Cavalieri's Principle

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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.

References in periodicals archive ?
In the early seventeenth century, Bonaventura Cavalieri and his circle also looked inside geometric shapes, arguing that you could establish the equivalence of two triangles, for example, by adding all the lines together that made them up.