| Charles Davies - Geometry - 1850 - 218 pages
...to any other rectangles whose bases are whole numbers : hence, AEFD : EBCF : : AE i EB. THEOREM VI. Any two rectangles are to each other as the products of their bases and altitudes. Let ABCD and AEGF be HD two rectangles : then will ABCD : AEGF :: ABxAD • AFxAE For,... | |
| 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,... | |
| 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... | |
| 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
...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.... | |
| Elias Loomis - Conic sections - 1857 - 242 pages
...hence it must be AE, and we have the proportion ABCD : AEFD : : AB : AE. Therefore, two rectangles, &c. PROPOSITION IV. THEOREM. Any two rectangles are to...same with the ratio of the product of AB by AD, to thj product of AE by AF ; that is, ABCD : AEGF : : AB x AD : AE x AF. Having placed the two rectangles... | |
| 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... | |
| |