| James Bates Thomson - Geometry - 1844 - 268 pages
...BE1. Cor. 2. 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 if A and B are the altitudes of two parallelograms, and C their base ; then A x C is equal to the area... | |
| Nathan Scholfield - 1845 - 894 pages
...partial triangles, which constitute their bases, multiplied by the common altitude. Hence the solidity of any polygonal prism, is equal to the product of its base by its altitude. Cor. 1. Comparing two prisms, which have the same altitude, the products of their bases by their altitudes... | |
| George Roberts Perkins - Geometry - 1847 - 326 pages
...partial triangles which constitute their bases, multiplied by the common altitude. Hence the solidity of any polygonal prism is equal to the product of...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 - 372 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
...partial triangles which constitute their bases, multiplied by the common altitude. Hence the solidity of any polygonal prism is equal to the product of...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
...the triangles which constitute their bases, multiplied by the common altitude. Hence, the solidity of any polygonal prism, is equal to the product of its base by its altitude. Cor. Since any two prisms are to each other as the products of their bases and altitudes, if the altitudes... | |
| Charles Davies - Geometry - 1854 - 436 pages
...the triangles which constitute their bases, multiplied by the common altitude. Hence, the solidity of any polygonal prism, is equal to the product of its base by its altitude. Cor. Since any two prisms are to each other as the products of their bases and altitudes, if the altitudes... | |
| Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...the triangles which constitute their bases, multiplied by the common altitude. Hence, the solidity of any polygonal prism, is equal to the product of its base by its altitude. Cor. Since any two prisms are to each other as the products of their bases and altitudes, if the altitudes... | |
| Elias Loomis - Conic sections - 1858 - 256 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.... | |
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