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).
Cavalieri's Principle
See also
Cross Section, Pappus's Centroid Theorem, Section, Shear, Volume, Volume TheoremExplore with Wolfram|Alpha
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.Referenced on Wolfram|Alpha
Cavalieri's PrincipleCite this as:
Weisstein, Eric W. "Cavalieri's Principle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CavalierisPrinciple.html