| 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,... | |
| 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 - 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;... | |
| 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... | |
| 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... | |
| 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... | |
| 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,... | |
| 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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