 | Johann Georg Heck - Encyclopedias and dictionaries - 1851 - 712 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... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 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. 197 division may be accomplished in various ways. One of the simplest is to pass all the planes of... | |
 | Charles Davies - Geometry - 1854 - 436 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 ;... | |
 | George Roberts Perkins - Geometry - 1856 - 460 pages
...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...their surfaces have the common angle BAE, produce the interior planes necessary for completing the third parallelopipedon AK, having the same altitude with... | |
 | 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... | |
 | 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 - 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
...to each other as their bases. SIXTH BOOK. x A THEOREM XI. Any two rectangular parallelopipedons are to each other as the products of their bases by their...their surfaces have the common angle BAE, produce the interior planes necessary for completing the third parallelopipedon AK, having the same altitude with... | |
 | 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... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...have Solid AG : Solid AZ : : AB CDXAE : AMN0 X AX. Hence, any two rectangular parallelopipedons are to each other as the products of their bases by their altitudes. 472. Scholium 1. We are consequently authorized to assume, as the measure of a rectangular parallelopipedon,... | |
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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. 
