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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. "
Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ... - Page 165
by George Roberts Perkins - 1856 - 235 pages
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Elements of Geometry

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...
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Elements of Geometry and Trigonometry: With Notes

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...
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Elements of Geometry...: Translated from the French for the Use of the ...

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...
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Elements of Geometry

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...
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Elements of Geometry

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...
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Elements of Geometry and Trigonometry: With Notes

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...
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Elements of Geometry and Trigonometry

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...
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Elements of Geometry and Trigonometry

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...
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Elements of Geometry and Trigonometry

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...
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Elements of Geometry

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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