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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. "
Elements of Geometry and Trigonometry: With Notes - Page 161
by Adrien Marie Legendre - 1830 - 316 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

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 - 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...
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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

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
...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...
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Elements of Geometry and Trigonometry

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...
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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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Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

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...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

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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