Bonaventura Fransesco Cavalieri (1598-1647) was a disciple of Galileo. The most influential of his books, Geometria Indivisibilibus Continuorum Nova quadam ratione promota, has ben completed in 1629 and published in 1635. The following excerpt, known as Cavalieri's theorem or Cavalieri's principle, is taken from Book VII, Theorem 1, Proposition 1.
If between the same parallels any two plane figures are constructed, and if in them, any straight lines being drawn equidistant from the parallels, the included portions of any one of these lines are equal, the plane figures are also equal to one another; and if between the same parallel planes any solid figures are constructed, and if in them, any planes being drawn equidistant from the parallel planes, the included plane figures out of any one of the planes so drawn are equal, the solid figures are likewise equal to one another.
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