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" Any two rectangular parallelopipedons are to each other as the products of their bases by their altitudes ; that is to say, as the products of their three dimensions. "
Elements of Geometry: With Practical Applications to Mensuration - Page 199
by Benjamin Greenleaf - 1863 - 320 pages
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 896 pages
...rectangular parallelopidons of the same altitude are to each other as their bases. PEOPOSITIQN XV. THEOREM. Any two rectangular parallelopipedons are to each...as the products of their bases by their altitudes, that is to say, as the products of their three dimensions. For, having placed the two solids AG, AZ,...
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A Treatise on Algebra: Containing the Latest Improvements. Adapted to the ...

Charles William Hackley - Algebra - 1846 - 503 pages
...supported by 2] pounds acting at the end of an arm 4 inches long? Ans. 2T8j pounds. (5) Triangles are to each other as the products of their bases by their altitudes. The bases of two triangles are to each other as 17 and 18, and their altitudes as 21 and 23. What is...
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 308 pages
...parallelopipedons of the same altitude are to each other as their bases. •.' ~ ' • . PROPOSITION I. THEOREM. Any two rectangular parallelopipedons are to each...as the products of their bases by their altitudes ; that is to sayf as: the products of their three dimensioiis. For, having placed the two solids AG,...
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Elementary Course of Geometry ...

Charles William Hackley - Geometry - 1847 - 248 pages
...appears that all prisms and cylinder-s of equal bases are to one another as their altitudes. D PROP. VI. Rectangular parallelopipedons are to each other as the products of their bases by their altitudes. The parallelopipedon AF B is to the parallelopipedon " CE as the base AG x the altitude GF, is to the...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1847 - 150 pages
...denotes its ratio to the unit of surface. 241. Theorem. Two rectangles, as ABCD, JlEFG (fig. 127) are to each other as the products of their bases by their altitudes, that is, ABCD : AEFG = AB Proof, a. Suppose the ratio of the bases AB to AE to be, for example, as...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...each other'as the cubes oi their homologous edges. as their altitudes ; and pyramids generally are to each other as the products of their bases by their altitudes. Scholium. The solidity of any polyedron may be found by dividing it into pyramids, by planes passing...
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 384 pages
...3. Two pyramids having equivalent bases are to each other as their altitudes. Cor. 4. Pyramids are to each other as the products of their bases by their altitudes. Scholium. The solidity of any polyedral body may be computed, by dividing the body into pyramids ;...
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Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 332 pages
...AG : sol. AK : : ABx AD : AOxAM. PROPOSITION X. THEOREM. Any two rectangular parallelopipedons-are to each other as the products of their bases by their altitudes; that is to say, as the products of their three dimensions. For, baring placed the two solids AG, AZ,...
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Young Scientist: A Practical Journal for Amateurs, Volume 1

1851 - 716 pages
...other as their altitudes ; of the same altitude, as their bases ; and generally, parallelograms are to each other as the products of their bases by their altitudes. The areas of two squares are to each other as the squares of their sides. The areas of two similar...
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Iconographic Encyclopaedia of Science, Literature, and Art, Volume 1

Johann Georg Heck - Encyclopedias and dictionaries - 1851 - 714 pages
...other as their altitudes ; of the same altitude, as their bases ; and generally, parallelograms are to each other as the products of their bases by their altitudes. The areas of two squares are to each other as the squares of their sides. The areas of two similar...
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