 ... 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
 | 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 by lnil/... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...: AEFD : : AB : AE. Therefore, two rectangles, &c. PROPOSITION IV. THEORSM. Any two rectangles are to each other as the products of their bases by their altitudes. Let ABCD, AEGF be two rectangles ; the ratio of the rectangle ABCD to the rectangle AEGF, is the same... | |
 | 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 by half... | |
 | Johann Georg Heck - Encyclopedias and dictionaries - 1860 - 332 pages
...same base, are to 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,... | |
 | 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... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 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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