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Le problème du continu pour la mathématisation galiléenne et la géométrie cavalierienne

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What reasons can a physicist have to reject the principle of a mathematical method, which he nonetheless uses (even in an implicit way) and which he used frequently in his unpublished works? We are concerned here with Galileo’s doubts and objections against Cavalieri’s “geometry of indivisibles.” One may be astonished by Galileo’s behaviour: Cavalieri’s principle is implied by the Galilean mathematization of naturally accelerated motion; some Galilean demonstrations in fact hinge on it. Yet, in the Discorsi (1638) Galileo seems to be opposed to this principle. e fundamental reason of Galileo’s reluctance with respect to Cavalieri’s geometry is to be sought in Galileo’s ideal of intelligibility. It is true that Galilean physics, and more particularly Galileo’s theories of motion and matter, faces deep paradoxes, which Cavalieri’s geometry succeeds to avoid, thanks to a clear determination of the concept of “aggregatum.” But while avoiding these difficulties, Cavalieri does not furnish any solution for the problems raised by Galilean physics.

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1. Archives Internationales d'Histoire des Sciences 00039810 1998; Vol 48: 65
2. Vivarium 00427543 2004; Vol 42: 86 http://dx.doi.org/10.1163/1568534042066910
3. Archive for the History of Exact Sciences 00039519 1985; Vol 31: 291
http://brill.metastore.ingenta.com/content/journals/10.1163/157338210x516260
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/content/journals/10.1163/157338210x516260
2010-01-01
2016-12-10

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