| 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 - 1822 - 367 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 XVI. LEMMA. If a pyramid SABCDE is cut by a plane abd parallel to its base, First, TJie... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 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 - 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 - 1828 - 346 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. 407. Cor. Comparing two prisms, which have the same altitude, the products of their bases... | |
| 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
...partial triangles, which constitute their bases, multiplied by the common altitude. Hence the solidity **of any polygonal prism, is equal to the product of...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 - 372 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...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... | |
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