| Nathan Scholfield - 1845 - 896 pages
...rectangular parallelopidons of the same altitude are to each other as their bases. PEOPOSITIQN XV. THEOREM. **Any two rectangular parallelopipedons are to each...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,... | |
| Charles William Hackley - Algebra - 1846 - 503 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 - 308 pages
...parallelopipedons of the same altitude are to each other as their bases. •.' ~ ' • . PROPOSITION I. THEOREM. **Any two rectangular parallelopipedons are to each...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,... | |
| Charles William Hackley - Geometry - 1847 - 248 pages
...appears that all prisms and cylinder-s of equal bases are to one another as their altitudes. D PROP. VI. **Rectangular parallelopipedons are to each other as the products of their bases by their altitudes.** The parallelopipedon AF B is to the parallelopipedon " CE as the base AG x the altitude GF, is to the... | |
| Benjamin Peirce - Geometry - 1847 - 150 pages
...denotes its ratio to the unit of surface. 241. Theorem. Two rectangles, as ABCD, JlEFG (fig. 127) are **to each other as the products of their bases by their altitudes,** that is, ABCD : AEFG = AB Proof, a. Suppose the ratio of the bases AB to AE to be, for example, as... | |
| 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... | |
| Charles Davies - Trigonometry - 1849 - 384 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 ;... | |
| 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 altitudes;** that is to say, as the products of their three dimensions. For, baring placed the two solids AG, AZ,... | |
| 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... | |
| Johann Georg Heck - Encyclopedias and dictionaries - 1851 - 714 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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