Elements of Solid Geometry
Elements of Solid Geometry
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In our eReader you can find the full English version of the book. Read Elements of Solid Geometry Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Elements of Solid Geometry
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The lateral faces of a frustum of a regular pyramid are congruent isosceles trape- zoids and its slant height is the altitude of any lateral face.
645. The lateral edges of a regular pyramid are equal, and the lateral faces of a regular pyramid are equal.
PROPOSITION XIII. THEOREM.
646. The lateral area of a regular pyramid is equal to half the product of the slant height by the perimeter of the base.
Given A-BCDEF, a regular pyramid, L its slant height, P the perimeter of its base, and S its l...ateral area.
To prove S = \ L x P.
Proof. The lateral faces ABC, ACD, etc. , are equal isos- celes A. 645 The common slant height L is the altitude of each A. . '. The area of each lateral face is = \L x its base. 425 . '. The sum of all the lateral faces =\ L X sum of bases.
But the sum of the bases = P.
Q E. D POLYHEDRONS. 49 647. COR. The lateral area of the frus- tum of a regular pyramid is equal to half the product of the slant height multiplied by the sum of the perimeters of its bases. If P is the perimeter of its lower base and p is the perimeter of its upper base, then S = % (P+P)L.
What to read after Elements of Solid Geometry?
You can find similar books in the "Read Also" column, or choose other free books by W H William Herschel Bruce to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
The lateral faces of a frustum of a regular pyramid are congruent isosceles trape- zoids and its slant height is the altitude of any lateral face.
645. The lateral edges of a regular pyramid are equal, and the lateral faces of a regular pyramid are equal.
PROPOSITION XIII. THEOREM.
646. The lateral area of a regular pyramid is equal to half the product of the slant height by the perimeter of the base.
Given A-BCDEF, a regular pyramid, L its slant height, P the perimeter of its base, and S its l...ateral area.
To prove S = \ L x P.
Proof. The lateral faces ABC, ACD, etc. , are equal isos- celes A. 645 The common slant height L is the altitude of each A. . '. The area of each lateral face is = \L x its base. 425 . '. The sum of all the lateral faces =\ L X sum of bases.
But the sum of the bases = P.
Q E. D POLYHEDRONS. 49 647. COR. The lateral area of the frus- tum of a regular pyramid is equal to half the product of the slant height multiplied by the sum of the perimeters of its bases. If P is the perimeter of its lower base and p is the perimeter of its upper base, then S = % (P+P)L.
What to read after Elements of Solid Geometry?
You can find similar books in the "Read Also" column, or choose other free books by W H William Herschel Bruce to read onlineMoreLess
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