 | Adrien Marie Legendre - Geometry - 1819 - 574 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 - 394 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, John Farrar - Geometry - 1825 - 294 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 - 276 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 - 394 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 - 376 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 - 288 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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... bases simply : hence two prisms of the same altitude are to each other as their bases. For a like reason, two prisms of the same base are to each other as their altitudes. 
