 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,...  Plane and Solid Geometry - Page 270by Elmer Adelbert Lyman - 1908 - 340 pagesFull view - About this book
 | George Albert Wentworth - Geometry - 1899 - 498 pages
...PROPOSITION XV. THEOREM. 645. 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, d, e,... | |
 | George Albert Wentworth - Geometry, Solid - 1899 - 248 pages
...PROPOSITION XV. THEOREM. 645. 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, d, e,... | |
 | William James Milne - Geometry - 1899 - 396 pages
...diagonals of a four.sided prism pass through a common point, the prism is a parallelopiped. Ex. 817. If a pyramid is cut by a plane parallel to its base, the pyramid cut off is similar to the given pyramid. Ex. 818. The lateral area of a right prism is... | |
 | Harvard University - Geometry - 1899 - 39 pages
...Corollary. The volume of any prism is equal to the product of its base and its altitude. THEOREM XI. If a pyramid is cut by a plane parallel to its base, 1st, the edges and the altitude are divided proportionally; 2d, the section is a polygon similar to... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...PROPOSITION XIV. THEOREM 586. If a pyramid be cut by a plane parallel to its base : (1) TJie lateral edges and the altitude are divided proportionally. (2) The section is a polygon similar to the base. Hyp. Pyramid O-ABCD is cut by plane II to the base, E, F, G, H are the points of intersection with... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...PROPOSITION XIV. THEOREM 586. If a pyramid be cut by a plane parallel to its base : (1) Tlie lateral edges and the altitude are divided proportionally. (2) The section is a polygon similar to the base. Hyp. Pyramid 0-ABCD is cut by plane II to the base, E, F, G, H are the points of intersection with... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...PROPOSITION XIV. THEOREM 586. If a pyramid be cut by a plane parallel to its base : (1) The lateral edges and the altitude are divided proportionally. (2) The section is a polygon similar to the base. Hyp. Pyramid 0-ABCD is cut by plane II to the base, E, F, G, H are the points of intersection with... | |
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...pyramid are all trapezoids, and of a regular pyramid are all equal trapezoids. PROPOSITION XIII 513. If a pyramid is cut by a plane parallel to its base, the edges and the altitude are divided in the same ratio, the section made by the plane is similar... | |
 | George Albert Wentworth - Geometry, Solid - 1902 - 246 pages
...PROPOSITION XV. THEOREM. 645. 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, d, e,... | |
 | George Albert Wentworth - Geometry - 1904 - 496 pages
...PROPOSITION XV. THEOREM. 645. 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, d, e,... | |
| |
