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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: Plane and Solid - Page 272
by John Macnie - 1895 - 374 pages
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...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, two prisms of the...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...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, two prisms of the...
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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...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. 5 lOvery prism...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1863 - 464 pages
...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 altitudes. Prisms...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 - 284 pages
...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 altitudes; prisms...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
...common altitude, which is the base ABCDE of the given prism multiplied by its altitude. 39. Corollary. Prisms having equivalent bases are to each other as...equal altitudes are to each other as their bases ; and any two prisms are to each other as the products of their bases and altitudes. PYRAMIDS. 40. Definitions....
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1872 - 382 pages
...common altitude, which is the base ABCDE of the given prism multiplied by its altitude. 39. Corollary. Prisms having equivalent bases are to each other as...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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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 Special Or Elementary Geometry

Edward Olney - Geometry - 1872 - 472 pages
...; and prisms of the same or equivalent bases are to each other as their altitudes; and, in general, prisms are to each other as the products of their bases and altitudes. PROPOSITION XIL 491. Theorem. — The volume of a right cylinder of revolution is equal to the product...
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A Treatise on Special Or Elementary Geometry, Volumes 1-2

Edward Olney - Geometry - 1872 - 562 pages
...; and prisms of the same or equivalent bases are to each other as their altitudes; and, in general, prisms are to each other as the products of their bases and altitudes. PROPOSITION XH. 49 1. Theorem. — The volume of a cylinder of revolution is equal to the product of...
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