A chronological approach to the Bonaventura Cavalieri’s indivisibles

Abstract

The aim of this paper is to conduct an investigation to determine the date of the appearance of the term indivisible in Cavalieri’s work. When were the term «indivisible» and the expression «way of the indivisibles» first used by Cavalieri? In what situation and with what purpose? To answer these questions, we have chosen to analyse Cavalieri’s correspondence systematically because it gives us privileged access to the appearance and use of the word «indivisible.» A chronological examination of Cavalieri’s surviving writings – notably his correspondence – reveals that the expression «way of the indivisibles», which gives a central role to the indivisibles in the achievement of his new method, does not appear before 1632. As for the term “indivisible,” it was not used until the publication of the two manuscripts setting out his new mathematical approach, the manuscript of the Nova planorum ac solidorum speculatio in sex libros distributa and that of the Planorum et solidorum libri sex, both completed in 1627.