 | George Washington Hull - 1807 - 408 sider
...Now, &ABC= \EHASEC. §220 But ED ABEC = axb. § 229 Hence &.ABC = I a X b. QED 232. COR. 1. — Two triangles are to each other as the products of their bases by their altitudes. COR. 2.— Two triangles having equal bases are to each other as their altitudes. COR. 3. — Two triangles... | |
 | Adrien Marie Legendre - 1819 - 574 sider
...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 sider
...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 sider
...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 sider
...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,... | |
 | James Hayward - 1829 - 228 sider
...area of a triangle Is half the product of the base multiplied by the height. Consequently airy two triangles are to each other as the products of their bases by their heights. 161. If we designate the height of a rectangle by #, and the base by 6, the area will be expressed... | |
 | Timothy Walker - 1829 - 156 sider
...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... | |
 | Francis Joseph Grund - 1834 - 212 sider
...in the last query ; namely, triangles upon the same basis, and of equal heights. 4th. The areas of triangles are to each other as the products of their bases by their heights : for the halves of these products being the areas of the triangles, the whole products must... | |
 | Adrien Marie Legendre - 1836 - 394 sider
...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 sider
...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... | |
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... two triangles are to each other as the products of their bases by their altitudes. 
