 | William E. Bell - Bridge building - 1857 - 250 pages
...altitudes, and those of the same altitude as their bases ; and, in all cases, they are proportioned to each other, as the products of their bases by their altitudes. Proposition XXIII. Theorem. The area of any triangle it measured by the product of it* bate multiplied... | |
 | William E. Bell - Bridges - 1859 - 226 pages
...altitudes, and those of the same altitude as their bases ; and, in all cases, they are proportioned to each other, as the products of their bases by their altitudes. Proposition XXTTT. Theorem. The area of any triangle is measured by the product of its base multiplied... | |
 | Elias Loomis - Conic sections - 1860 - 246 pages
...have the proportion ABCD : AEFD : : AB : AE. Therefore, two rectangles, &c. PROPOSITION IV. THEOR3M. Any two rectangles are to each other as the products...same with the ratio of the product of AB by AD, to thj product of AE by AF; that is, ABCD : AEGF :: AB x AD : AE xAF. Having placed the two rectangles... | |
 | Johann Georg Heck - Encyclopedias and dictionaries - 1860 - 332 pages
...each other as their altitudes; of the same altitude, as their bases; and generally, parallelograms are to each other as the products of their bases by their altitudes. The areas of two squares are to each other as the squares of their sides. The areas of two similar... | |
 | George Roberts Perkins - Geometry - 1860 - 472 pages
...to each other as their bases. SIXTH BOOK. x A THEOREM XI. 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,... | |
 | Elias Loomis - Conic sections - 1861 - 254 pages
...rectangle ABCD to the rectangle AEGF, is the same with the ratio of the product of AB by AD, to thj product of AE by AF ; that is, ABCD : AEGF : : AB X AD : Having placed the two rectangles so that the angles at A are vertical, produce the sides GE, CD till... | |
 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...the same base, or equivalent bases, are to each other as their altitudes. 491. Cor. 4. Pyramids are to each other as the products of their bases by their altitudes. 492. Scholium. The solidity of any polyedron may be found by dividing it into pyramids, by passing... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...have Solid AG : Solid AZ : : AB CDXAE : AMN0 X AX. Hence, any two rectangular parallelopipedons are to each other as the products of their bases by their altitudes. 472. Scholium 1. We are consequently authorized to assume, as the measure of a rectangular parallelopipedon,... | |
 | Benjamin Greenleaf - 1863 - 338 pages
...57. 5. If a -f- x : a — x : : 11 : 7, what is the ratio of a to x '! Ans. 9 : 2. 6. 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 to 18, and their altitudes as 21 to 23 ; required... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...the same base, or equivalent bases, are to each other as their altitudes. 491. Cor. 4. Pyramids are to each other as the products of their bases by their altitudes. 492. Scholium. The solidity of 'any polyedron may be found by dividing it into pyramids, by passing... | |
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Any two rectangles are to each other as the products of their bases by their altitudes. 
