| John Playfair - Euclid's Elements - 1842 - 332 pages
...has to the parallelogram CF the ratio which is compounded of the ratios of the sides. . COR. Hence, any two rectangles are to each other as the products of their bases multiplied by their altitudes. SCHOLIUM. Hence the product of the base by the altitude may be assumed... | |
| Nathan Scholfield - 1845 - 894 pages
...Hence, rectangles having the same altitude are to each other as their bases. H PROPOSITION VI. THEOREM. Any two rectangles are to each other as the products of their bases multiplied by their altitudes. Let ABCD, AEGF, be two rectangles ; then will the rectangle, ABCD :... | |
| Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...AC has to the parallelogram CF the ratio which is compounded of the ratios of the sides. COR. Hence, any two rectangles are to each other as the products of their bases multiplied by their altitudes. SCHOLIUM. Hence the product of the base by the altitude may be assumed... | |
| Charles William Hackley - Algebra - 1846 - 542 pages
...supported by 2] pounds acting at the end of an arm 4§ inches long? Ans. 2T8j pounds. (5) Triangles are to each other as the products of their bases by their altitudes. The bases of two triangles are to each other as 17 and 18, and their altitudes as 21 and 23. What is... | |
| Charles William Hackley - Geometry - 1847 - 248 pages
...It is only necessary to suppose P and Q parallelograms to prove this. (See also th. 19.) THEOREM LX. Rectangles are to each other as the products of their bases by their altitudes. For, in the last figure, let the two rectangles P and Q be unequal, and be placed as before. Then (th.... | |
| George Roberts Perkins - Geometry - 1847 - 326 pages
...other as their bases. •.' ~ ' • . PROPOSITION I. THEOREM. Any two rectangular parallelopipedons are to each other as the products of their bases by their altitudes ; that is to sayf as: the products of their three dimensioiis. For, having placed the two solids AG,... | |
| Benjamin Peirce - Geometry - 1847 - 204 pages
...denotes its ratio to the unit of surface. 241. Theorem. Two rectangles, as ABCD, JlEFG (fig. 127) are to each other as the products of their bases by their altitudes, that is, ABCD : AEFG = AB Proof, a. Suppose the ratio of the bases AB to AE to be, for example, as... | |
| Charles Davies - Trigonometry - 1849 - 372 pages
...ABCD, AEFD, of the same altitude, are to each other as their bases AB, AE. PROPOSITION IV. THEOREM. Any two rectangles are to each other as the products of their base* multiplied by their altitudes. Let ABCD, AEGF, be two rectangles ; then will the rectangle, ABCD... | |
| Elias Loomis - Conic sections - 1849 - 252 pages
...each other'as the cubes oi their homologous edges. as their altitudes ; and pyramids generally are to each other as the products of their bases by their altitudes. Scholium. The solidity of any polyedron may be found by dividing it into pyramids, by planes passing... | |
| 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,... | |
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