 | 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,... | |
 | 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... | |
 | 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... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...any two rectangles having equal altitudes, are to each other as their bases. PROPOSITION IV. THEOEEM. Any two rectangles are to each other as the products of their bases and altitudes. Let ABCD, AEGF, be two rectangles ; then will the rectangle, ABCD : AEGF :: ABxAD :... | |
 | Charles Davies - Geometry - 1886 - 340 pages
...to any other rectangles whose bases are whole numbers : hence, AEFD : EBCF : : AE : EBTHEOREM VIAny two rectangles are to each other as the products of their bases and altitudesLet ABCD and AEGF be two rectangles : then will ABCD : AEGF - : ABxAD : AFxAE For, having... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...is equal to AE. Hence, any two rectangles having equal altitudes, are to each other as their bases. PROPOSITION IV. THEOREM. Any two rectangles are to each other as the products of their bases and altitudes. Let ABCD, AEGF, be two rectangles; then will the rectangle, ABCD : AEGF :: ABxAD : AExAF.... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...is equal to AE. Hence, any two rectangles having equal altitudes, are to each other as their bases. PROPOSITION IV. THEOREM. Any two rectangles are to each other as the products of the'r bases and altitudes. Let ABCD, AEGF, be two rectangles; then will the rectangle, ABCD : AEGF... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...bases ; pyramids of the same base are to each other as their altitudes ; and pyramids generally are to each other as the products of their bases by their altitudes. Cor. 3. Similar pyramids are to each other as the cubes of their homologous edges. Scholium. The solidity... | |
 | 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... | |
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Any two rectangles are to each other as the products of their bases by their altitudes. 
