 | Charles Davies - Geometry - 1886 - 340 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,... | |
 | 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]... | |
 | 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... | |
 | 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... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 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;... | |
 | Elias Loomis - Conic sections - 1858 - 256 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... | |
 | William E. Bell - Bridge building - 1857 - 250 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... | |
 | William E. Bell - Bridges - 1859 - 226 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... | |
 | George Roberts Perkins - Geometry - 1860 - 472 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,... | |
 | 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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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. 
