 | William Guy Peck - Conic sections - 1876 - 412 pages
...be proved. Cor. 1. The section QS, is to the base CE, as the square of the distance of the section from the vertex, is to the square of the altitude of the pyramid. For, the section being similar to the base, we have, (P. 12, Cor. 2, B. 4), PQRS : ACDE : : PQ2 : AC2.... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...to the base ABCDE. § 278 QED 666. COROLLARY 1. Any section of a pyramid, parallel to its base is to the base as the square of its distance from the vertex is to the square of the altitude of the pyramid. Since Il_fZ*)=£*. VO \VB/ AB T~o2 ~¿Tbz Squaring = о ab с de ab Bllt (similar polygons are to each... | |
 | George Bruce Halsted - Geometry - 1885 - 389 pages
...a plane parallel to its base, the section is to the base as the square of the perpendicular on it, from the vertex > is to the square of the altitude of the pyramid. The section and base are similar, since corresponding diagonals cut them into triangles similar in... | |
 | William Chauvenet - Geometry - 1887 - 346 pages
...the base. Corollary I. If a pyramid is cut by a plane parallel to its base, the area of the section is to the area of the base as the square of its distance...vertex is to the square of the altitude of the pyramid. Corollary II. If two pyramids have equal altitudes and equivalent bases, sections made by planes parallel... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...IB~"BC~~CD"" > 40. COROLLARY I. If a pyramid is cut by a plane parallel to its base, the area of the section is to the area of the base as the square of its distance...vertex is to the square of the altitude of the pyramid. For but ab IB Sa SA Therefore abcde ABODE'' So SO' 41. COROLLARY II. If two pyramids have equal altitudes... | |
 | William Chauvenet - Geometry - 1888 - 346 pages
...similar. _JJ 40. COROLLARY I. If a pyramid is cut by a plane parallel to its base, the area of the section is to the area of the base as the square of its distance from the vertex is to the square of ilie altitude of the pyramid. For abcde of? , TT7 but ab = Sa = So AB SA ~ SO' Therefore abcde So*... | |
 | Seth Thayer Stewart - Geometry - 1891 - 428 pages
...AB CDEFG being any pyramid, etc. Corollary I. If a cross section is parallel to the base, its area is to the area of the base, as the square of its distance from the apex is to the square of the altitude of the pyramid. Corollary II. If two or more pyramids have equal... | |
 | George Albert Wentworth - Geometry - 1888 - 466 pages
...similar to the base ABCDE. § 319 QE o. 599. COR. 1. Any section of a pyramid parallel to its base is to the base as the square of its distance from the vertex is to the square of the altitude of the pyramid. Vo_fVb_\_ab . Vo^ _ a? g qf., --- - ~ But abcde =-gL-. §376 ABCDE N abcde Vo ABCDE vO2 600. COR. 2.... | |
 | William Chauvenet - 1893 - 340 pages
...the base. Corollary I. If a pyramid is cut by a plane parallel to its base, the area of the section is to the area of the base as the square of its distance...vertex is to the square of the altitude of the pyramid. Corollary II. If two pyramids have equal altitudes and equivalent bases, sections made by planes parallel... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...is a polygon similar to the base. 599. Cor. 1. Any section of a pyramid parallel to its base is to the base as the square of its distance from the vertex is to the square of the altitude of the pyramid. 600. Cor. 2. If two pyramids having equal altitudes are cut by planes parallel to their bases, and... | |
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If a pyramid is cut by a plane parallel to its base, the area of the section is to the area of the base as the square of its distance from the vertex is to the square of the altitude of the pyramid. 
