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 ?
The total volume of white matter, V(wm), was calculated from Cavalieri's principle (Gundersen et al.
Thus, we evaluated the impact of VCT with the Vasotrain-447 on diabetic foot ulcers using the stereological method based on Cavalieri's principle.
In this research, we estimated before and after treatment the foot ulcer surface area stereologically using the regular point-counting grid method based on Cavalieri's principle [14-15].