The volumes (or areas) of two solids (or plane figures) are equal if the areas (or lengths) of corresponding sections drawn parallel to some given plane (or line) are equal. This statement, already familiar to the ancient Greeks, is generally called Cavalieri's principle, although B. Cavalieri (1635) did not accept it as a principle, but proved it.
Cavalieri principle. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Cavalieri_principle&oldid=25123