 | Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 468 pages
...and call it Prop. XIV. 505. Cor. I. Can you show that any section of a pyramid || to the base is to the base as the square of its distance from the vertex is to the square of the altitude of the pyramid ? Sug. Compare the two polygons with two homologous sides, the segments of an edge, etc. 506. by a... | |
 | Webster Wells - Geometry - 1899 - 180 pages
...from (1), § 514, -JT1A* l^-^l S~\ T>l (§514,1) AB OA = OPI ~ OP' area A'B'C'D' =OP2 area ABCD Hence, the area of a section of a pyramid, parallel to the...vertex is to the square of the altitude of the pyramid. 516. Cor. II. If two pyramids have equal altitudes and equivalent bases, sections parallel to the bases... | |
 | Webster Wells - Geometry - 1899 - 196 pages
...^1_O ^/^l (§514,1) area ABCD Al? A'B' = O^4' AB OA = OP' OP. area^4'B'C'jP'=OP2 area ABCD op2 Hence, the area of a section of a pyramid, parallel to the...vertex is to the square of the altitude of the pyramid. SOLIP GEOMETRY. —BOOK VII. 516. Cor. II. If two pyramids have equal altitudes equivalent bases, sections... | |
 | Harvard University - Geometry - 1899 - 39 pages
...divided proportionally; 2d, the section is a polygon similar to the base ; 3d, 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. If two pyramids have equal altitudes and equivalent bases, sections made by planes parallel... | |
 | George Albert Wentworth - Geometry, Solid - 1899 - 248 pages
...QED 646. COR. 1. Any section of a pyramid parallel to the base is to the base as the square of the distance from the vertex is to the square of the altitude of the pyramid. §338 VO \VAJ AB '"VO2 ZB2 But ___^ ABCDE AB abcde Vo Ax. 1 ABCDE VO 647. COR. 2. If two pyramids having... | |
 | George Albert Wentworth - Geometry - 1899 - 500 pages
...QED 646. COR. 1. Any section of a pyramid parallel to the base is to the base as the square of the distance from the vertex is to the square of the altitude of the pyramid. For ro - ( Va \ - ^L. .Yn__^? \7Zj-Js -'VO'-JB' But __ = ABCDE AIf abcde Vo ' ABCDE VO* Ax. 1 647.... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...polygon EFGH is similar to ABCD. (289) 587. COR. 1. A section of a pyramid parallel to the base is to the base as the square of its distance from the vertex is to the square of the altitude of the pyramid. EFGH : ABCD = EF2 : AJ? (371) But EF2 : AB2 = OE.:OA' = ON* : OM2. (Why ?) ... EFGH : ABCD = ON2 :... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...polygon EFGH is similar to ABCD. (289) 587. COR. 1. A section of a pyramid parallel to the base is to the base as the square of its distance from the vertex is to the square of the altitude of the pyramid. EFGH :ABCD = EF2 : AB2 (371) But EF2 : AT? = OE2 : OZ2 = ON* : OM2. (Why ?) .-. EFGH: ABCD = ON2 :... | |
 | Arthur Schultze - 1901 - 392 pages
...polygon EFGH is similar to ABCD. (289) 587. COR. 1. A section of a pyramid parallel to the base is to the base as the square of its distance from the vertex is to the square of the altitude of the pyramid. EFGH : ABCD =EF':AB' (371) But 'EF.AB = OE:OA=ON':OM. (Why?) .-. EFGH: ABCD = ON2 : OM\ 588. COR. 2.... | |
 | George Albert Wentworth - Geometry, Solid - 1902 - 248 pages
...QED 646. COR. 1. Any section of a pyramid parallel to the base is to the base as the square of the distance from the vertex is to the square of the altitude of the pyramid. Vo f Va\ ab Vo ab But ABCDE AB* abcde _ Vo ABCDE ~ VO 2 Ax. 1 647. COR. 2. If two pyramids having equal... | |
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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. 
