| George Roberts Perkins - Geometry - 1860 - 474 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,... | |
| 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... | |
| 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 - 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 - 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 - 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 - 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... | |
| Richard Wormell - Geometry, Modern - 1868 - 286 pages
...rectangles are contained in each ; that is, as the number of units in their bases. The surfaces of two rectangles are to each other as the products of their bases and heights. 279. Let the rectangles be placed so that their sides are on two straight lines at right-angles,... | |
| Richard Wormell - Geometry, Plane - 1870 - 304 pages
...rectangles are contained in each ; that is, as the number of units in their bases. The surfaces of two rectangles are to each other as the products of their bases and heights. 279. Let the rectangles be placed so that their sides are on two straight lines at right-angles,... | |
| Elias Loomis - Geometry - 1871 - 302 pages
...rectangles, &c. PROPOSITION IV. THEOB3M. Any two rectangles are to each other as the products of then bases by their altitudes. Let ABCD, AEGF be two rectangles...AD, to thj product of AE by AF; that is, ABCD : AEGF :: ABx AD : Having placed the two rectangles so that the angles at A are veitical, pro'duce the sides... | |
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