COR. II. The volumes of two similar cylinders of revolution are to each other as the cubes of their altitudes or as the cubes of their radii (or their diameters'). Proof. Left to the pupil. See 633. 7. Which generates the greater...
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Plane and Solid Geometry

Webster Wells, Walter Wilson Hart - Geometry - 1916 - 490 pages
...squares of their 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 their bases. Hypothesis. S and s are the lateral areas, T and t are the total areas, V and...
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Plane and Solid Geometry

William Betz - Geometry - 1916 - 536 pages
...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 of their radii. Given two similar cylinders of revolution, with lateral areas / and /', total areas t...
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Solid Geometry

William Betz, Harrison Emmett Webb - Geometry, Solid - 1916 - 214 pages
...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 of their radii. Given two similar cylinders of revolution, with lateral areas / and /', total areas t...
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Plane and Solid Geometry

Webster Wells, Walter Wilson Hart - Geometry - 1916 - 504 pages
...the radii of their bases; and their volumes are to each other as the cubes of their slant heights, or as the cubes of their altitudes, or as the cubes of the radii of their bases. Hypothesis. $ and s are the lateral areas, T and t the total areas, F~and v are...
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Solid Geometry Developed by the Syllabus Method

Eugene Randolph Smith - Geometry, Solid - 1918 - 232 pages
...parallel. Show also that this is not true if the lines AB and A'B' are perpendicular to plane P. 522. Similar cylinders are to each other as the cubes of...altitudes, or as the cubes of the diameters of their bases. 523. Show that the projections of parallel lines on the same plane are parallel, but that the converse...
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The Encyclopedia Americana: A Library of Universal Knowledge, Volume 25

Encyclopedias and dictionaries - 1920 - 934 pages
...of their slant heights, or of their altitudes, and 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. SIMILE, a common figure of speech, in which two things which have some strong...
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The Encyclopedia Americana: A Library of Universal Knowledge, Volume 25

Encyclopedias and dictionaries - 1920
...or as the squares of the radii of their bases. The volumes of similar cylinders of revolution are to each other as the cubes of their altitudes, or as the cubes of their radii. Similar cones of revolution are those generated by similar right triangles revolving round...
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