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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. "
Elements of Geometry and Trigonometry: With Notes - Σελίδα 157
των Adrien Marie Legendre - 1828 - 316 σελίδες
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Elements of Geometry

Adrien Marie Legendre - 1819 - 574 σελίδες
...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...

Elements of Geometry

Adrien Marie Legendre - 1825 - 276 σελίδες
...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,...

Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - 1825 - 280 σελίδες
...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...

Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - 1825 - 294 σελίδες
...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...

Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - 1829 - 156 σελίδες
...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...

Elements of Geometry and Trigonometry

Adrien Marie Legendre - 1836 - 394 σελίδες
...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 ;...

Elements of Geometry and Trigonometry

Adrien Marie Legendre - 1837 - 376 σελίδες
...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...

An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - 1837 - 216 σελίδες
...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...

Elements of Geometry and Trigonometry

Adrien Marie Legendre - 1838 - 382 σελίδες
...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...

Elements of Geometry

Adrien Marie Legendre - 1841 - 288 σελίδες
...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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