Bonaventure Cavalieri

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Bonaventure Cavalieri

Bonaventure Francesco Cavalieri (* 1598 probably in Milan ; † December 3 or November 30, 1647 in Bologna ; with scholar name Cavalerius ) was an Italian Jesuit , mathematician and astronomer .


Bonaventura Cavalieri worked in the field of geometry and taught at the University of Bologna . At the same time he was the prior of a Jesuit monastery. His calculations of surfaces and volumes anticipate methods of calculus .

Cavalieri became known mainly through the principle of indivisibility . This principle had already been used in a preliminary form by Johannes Kepler in 1604 and 1615 . The early version of 1635 assumes that a line is made up of an infinite number of points with no size, a surface is made up of an infinite number of lines with no width, and a body is made up of an infinite number of surfaces without height. In response to objections, he reformulated the principle and so published it in 1647 with a defense of the theory. In 1653 his works were reissued with later corrections.

The Cavalierian principle states that two bodies have the same volume if all plane cuts have the same area, which are made parallel to a given basic plane and at the same intervals.

Stefano degli Angeli (1623–1697) was his pupil. He wanted Michelangelo Ricci and Evangelista Torricelli as editors of his posthumous writings. Torricelli died shortly before him and Ricci couldn't find time. They weren't published until 1919.


  • Lo specchio ustorio , 1632
  • Geometria indivisibilibus , 1635
  • Exercitationes Geometricae , 1647



  • Amir R. Alexander: The struggle for the infinitely small . In: Spectrum of Science, October 2015 issue ( )

Web links

Commons : Bonaventura Cavalieri  - collection of images, videos and audio files

Individual evidence

  1. Jürgen Elstrodt: Measure and integration theory. 4th edition, Springer, Berlin 2005, ISBN 3-540-21390-2 , p. 167.