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" THEOREM. 611. -A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism, and whose vertices are the three vertices of the inclined section. "
A Treatise on Elementary Geometry: With Appendices Containing a Collection ... - Σελίδα 219
των William Chauvenet - 1872 - 368 σελίδες
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Elements of Geometry Upon the Inductive Method: To which is Added an ...

James Hayward - 1829 - 172 σελίδες
...plane DEF were inclined to the base, we should say — A truncated triangular prism is equivalent to three pyramids whose common base is the base of the prism, and whose heights are respectively equal to the distances of the opposite vertices from the base. 255. As all...

An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - 1837 - 159 σελίδες
...base of the truncated prism is the same as the base of the prism from which it is cut. 392. Theorem.. A truncated triangular prism is equivalent to the sum of three pyramids, which have for their common base the base of the prism, and for their vertices the three vertices of...

An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - 1847 - 150 σελίδες
...base of the truncated prism is the same as the base of the prism from which it is cut. 392. Theorem. A truncated triangular prism is equivalent to the sum of three pyramids, which have for their common base the base of the prism, and for their vertices the three vertices of...

A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1871 - 368 σελίδες
...same expression as for that of the triangular frustum ; namely, TRUNCATED TRIANGULAR PRISM. x _<"'* v PROPOSITION XXII.— THEOREM. 60. A truncated triangular...dividing the truncated prism into the three pyramids, E-ABC, E-ACD and E-CDF. The first of these pyramids, E-ABC, has the base AB C and the vertex E. The...

A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1871 - 368 σελίδες
...volume of the given frustum the same expression as for that of the triangular frustum ; namely, \p\ TRUNCATED TRIANGULAR PRISM. PROPOSITION XXII.— THEOREM....of three pyramids whose common base is the base of Hie prism, and whose vertices are the three vertices of the inclined section. Let ABC-DEF be a truncated...

Catalogue - Harvard University

Harvard University - 1876
...section of a pyramid made by a plane parallel to the base is a polygon similar to the base. 6. Prove that a truncated triangular prism is equivalent to the sum of three pyramids, which have for their common base the base of tlie prism, and for their vertices the three vertices...

Elements of Plane and Solid Geometry

George Albert Wentworth - 1877 - 398 σελίδες
...bases is equivalent to a mean proportional between their equivalents. PROPOSITION XXI. THEOREM. 581. A truncated triangular prism is equivalent to the...vertices are the three vertices of the inclined section. F Let AB CD EF be a truncated triangular prism, wiose base is ABC, and inclined section DE F. We are...

Elements of Plane and Solid Geometry

George Albert Wentworth - 1877 - 398 σελίδες
...between their equivalents. PROPOSITION XXI. THEOREM. 581. A truncated triangular prism is equivalent fo the sum of three pyramids whose common base is the...vertices are the three vertices of the inclined section. D, Let AB CD EF be a truncated triangular prism whose base is ABC, and inclined section DE F. We are...

Elements of Plane and Solid Geometry

George Albert Wentworth - 1877 - 398 σελίδες
...equivalents: PROPOSITION XXI. THEOREM. 581. A truncated triangular prism is equivalent to the »um of three pyramids whose common base is the base of...vertices are the three vertices of the inclined section. F Д Let AB CD EF be a truncated triangular prism whose base is ABC, and inclined section DE F. We...

An Elementary Geometry: Plane, Solid, and Spherical : with Numerous ...

William Frothingham Bradbury - 1877 - 240 σελίδες
...pyramid C-ABE is equivalent to B-DEF. Therefore the truncated triangular prism ABC -DEF is equivalent to three pyramids whose common base is the base of the...vertices are the three vertices of the inclined section. 771 Cor. 1. If the truncated triangular prism is right, the three lateral edges will be the altitudes...




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