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" Two prisms are to each other as the products of their bases by their altitudes ; prisms having equivalent bases are to each other as their altitudes; prisms having equal altitudes are to each other as their bases ; prisms having equivalent bases and equal... "
Elements of Geometry and the First Principles of Modern Geometry - Page 170
by Wm. H. H. Phillips - 1878 - 209 pages
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...the solidity of any polygonal prism, is equal to the product of its base by its altitude. Cor. Since any two prisms are to each other as the products of their bases and altitudes, if the altitudes be equal, they will be to each other as their bases simply; hence,...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...the solidity of any polygonal prism, is equal to the product of its base by its altitude. Cor. Since any two prisms are to each other as the products of their bases and altitudes, if the altitudes be equal, they will be to each other as their bases simply; hence,...
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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - Mathematics - 1855 - 630 pages
...prisms, are to each other as the products of perimeters of their bases and altitudes. The volumes of any two prisms are to each other as the products of their bases and altitudes. 4. The sections made in the same prism by secant parallel planes are equal polygons....
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1863 - 455 pages
...was to be proved. Cor. Any two prisms are to each other as the products of their bases and altitudes. Prisms having equal bases are to each other as their...equal altitudes are to each other as their bases. B PROPOSITION XV. THEOREM. Two triangular pyramids having equal bases and equal altitudes^ are equal...
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The Normal Elementary Geometry: Embracing a Brief Treatise on Mensuration ...

Edward Brooks - Geometry - 1868 - 294 pages
...etc. Cor. 1. Any two prisms are to each other as the products of their bases and altitudes. Cor. 2. Prisms having equal bases are to each other as their...equal altitudes are to each other as their bases. THEOREM VII. Similar triangular prisms are to each other as the cubes of their homologous edges. Let...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...the base ABCDE of the given prism multiplied by its altitude. 39. Corollary. Prisms having equivalent bases are to each other as their altitudes ; prisms...prisms are to each other as the products of their bases and altitudes. PYRAMIDS. 40. Definitions. A pyramid is a polyedron bounded by a polygon and triangular...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1872 - 464 pages
...two prisms are to each other as the products of their bases and altitudes. Prisms having equal basea are to each other as their altitudes. Prisms having...equal altitudes are to each other as their bases. PROPOSITION XV. THEOREM. Two tr1angular pyramids having equal bases and equal altitudes, are equal...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1872 - 382 pages
...the base ABCDE of the given prism multiplied by its altitude. 39. Corollary. Prisms having equivalent bases are to each other as their altitudes ; prisms having equal altitudes are to each othef as their bases ; and any two prisms are to each other as the prod i of their bases and altitudes....
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An Elementary Geometry

William Frothingham Bradbury - Geometry - 1872 - 124 pages
...three dimensions. 71. In a cube the square of a diagonal is three times the square of an edge. 72. Prisms are to each other as the products of their bases by their altitudes. (25.) 74. Polygons formed by parallel planes cutting a pyramid are as the squares of their distances...
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An Elementary Geometry and Trigonometry

William Frothingham Bradbury - Geometry - 1872 - 238 pages
...three dimensions. 71. In a cube the square of a diagonal is three times the square of an edge. 72. Prisms are to each other as the products of their bases by their altitudes. (25.) 73. Prisms \vith equivalent bases are as their altitudes; with equal altitudes, as their bases....
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