... any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V. THEOREM. 403. The area of a triangle is equal to half the product of its base by its altitude. Elements of Plane and Solid Geometry - Page 179by George Albert Wentworth - 1877 - 398 pagesFull view - About this book
| 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 - 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 - 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... | |
| Adrien Marie Legendre - Geometry - 1836 - 359 pages
...to each other as their bases. PROPOSITION XIII. 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. c EH \K \ i L I V 6 A B > \ ro\ I3 \ t C... | |
| 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... | |
| Nathan Scholfield - 1845 - 896 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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