Cavalieri's Principle

If the areas of the cross sectionsof two solids by any plane parallel to a given plane are invariablyequal, then the two solids have the same volume. This proposi-tion (and the analogous one for plane figures), which was alreadywell-known to ancient Greek mathematicians, is usually calledCavalieri’s principle, although the Italian mathematicianF. B. Cavalieri in his Geometry (1635) does not take it as aprinciple but proves it.