Prismoid sentence example

prismoid
  • If R and S are the ends of a prismoid, A and B their areas, h the perpendicular distance between them, and C the area of a section by a plane parallel to R and S and midway between them, the volume of the prismoid is *h(A+4C+B).

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  • The most instructive is to regard the prismoid as built up (by addition or subtraction) of simpler figures, which are particular cases of it.

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  • Then the prismoid is divided into a pyramid with vertex P and base ABCD ..., and a series of tetrahedra, such as PABa or PAab.

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  • By (i) and (iii), the formula holds for each of these figures; and therefore it holds for the prismoid as a whole.

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  • In the ordinary case three of the four lateral surfaces of the prismoid are at right angles to the two ends.

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  • This formula applies to such figures as the cone, the sphere, the ellipsoid and the prismoid.

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  • The proposition can then be established for a prismoid generally by the method of § 27 (iv).

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