| 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 - Geometry - 1825 - 280 pages
...as their bases AB, AE. THEOREM. 172. Any two rectangles ABCD, AEGF (fig. 101), are to each Fig. 101. **other, as the products of their bases by their altitudes, that is,** ABCD : AEGF : : AB x AD : AE x AF. Demonstration. Having disposed the two rectangles in such a manner,... | |
| 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 - 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... | |
| Timothy Walker - Geometry - 1829 - 129 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 - 359 pages
...3. Two pyramids having equivalent bases are to each other as their altitudes. Cor. 4. Pyramids are **to each other as the products of their bases by their altitudes.** Scholium. The solidity of any polyedral body may be computed, by dividing the body into pyramids ;... | |
| Adrien Marie Legendre - Geometry - 1837 - 359 pages
...their altitudes, that is to say, as the products of their three dimensions. VK \ \ V a A I» \ \ \ o\ \ **For, having placed the tWo solids AG, AZ, so that their surfaces have the common angle BAE, produce** th« planes necessary for completing the third parallelopipedon AK having the same altitude with the... | |
| Benjamin Peirce - Geometry - 1837 - 159 pages
...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 - 1838 - 359 pages
...their bases. PROPOSITION XIII. THEOREM. Any two rectangular parallelopipedons are to each other as tht **products of their bases by their altitudes, that is...to say, as the products of their three dimensions.** r ^ V \ A f A \ \ 1 0\ B \ _ \n T 156 GEOMETRY. For, having placed the two solids AG, AZ, so that their... | |
| 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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