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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: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 308 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,...the same base are to each other as their altitudes. PROPOSITION XII. THEOREM. Similar prisms. are to one another as the cube of ., • • their homologous...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...altitude, the products of the bases by the altitudes, will be as the bases (Prop. VIII., B. II.); hence prisms of the same altitude are to each other as their bases. For the same reason, prisms of the same base are to each other as their altitudes ; and prisms generally...
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 384 pages
...BE A & 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: is equal to the area of...
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Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 332 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,...the same base are to each other as their altitudes. PROPOSITION XIITHEOREM. Similar prisms are to one another as the cube of their homologous sides. Let...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...products of their bases and altitudes, if the altitudes be equal, they will be to each other as their bases simply; hence, two prisms of the same altitude are to each other as tfieir bases. For a like reason, two prisms having equivalent bases are to each other as their altitudes....
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...products of their bases and altitudes, if the altitudes be equal, they will be to each other as their bases simply; hence, two prisms of the same altitude are to each otl'er as their bases. For a like reason, two prisms having equivalent bases are to each other as their...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1856 - 235 pages
...altitude. Hence the volume of any polygonal prism is equal to the product of its base by its altitude. Cor, Comparing two prisms which have the same altitude,...the same base are to each other as their altitudes. THEOREM XIII. Similar prisms are to one another as the cubes of their homoloLet P and p be two prisms,...
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Elements of Geometry and Trigonometry from the Works of A. M. Legendre ...

Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 444 pages
...products of their bases and altitudes, if the altitudes be equal, they will be to each other as their bases simply; hence, two prisms of the same altitude...other as their bases. For a like reason, two prisms having equivalent loses are to each other as their altitudes. s PROPOSITION XV. THEOREM. Two triangular...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 234 pages
...ABxAF. 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 magnitudes have the same ratio that their equimultiples have (Prop. VIII., B. II.). PROPOSITION VI....
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 443 pages
...altitude. Hence the volume of any polygonal prism is equal to the product of its base by its altitude. Cor. Comparing two prisms which have the same altitude,...the same base are to each other as their altitudes. THROREM X1II. Similar prisms are to one another as the cubss of their homologous sides. Let P and p...
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