| Adrien Marie Legendre - Geometry - 1819 - 574 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 - 294 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, 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 - 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
...their bases. Cor. 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 ;... | |
| 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 - 288 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... | |
| 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,... | |
| Charles William Hackley - Algebra - 1846 - 542 pages
...supported by 2] pounds acting at the end of an arm 4§ inches long? Ans. 2T8j pounds. (5) Triangles are to each other as the products of their bases by their altitudes. The bases of two triangles are to each other as 17 and 18, and their altitudes as 21 and 23. What is... | |
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