 | Adrien Marie Legendre - 1819 - 574 Seiten
...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 - 1825 - 280 Seiten
...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 - 1825 - 294 Seiten
...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 - 1828 - 346 Seiten
...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 - 1829 - 156 Seiten
...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 - 1830 - 344 Seiten
...rectangular parallelopipedons of the same altitude are to each other as their bases. THEOREM. 404. Any two rectangular parallelopipedons are to each...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,... | |
 | Adrien Marie Legendre - 1836 - 394 Seiten
...parallelopipedons of the same altitude are to each other as their bases. PROPOSITION XIII. THEOREM. Any two rectangular parallelopipedons are to each...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 - 1837 - 216 Seiten
...denotes its ratio to the unit of surface. 241. Theorem. Two rectangles, as ABCD, AEFG (fig. 127) are to each other as the products of their bases by their altitudes, that is, ABCD : AEFG = AB X AC : AS X AF. Demonstration. Suppose the ratio of the bases AB to AE to... | |
 | Adrien Marie Legendre - 1841 - 288 Seiten
...solid AG : solid AZ : : AB 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... | |
 | James Bates Thomson - 1844 - 268 Seiten
...parallelopipedons having the same altitudes, are to each other as their bases. PROPOSITION XI. THEOREM. Any two rectangular parallelopipedons are to each...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,... | |
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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. 
