| James Bates Thomson - Geometry - 1844 - 268 pages
...are to each other as their bases. PROPOSITION XI. THEOREM. Any two rectangular parallelopipedons are to each other as the products of their bases by their altitudes ; that is, as the products of their three dimensions. For, having placed I f1~ the two solids AG, AZ, so that... | |
| Nathan Scholfield - 1845 - 894 pages
...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...dimensions. For, having placed the two solids AG, AZ, (see diagram to Prop. XIV.), so that their surfaces have the common angle BAE, produce the planes necessary... | |
| Charles William Hackley - Algebra - 1846 - 542 pages
...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... | |
| George Roberts Perkins - Geometry - 1847 - 326 pages
...other as their bases. •.' ~ ' • . PROPOSITION I. THEOREM. Any two rectangular parallelopipedons are to each other as the products of their bases by their altitudes ; that is to sayf as: the products of their three dimensioiis. For, having placed the two solids AG, AZ so that... | |
| Benjamin Peirce - Geometry - 1847 - 204 pages
...cone is one third of the product of its base by its altitude. 386. Corollary. Pyramids or cones are to each other as the products of their bases by their altitudes. 387. Corollary. Pyramids or cones of the same altitude are to each other as their bases ; and those... | |
| Charles William Hackley - Geometry - 1847 - 248 pages
...necessary to suppose P and Q parallelograms to prove this. (See also th. 19.) THEOREM LX. Rectangles are to each other as the products of their bases by their altitudes. For, in the last figure, let the two rectangles P and Q be unequal, and be placed as before. Then (th.... | |
| Charles Davies - Trigonometry - 1849 - 372 pages
...3. Two pyramids having equivalent bases are to each other as their altitudes. Cor. 4. Pyramids are to each other as the products of their bases by their altitudes. Scholium. The solidity of any polyedral body may be computed, by dividing the body into pyramids ;... | |
| Elias Loomis - Conic sections - 1849 - 252 pages
...each other'as the cubes oi their homologous edges. as their altitudes ; and pyramids generally are to each other as the products of their bases by their altitudes. Scholium. The solidity of any polyedron may be found by dividing it into pyramids, by planes passing... | |
| George Roberts Perkins - Geometry - 1850 - 332 pages
...AG : sol. AK : : ABx AD : AOxAM. PROPOSITION X. THEOREM. Any two rectangular parallelopipedons-are to each other as the products of their bases by their...say, as the products of their three dimensions. For, baring placed the two solids AG, AZ, so that their surfaces have the common angle BAE, produce the... | |
| 1851 - 716 pages
...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... | |
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