| James Bates Thomson - Geometry - 1844 - 237 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 - 896 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 - 308 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 - 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
...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 - Geometry - 1857 - 444 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 - 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.... | |
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