Mixed Mathematics 169“Galileo and the Mixed Sciences,” in Method and Order in Renaissance Philosophy of
Nature: The Aristotle Commentary Tradition, ed. Daniel A. Di Liscia, Eckhard Kessler, and
Charlotte Methuen (Aldershot, UK: Ashgate, 1997), 253–70, who stresses the differ-
ences between Galileo’s concern with demonstrative truth and the concern by Jesuits
and others with the hypothetical dimensions of a “mixed” science like astronomy.
- J. B. Baliani, De motu naturali (Genoa, 1646), 8: “Rimari caepi; an deprehen-
derim aliorum erit iudicium” (unless otherwise noted, all translations in this chapter
are mine). - Ibid., 97–98: “Hactenus mihi videor de scientia motus naturalis gravium soli-
dorum satis pro viribus dixisse, dum ex quibusdam proprietatibus sensui notis, plures
ignotae deductae, & patefactae sunt: in hoc enim solummodo ex Aristotele omnis
scientia versatur; ut in praxi apud Euclidem, & alios, qui veras, & simplices scientias
tractant, videre est: unde nec agit Geometra de natura quantitatis, nec Musicus de
natura soni, nec perspectivus de natura luminis, nec mechanicus de natura ponderis.
At vero meus intellectus non omnino acquiescit, ni causas priores, à quibus his effectus
demum proveniunt, si non assequatur, saltem investiget.. .” - Ibid., 98: “non effectus, sed rerum naturae”; 98–102. See, for a discussion of
Baliani’s physical account of fall, Serge Moscovici, L’expérience du mouvement: Jean-
Baptiste Baliani disciple et critique de Galilée (Paris: Hermann, 1967), 56–72. Baliani’s
account resembles Fabri’s; see Dear, Discipline and Experience, 138–44 on Honoré Fabri,
Baliani, and their related criticisms of Galileo’s assertions concerning falling bodies;
also Bertoloni Meli, Thinking with Objects, 120–26; Carla Rita Palmerino, “Two Jesuit
Responses to Galileo’s Science of Motion: Honore’ Fabri and Pierre Le Cazre,” in The
New Science and Jesuit Science: Seventeenth- Century Perspectives, ed. Mordechai Feingold
(Dordrecht: Kluwer, 2003), 187–227. - Beeckman, Journal tenu par Isaac Beeckman de 1604 à 1634, ed. Cornelis de
Waard (The Hague: Martinus Nijhoff, 1939–1953), 4 vols., 1:244. “Hic Picto cum
multis Jesuitis alijsque studiosis virisque doctis versatus est. Dicit tamen se nunquam
neminem reperisse, praeter me, qui hoc modo, quo ego gaudeo, studendi utatur ac-
curatèque cum Mathematicâ Physicam jungat. Neque etiam ego, praeter illum, nemini
locutus sum hujusmodi studij.” “Picto” is Descartes: see Journal, 1:237. - Ibid., 1:244: “Physico- mathematici paucissimi.” Beeckman generally preferred
the formulation “mathematico- physica”; see, e.g., Journal, 4:196, 200, a letter of 1630
to Descartes where Beeckman is concerned about his priority. See esp. Desmond M.
Clarke, Descartes: A Biography (Cambridge: Cambridge University Press, 2006), 46–52,
and Klaas van Berkel, “Descartes’ Debt to Beeckman: Inspiration, Cooperation, Con-
fl ict,” in Descartes’ Natural Philosophy, ed. Stephen Gaukroger, John Schuster, and John
Sutton (London: Routledge, 2000), 46–59. - Stephen Gaukroger, Descartes: An Intellectual Biography (Oxford: Clarendon
Press, 1995), ch. 3; Stephen Gaukroger and John A. Schuster, “The Hydrostatic Paradox
and the Origins of Cartesian Dynamics,” Studies in History and Philosophy of Science 33
(2002): 535–72, esp. 550–58; William R. Shea, The Magic of Numbers and Motion: The
Scientifi c Career of René Descartes (New York: Science History Publications, 1991), 77–86. - Dear, Discipline and Experience, 168–79; note the disagreement with Gauk-
roger and Schuster, “Hydrostatic Paradox,” 537n2, who underestimate the new term’s
fl exibility.