| George Roberts Perkins - Geometry - 1847 - 308 pages
...altitude. Hence the solidity of any polygonal prism is equal to the product of its base by its altitude. **Cor. Comparing two prisms which have the same altitude,...the same base are to each other as their altitudes.** PROPOSITION XII. THEOREM. Similar prisms. are to one another as the cube of ., • • their homologous... | |
| Elias Loomis - Conic sections - 1849 - 252 pages
...altitude, the products of the bases by the altitudes, will be as the bases (Prop. VIII., B. II.); hence **prisms of the same altitude are to each other as their bases. For** the same reason, prisms of the same base are to each other as their altitudes ; and prisms generally... | |
| Charles Davies - Trigonometry - 1849 - 384 pages
...BE A & Cor. Parallelograms of the same base are to each other as their altitudes; and parallelograms **of the same altitude are to each other as their bases: for,** let B be the common base, and C and D the altitudes of two parallelograms: is equal to the area of... | |
| George Roberts Perkins - Geometry - 1850 - 332 pages
...altitude. Hence the solidity of any polygonal prism is equal to the product of its base by its altitude. **Cor. Comparing two prisms which have the same altitude,...the same base are to each other as their altitudes.** PROPOSITION XIITHEOREM. Similar prisms are to one another as the cube of their homologous sides. Let... | |
| Adrien Marie Legendre - Geometry - 1852 - 436 pages
...products of their bases and altitudes, if the altitudes be equal, they will be to each other as their **bases simply; hence, two prisms of the same altitude are to each other as** tfieir bases. For a like reason, two prisms having equivalent bases are to each other as their altitudes.... | |
| Charles Davies - Geometry - 1854 - 436 pages
...products of their bases and altitudes, if the altitudes be equal, they will be to each other as their **bases simply; hence, two prisms of the same altitude are to each** otl'er as their bases. For a like reason, two prisms having equivalent bases are to each other as their... | |
| George Roberts Perkins - Geometry - 1856 - 235 pages
...altitude. Hence the volume of any polygonal prism is equal to the product of its base by its altitude. **Cor, Comparing two prisms which have the same altitude,...the same base are to each other as their altitudes.** THEOREM XIII. Similar prisms are to one another as the cubes of their homoloLet P and p be two prisms,... | |
| Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 444 pages
...products of their bases and altitudes, if the altitudes be equal, they will be to each other as their **bases simply; hence, two prisms of the same altitude...other as their bases. For a like reason, two prisms** having equivalent loses are to each other as their altitudes. s PROPOSITION XV. THEOREM. Two triangular... | |
| Elias Loomis - Conic sections - 1858 - 234 pages
...ABxAF. Cor. Parallelograms of the same base are to each other as their altitudes, and parallelograms **of the same altitude are to each other as their bases ; for** magnitudes have the same ratio that their equimultiples have (Prop. VIII., B. II.). PROPOSITION VI.... | |
| George Roberts Perkins - Geometry - 1860 - 443 pages
...altitude. Hence the volume of any polygonal prism is equal to the product of its base by its altitude. **Cor. Comparing two prisms which have the same altitude,...the same base are to each other as their altitudes.** THROREM X1II. Similar prisms are to one another as the cubss of their homologous sides. Let P and p... | |
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