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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 Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1886 - 334 pages
...two rectangular parallelopipedons are to each other as the product of their three dimensions. Sch. We are consequently authorized to assume, as the measure...a rectangular parallelopipedon, the product of its three dimensions. In order to comprehend the nature of this measurement, it is necessary to reflect,...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...bases ABCD and AMNO, put ABxAD and A Ox AM, and we shall have, solAG : solAZ : : ABxADxAE : AOxAMxAX: hence, any two rectangular parallelopipe'dons are to each other, as the products of their three dimensions. Scholium 1. The magnitude of a solid, its volume 01 extent, is called its solidity]...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...BCD and AMNO, put AB x AD and AOxAJIf, and we shall have, sol. AG : sol.AZ :: ABxADxAE : AOxAMxAX: hence, any two rectangular parallelopipedons are to each other, as the products of their three dimensions. Scholium 1. The magnitude of a solid, its volume 01 extent, is called its solidity...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1856 - 460 pages
...two rectangular parallelopipedons of the same altitude are to each other as their bases. THEOREM XI. Any two rectangular parallelopipedons are to each other as the products of their Iases Iy their altitudes / that is to say, as the products of their three dimensions. For, having placed...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1857 - 444 pages
...bases ABCD and AMNO, put ABxAD and AOxAM, and we shall have, sol. AG : sol. AZ : : ABxADxAE : AOxAMxAX hence, any two rectangular parallelopipedons are to each other, as the products of their three dimensions. Scholium 1. The magnitude of a solid, its volume 01 extent, is called its solidity;...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 234 pages
...: AEFD : : AB : AE. Therefore, two rectangles, &c. PROPOSITION IV. THEORSM. Any two rectangles are to each other as the products of their bases by their altitudes. Let ABCD, AEGF be two rectangles ; the ratio of the rectangle ABCD to the rectangle AEGF, is the same...
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Carpentry Made Easy: Or, The Science and Art of Framing, on a New and ...

William E. Bell - Bridge building - 1857 - 254 pages
...altitudes, and those of the same altitude as their bases ; and, in all cases, they are proportioned to each other, as the products of their bases by their altitudes. Proposition XXIII. Theorem. The area of any triangle it measured by the product of it* bate multiplied...
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Carpentry Made Easy, Or, The Science and Art of Framing, on a New and ...

William E. Bell - Bridges - 1859 - 224 pages
...altitudes, and those of the same altitude as their bases ; and, in all cases, they are proportioned to each other, as the products of their bases by their altitudes. Proposition XXTTT. Theorem. The area of any triangle is measured by the product of its base multiplied...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 443 pages
...parallelopipedons of the same altitude are to each other as their bases. SIXTH BOOK. x A THEOREM XI. 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,...
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Iconographic Encyclopaedia of Science, Literature & Art, Volume 1

Johann Georg Heck - Encyclopedias and dictionaries - 1860 - 332 pages
...each 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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