Cavalieri’s Principle

Bonaventura Cavalieri Born in 1598 in Milan, Italy Joined the Jesuati that followed the rule of St. Augustine Greatly influenced by the work of Euclid Met Galileo and followed his work

Appointed Professor of Mathematics at the University of Bolgna Developed Method of Indivisibles

Published work, entitled “Geometria Indivisibilibus Coninuorum Nova Quadam Ratione Promota” or “A Certain Method for the Development of a New Geometry of Continuous Indivisibles” His published work was not taken well

In reply to the criticism, he wrote “Exercitationes Geometricae Sex” or “Six Geometrical Exercises” After which, the Method of Indivisibles (or Cavalieri’s principle) became widely accepted

Method of Indivisibles Also known as Cavalieri’s principle “Cavalieri’s principle says that solids with equal altitudes and identical cross-sectional areas at each height have the same volume. This follows immediately from the definition of volume, because the cross-sectional area function A(x) and the interval [a,b] are the same for both solids”(Hass, Weir, & Thomas, 2006, p. 393).

Turn to a partner and discuss how you would state that definition in your own words. – Use this illustration, if necessary

Works Cited Hass, J., Weir, M. D., & Thomas, G. B. (2006). University Calculus (1st ed.). Addison Wesley. Bonaventura Cavalieri (Italian mathematician) -- Britannica Online Encyclopedia. (n.d.).Encyclopedia Britannica. Retrieved November 26, 2012, from /Bonaventura-Cavalieri