 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...Corollary. The volume of any prism is equal to the product of its base by its altitude. PROPOSITION XIII. 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... | |
 | Edward Albert Bowser - Geometry - 1890 - 414 pages
...and the sides of the base are 24, 20, and 20 inches. SOLID GEOMETRY. Proposition 1 4. Theorem. 623. If a pyramid is cut by a plane parallel to its base : (1) The edges and the altitude are divided proportionally. (2) TJie section is a polygon similar... | |
 | William Chauvenet - 1893 - 340 pages
...Corollary. The volume of any prism is equal to the product of its base by its altitude. PROPOSITION XIII. 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... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...one-half the sum of the perimeters of the bases multiplied by the slant height of the frustum. 598. If a pyramid is cut by a plane parallel to its base, I. The edges and altitude are divided proportionally : II. The section is a polygon similar to the... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 376 pages
...A'C' X A'D' § 73 A'B' ,AB_, A'B'' ~7u? A'C' A'D' A'B' That is, vol. A BCD QED vol. A'B'CD' A'B' 680. COR. If a pyramid is cut by a plane parallel to its...cubes of any two homologous edges. Hint. — Prove the lateral edges divided proportionally and hence the homologous faces of the two pyramids similar... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 574 pages
...the perpendicular distance from the vertex to the plane of the base. PROPOSITION XVIII. THEOREM 693. If a pyramid is cut by a plane parallel to its base : I. The lateral edges and the altitude are divided proportionally. II. The section is a polygon similar... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1898 - 324 pages
...— — .A. A'B' A'C A'D' AB AB AB = xx & 7 1 5 A'B' A'B' AB' „, . vo\. ABCD ~AB' That is, - - = QED 728. COR. If a pyramid is cut by a plane parallel...similar triangular pyramids as shown in the figure. ~OA* vol. O-ABC _ vol. O-ACD _ vol. O-ADE ~vol. OA 'C'D'~ ' Then = vol. OA'B'C' Now apply § 265. vol.... | |
 | Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 468 pages
...pyramid whose vertex is at the center of the cube. Compare the volumes ot the cube and pyramid. 496. If a pyramid is cut by a plane parallel to its base,...each other as the cubes of any two homologous edges. Prove. REGULAR POLYEDRONS. DEFINITION. A regular polyedron is a polyedron whose faces are equal regular... | |
 | Yale University - 1898 - 212 pages
...straight lines at their point of intersection, it is perpendicular to the plane of those lines. 3. If a pyramid is cut by a plane parallel to its base, (a) the edges and altitude are divided proportionally; (b) the section is a polygon similar to the... | |
 | James Howard Gore - Geometry - 1898 - 232 pages
...cone is a truncated cone whose cutting planes or bases are parallel. PROPOSITION IX. THEOREM. 454. If a pyramid is cut by a plane parallel to its base: (1) The edges and the altitude are divided proportionally. (2) The section is a polygon similar to... | |
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If a pyramid is cut by a plane parallel to its base, the... 
