 | Charles Davies - Geometry - 1854 - 436 pages
...the second, each to each (B. vI., P. 18). Hence, the two sections NOPQR, STVXY, are equal polygons. Cor. Every section of a prism, parallel to the bases,...THEOREM. If a pyramid be cut by a plane parallel to its base: 1st. The edges and the altitude will be divided proportionally : 2d. The section will be... | |
 | Edward Brooks - Geometry - 1868 - 284 pages
...into one-half of the slant height SH; that is, the convex surface of the pyramid equals THEOREM IX. If a pyramid be cut by a plane parallel to the base; 1. The edges and altitude will be divided proportionally. 2. The section will be a polygon similar to the base. Let... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...parallel to the bases, are equal in all their parts. PROPOSITION III. THEOREM. If a pyramid be out by u plane parallel to the base ' 1°. The edges and the...The section will be a polygon similar to the base. 1°. The edges and altitude will be divided proportionally. Fo1, conceive a plane to be passed through... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...of a prism, and every section of a prism, parallel to the bases, are equal in all their parts. — PROPOSITION III. THEOREM. If a pyramid be cut by a...The section will be a polygon similar to the base. Let the pyramid S-ABCDE, whose altitude is SO, be cut by the plane abode, parallel to the base ARCDE,... | |
 | Isaac Sharpless - Geometry - 1879 - 282 pages
...multiplied by ha/f the slant height. Proposition 12. Theorem.—If a plane be passed cutting a pyramid parallel to the base— 1. The edges and the altitude will be cut proportionally. 2. The section is a figure similar to the base. 1. Let a plane cut the cone A-BCD... | |
 | Simon Newcomb - Geometry - 1881 - 418 pages
...plane parallel to the base, that part which remains is called a frustrum of a pyramid. THEOREM IX. 699. If a pyramid be cut by a plane parallel to the base, then — I. The edges and the altitude are similarly divided. II . The section is similar to the base.... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...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. 1°. The edges... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 522 pages
...volume of any prism is equal to the product of the area of its base by its altitude. PROPOSITION XV. If a pyramid be cut by a plane parallel to the base: I. The edges and altitude are divided proportionally. II. The section is a polygon similar to the base... | |
 | John Macnie - Geometry - 1895 - 386 pages
...lower base 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 :... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 344 pages
...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 to the base, (1) the edges and altitude are divided proportionally, (2) the section is similar to the base. If the planes in the above... | |
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The upper end of the frustum of a pyramid or cone is called the upper base... 
