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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 William Henry Harrison Phillips - 1878 - 209 pages
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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - Mathematics - 1872 - 602 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 base» 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: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 500 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...having equal altitudes are to each other as their buses. B PROPOSITION XV. THEOREM. Two triangular pyramids having equal bases and equal altitudes, are...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1875 - 390 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. Any two prisms having equivalent bases and equal altitudes are equivalent. PYRAMIDS....
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1875 - 466 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 other as their base's; and any two prisms are to each other as the product* of their bases and altitudes. Any two...
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Manual of Geometry and Conic Sections: With Applications to Trigonometry and ...

William Guy Peck - Conic sections - 1876 - 376 pages
...of the given prism is equal to the product of its base and altitude, which was to be proved. Cor. 1. Any two prisms are to each other as the products of their bases and altitudes. Cor. 2. Two similar prisms are to each other as the cubes of their homologous edges....
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...that is the entire base by the altitude of the prism. QED 544. COROLLARY. Prisms having equivalent bases are to . each other as their altitudes ; prisms...bases ; and any two prisms are to each other as the product of 'their bases and altitudes. Any two prisms having equivalent bases and equal altitudes are...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...that is the entire base by the altitude of the prism. QED 544. COROLLARY. Prisms having equivalent bases are to each other as their altitudes ; prisms...other as their bases : and any two prisms are to each "'""r as the product of their bases and altitudes. Any two '» urns havi- ^nt bases and equal altitudes...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...323. Cor. 2. Parallelograms having equal bases are to each other as their altitudes ; parallelograms having equal altitudes are to each other as their bases ; and any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V....
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Conic sections - 1880 - 452 pages
...their ba&es. For the same reason, prisms having equivalent bases are to each other as their altitudes ; and any two prisms are to each other as the products of their bases and altitudes. PROPOSITION xu. THEOREM. Similar %irisms are to each other as the cubes of their homologous...
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Elements of Geometry

George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...323. Cor. 2. Parallelograms having equal bases are to each other as their altitudes ; parallelograms having equal altitudes are to each other as their bases ; and any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V....
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