 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.  Solid Geometry - Page 297by Wooster Woodruff Beman, David Eugene Smith - 1900 - 139 pagesFull view - About this book
 | Fletcher Durell - 1911 - 234 pages
...the sum of the perimeters of its bases multiplied by its slant height. PROPOSITION XV. THEOREM 644. If a pyramid is cut by a plane parallel to the base, I. The lateral edges and the altitude are divided proportionally; II. The section is a polygon similar... | |
 | Clara Avis Hart, Daniel D. Feldman, Virgil Snyder - Geometry, Solid - 1912 - 230 pages
...faces of a frustum of a regular pyramid are equal isosceles trapezoids. PROPOSITION II. THEOREM 756. If a pyramid is 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... | |
 | William Herschel Bruce, Claude Carr Cody - Geometry, Solid - 1912 - 134 pages
...parallelopiped whose dimensions are 6 ft., 8 ft., and 36 ft., respectively. PROPOSITION XIV. THEOREM. 648. If a pyramid is cut by a plane parallel to the base, Given the pyramid V-ABCDE cut by the plane QR || the base and intersecting the lateral edges in a,... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...perimeters of the bases multiplied by the slant height of the frustum. PROPOSITION XIV. THEOREM 555. If a pyramid is cut by a plane parallel to the base...altitude are divided proportionally. 2. The section is a polygon similar to the base. Given the pyramid V-ABCDE cut by a plane parallel to its base, intersecting... | |
 | Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1913 - 376 pages
...area ? What is its total area ? Ans. 60 sq. in. ; 96 sq. in. POLYHEDRONS [VII, § 300 300. Theorem IX. If a pyramid is cut by a plane parallel to the base, (a) The altitude and the lateral edges are divided proportionally ; (b) Tiie section is a polygon similar... | |
 | Walter Burton Ford, Charles Ammerman - Geometry, Solid - 1913 - 184 pages
...in. What is its lateral area ? What is its total area ? Ans. 60 sq. in.; 96 sq. in. 300. Theorem IX. If a pyramid is cut by a plane parallel to the base, (a) The altitude and the lateral edges are divided proportionally; (b) The section is a polygon similar... | |
 | Horace Wilmer Marsh - Mathematics - 1914 - 306 pages
...one-half the slant height times the sum of the perimeters of the bases. IX THEOREM 17 // a pyramid be cut by a plane parallel to the base, (1) the edges and the altitude are divided proportionally, (2) the section is a polygon similar to the base. To prove... | |
 | William Betz - Geometry - 1916 - 536 pages
...Tabulate the results obtained, and show that the formula applies in each case. PROPOSITION V. THEOEEM 660. If a pyramid is cut by a plane parallel to the base : 1. The edges and the altitude are divided proportionally. 2. The section made is a polygon similar to the base. v Given... | |
 | John Charles Stone, James Franklin Millis - Geometry, Solid - 1916 - 196 pages
...required to cover it. How many squares (a square is 100 sq. ft.) of slate are required ? 390. Theorem. — If a pyramid is cut by a plane parallel to the base: (1) the lateral edges and the altitude are divided proportionally ; (2) the section is a polygon similar to... | |
 | Ernst Rudolph Breslich - Logarithms - 1917 - 408 pages
...of a cylinder are congruent. 3. All right sections of a cylinder are congruent. • 260. Theorem: // a pyramid is cut by a plane parallel to the base:...altitude are divided proportionally. 2. The section is a polygon similar to the base. 3. The areas of the section and the base are proportional to the squares... | |
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