 | Adrien Marie Legendre - 1819 - 574 pagina’s
...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 pagina’s
...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 pagina’s
...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 pagina’s
...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,... | |
 | James Hayward - 1829 - 218 pagina’s
...its height, and CE X CG is the product of the base of the rectangle CEFG by its height. Therefore — Two rectangles are to each other as the products of their bases by their heights. 159. It is usual to estimate areas by square feet, square yards, square rods, &c. By a square... | |
 | Timothy Walker - 1829 - 156 pagina’s
...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... | |
 | John Playfair - 1835 - 336 pagina’s
...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... | |
 | Adrien Marie Legendre - 1836 - 394 pagina’s
...ABCD, AEFD, of the same altitude, are to each other as theii bases AB, AE. PROPOSITION IV. 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 rect angle, ABCD :... | |
 | Benjamin Peirce - 1837 - 216 pagina’s
...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 pagina’s
...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... | |
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The areas of two rectangles are to each other as the products of their bases by their altitudes. 
