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" If a pyramid is cut by a plane parallel to the base : 1. The edges and altitude are divided proportionally. 2. The section is a polygon similar to the base. Let V-ABCDE be cut by a plane parallel to its base, intersecting the lateral edges in a, b, c,... "
New Plane and Solid Geometry - Page 297
by Wooster Woodruff Beman, David Eugene Smith - 1899 - 382 pages
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1863 - 464 pages
...a prism, parallel to the bases, is equal to either base. PROPOSITION III. THEOREM. If a pyramid be cut by a plane parallel to the base : 1°. The edges and the altitude will be divided proportionally : 2°. The section will be a polygon similar to the base....
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 500 pages
...parallel to the bases, are equal in all their parts. — PROPOSITION III. THEOREM. If a pyramid be cut by a plane parallel to the base ' 1°. The edges and the altitude will be divided proportionally: 2°. The section will be a polygon similar to the base....
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Complete Arithmetic: Theoretical and Practical

William Guy Peck - Arithmetic - 1877 - 430 pages
...called Lateral Faces. The lateral faces meet at a point which is called the Vertex of the pyramid. If a pyramid is cut by a plane parallel to the base, the part included between this plane and the base is called a Frustum of a Pyramid. The Altitude of...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...any section of a prism parallel to the bases, are equal in all respects. PROPOSITION III. THEOREM. If a pyramid is cut by a plane parallel to the base : 1*. Th,e edges and the altitude are divided proportionally: 2°. The section is a polygon similar to the base. GEOMETRY....
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 344 pages
...IV, is general ; the center of similitude and the given figures may or may not be in the same plane. COROLLARIES. 1. If a pyramid is cut by a plane parallel...section is similar to the base. If the planes in the above proof are on the same side of V, step 4 proves (1), and step 3 proves (2). 2. In pyramids having...
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...IV, is general ; the center of similitude and the given figures may or may not be in the same plane. COROLLARIES. 1. If a pyramid is cut by a plane parallel...section is similar to the base. If the planes in the above proof are on the same side of V, step 4 proves (1), and step 3 proves (2). 2. In pyramids having...
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Elements of Geometry: Plane and Solid

John Macnie - Geometry - 1895 - 386 pages
...of the frustum ; the parallel section, the upper base. PROPOSITION XI. THEOREM. 545. // a pyramid be cut by a plane parallel to the base : 1°. The edges and altitude will be divided proportionally. 2?. The section is a polygon similar to the base. Given : A pyramid...
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Regents Examination Papers

University of the State of New York. Examination dept - Examinations - 1895 - 436 pages
...angles formed by the edges of any convex polyedral angle is less than four right angles. 4-5 Prove that if a pyramid is cut by a plane parallel to the base the section will be a polygon similar to the base. 6 State and prove the formula for the volume of...
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Documents of the Senate of the State of New York, Volume 11

New York (State). Legislature. Senate - Government publications - 1897 - 1306 pages
...that the sum of two face angles of a triedral angle is greater than the third angle. 5-6 Prove that if a pyramid is cut by a plane parallel to the base, (a) the edges and altitude are divided proportionally, (6) the section is a polygon similar to the...
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Entrance Examinations in Mathematics, 1884 to 1898 [with Supplements to 1900]

Yale University - 1898 - 212 pages
...parallel, (b) If one oí two parallel planes is perpendicular to a straight line, the other is also. 3. If a pyramid is cut by a plane parallel to the base, the edges and altitude are divided proportionally, and the section made is a polygon similar to the...
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