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Cavalieri's Principle

1. If the lengths of every one-dimensional slice are equal for two regions, then the regions have equal Areas.

2. If the Areas of every two-dimensional slice (Cross-Section) are equal for two Solids, then the Solids have equal Volumes.

See also Cross-Section, Pappus's Centroid Theorem


References

Beyer, W. H. (Ed.) CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 126 and 132, 1987.




© 1996-9 Eric W. Weisstein
1999-05-26