| Adrien Marie Legendre - Geometry - 1819 - 208 pages
...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
...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 - 1825 - 224 pages
...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 - 316 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,... | |
| James Hayward - Geometry - 1829 - 218 pages
...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 - Geometry - 1829 - 158 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... | |
| John Playfair - Euclid's Elements - 1835 - 316 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... | |
| Adrien Marie Legendre - Geometry - 1836 - 359 pages
...the bases, two rectangles 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 - Geometry - 1837 - 216 pages
...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 - Geometry - 1841 - 235 pages
...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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