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Cavalieri's Principle


If, in two solids of equal altitude, the sections made by planes parallel to and at the same distance from their respective bases are always equal, then the volumes of the two solids are equal (Kern and Bland 1948, p. 26).


See also

Cross Section, Pappus's Centroid Theorem, Section, Shear, Volume, Volume Theorem

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References

Beyer, W. H. (Ed.). CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 126 and 132, 1987.Harris, J. W. and Stocker, H. "Cavalieri's Theorem." §4.1.1 in Handbook of Mathematics and Computational Science. New York: Springer-Verlag, p. 95, 1998.Kern, W. F. and Bland, J. R. "Cavalieri's Theorem" and "Proof of Cavalieri's Theorem." §11 and 49 in Solid Mensuration with Proofs, 2nd ed. New York: Wiley, pp. 25-27 and 145-146, 1948.

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Cavalieri's Principle

Cite this as:

Weisstein, Eric W. "Cavalieri's Principle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CavalierisPrinciple.html

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