| Adrien Marie Legendre - Geometry - 1819 - 208 pages
...have the same altitude, the products of the bases by the altitudes will be as the bases ; therefore **two prisms of the same altitude are to each other as their bases ; for a** similar reason, two prisms of the same base are to each other as their altitudes. LEMMA. 408. If a... | |
| Adrien Marie Legendre - Geometry - 1825 - 224 pages
...have the same altitude, the products of the bases by the altitudes will be as the bases ; therefore **two prisms of the same altitude are to each other as their bases ; for a** similar reason, too prisms of the same base are to each other as their altitudes. LEMMA. 408. If a... | |
| Adrien Marie Legendre - Geometry - 1825 - 224 pages
...have the same altitude, the products of the bases by the altitudes will be as the bases ; therefore **two prisms of the same altitude are to each other as their bases ,- for a** similar reason, two prisms of the same base are to each other as their altitudes. LEMMA. 408. If a... | |
| Adrien Marie Legendre - Geometry - 1825 - 280 pages
...Corollary. 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,** .#, B, C, being any three magnitudes whatever, we have generally Ax C:Bx C::rf:B. THEOREM. 1 76. The... | |
| Adrien Marie Legendre - Geometry - 1836 - 359 pages
...ABCD. 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: then. BxC:BxD::C:D, (Book... | |
| Adrien Marie Legendre - Geometry - 1837 - 359 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,...simply ; hence two prisms of the same altitude are to** eack other as their bases. For a like reason, two prisms of the same base are to each other as their... | |
| Adrien Marie Legendre - Geometry - 1839 - 269 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,...each other as their bases. For a like reason, two** pi-isms of the same base are to each other as their altitudes. And when neither their bases nor their... | |
| Adrien Marie Legendre - Geometry - 1841 - 235 pages
...Corollary. 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, A,** B, C, being any three magnitudes whatever, we have generally A x C :B x C ::A:B. THEOREM. 176. The... | |
| 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
...ABCD. 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 : then, BxC : BxD: :C : D,... | |
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