 | Adrien Marie Legendre - Geometry - 1819 - 574 pages
...AD, AO x AM, which will give solid AG : solid AZ : : AE x AD x AE : AO X AM X AX. Therefore any two rectangular parallelopipeds are to each other as the products of their bases by their altitudes, or as the products of their three dimensions. 405. Scholium. Hence we may take for the measure of a... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...rectangular parallelopipeds of the same altitude are to each other as their bases. THEOREM. 404. Any two rectangular parallelopipeds are to each other as the products of their bases by their altitudes, or as the products of their three dimensions. Fig. 213. Demonstration. Having placed the two solids... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 294 pages
...rectangular parallelopipeds of the same altitude are to each other as their bases. THEOREM. 404. Any two rectangular parallelopipeds are to each other as the products of their bases by their altitudes, or as the products of their three dimensions. Fig. 213. Demonstration. Having placed the two solids... | |
 | Adrien Marie Legendre - Geometry - 1828 - 346 pages
...altitude are to each other as their bases. THEOREM. 404. Any two rectangular parallelepipedons 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, having placed the two solids AG, AZ,... | |
 | Timothy Walker - Geometry - 1829 - 156 pages
...of the preceding demonstrations. COR. — Two prisms, two pyramids, two cylinders, or two rones are to each, other as the products of their bases by their altitudes. If the altitudes are the same, they ore as their bases. If the bases are the same, thty are as t/icir... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...to each other as their bases. PROPOSITION XIII. 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. c EH \K \ i L I V 6 A B > \ ro\ I3 \ t C... | |
 | Benjamin Peirce - Geometry - 1837 - 216 pages
...cylinder is equivalent to a right prism or cylinder of the same base and altitude. 357. Theorem. Two right parallelopipeds are to each other as the products of their bases by their altitudes. Demonstration. Let the two right parallelopipeds be ABCD EFGH, AKLM NOPQ (fig. 168) which we will denote... | |
 | Adrien Marie Legendre - Geometry - 1841 - 288 pages
...rectangular parallelopipeds of the same altitude are to each other as their bases. THEOREM. 404. Any two rectangular parallelopipeds are to each other as the products of their bases by their altitudes, or as the products of their three dimensions. Demonstration. Having placed the two solids AG, AZ Fig.... | |
 | James Bates Thomson - Geometry - 1844 - 268 pages
...are to each other as their bases. PROPOSITION XI. THEOREM. Any two rectangular parallelopipedons are to each other as the products of their bases by their altitudes ; that is, as the products of their three dimensions. For, having placed I f1~ the two solids AG, AZ,... | |
 | Nathan Scholfield - 1845 - 894 pages
...are to each other as their bases. PEOPOSITIQN XV. 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, having placed the two solids AG, AZ,... | |
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Any two rectangles are to each other as the products of their bases by their altitudes. 
