 ... 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.  New Plane and Solid Geometry - Sivu 138tekijä(t) Webster Wells - 1908 - 298 sivuaKoko teos - Tietoja tästä kirjasta
 | Adrien Marie Legendre - 1819 - 574 sivua
...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 - 1825 - 294 sivua
...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 - 1825 - 280 sivua
...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 - 1828 - 346 sivua
...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 - 1829 - 156 sivua
...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 - 1836 - 394 sivua
...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 - 1837 - 216 sivua
...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 - 1841 - 288 sivua
...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 sivua
...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 - 1846 - 542 sivua
...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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