A Companion to Hobbes. Группа авторов

1916. William Oughtred: A Great Seventeenth-Century Teacher of Mathematics. London and Chicago: Open Court.

      7 Cavalieri, Bonaventura. 1635. Geometria Indivisibilibus Continuorum Nova Quadam Ratione Promota. Bologna: J. Monti.

      8 Clavius, Christopher. 1612. Christophori Clavii Bamburgensis E Societate Jesu Opera Mathematica, 5 vols. Mainz: R. Eltz.

      9 Debus, Allen G. 1970. Science and Education in Seventeenth-Century England: The Webster-Ward Debate. London: Macdonald.

      10 Descartes, René. 1964–1996. Œuvres de Descartes, edited by Charles Adam and Paul Tannery. Revised edn. 11 vols. Paris: Vrin. cited asAT

      11 Dunlop, Katherine. 2016. “Hobbes’s Mathematical Thought.” In The Oxford Handbook of Hobbes, edited by Aloysius P. Martinich and Kinch Hoekstra, 76–104. Oxford: Oxford University Press.

      12 Euclid. [1925] 1956. The Thirteen Books of Euclid’s “Elements” Translated from the Text of Heiberg. edited and translated by Thomas L. Heath, 3 vols. Cambridge: Cambridge University Press. Reprint New York: Dover.

      13 Grant, Hardy. 1996. “Hobbes and Mathematics.” In The Cambridge Companion to Hobbes, edited by Tom Sorell, 108–29. Cambridge: Cambridge University Press.

      14 Hobbes, Thomas. 1660. Examinatio et emendation mathematicæ hodiernæ. London: J. Crooke.

      15 Hobbes, Thomas. 1839–1845a. The English Works of Thomas Hobbes, 11 vols., edited by Sir William Molesworth. London: John Bohn. Cited as EW.

      16 Hobbes, Thomas. 1839–1845b. Thomæ Hobbes malmesburiensis opera philosophica, 5 vols., edited by Gulielmi Molesworth. London: John Bohn. Cited as OL.

      17 Hobbes, Thomas. 2012. Leviathan, 2 vols., edited by Noel Malcolm. Oxford: Clarendon Press. [First published 1651].

      18 Huygens, Christiaan. 1888–1950. Les œuvres completes de Christiaan Huygens, edited by La Société Hollandaise des Sciences, 22 vols. The Hague: Nijhoff.

      19 Jesseph, Douglas. 1999. Squaring the Circle: The War between Hobbes and Wallis. Chicago: University of Chicago Press.

      20 Jesseph, Douglas. 2016. “Geometry.” In The Cambridge Descartes Lexicon, edited by Lawrence Nolan, 321–9. Cambridge: Cambridge University Press.

      21 Jesseph, Douglas. 2017. “Hobbes on the Ratios of Motions and Magnitudes: The Central Task of De Corpore, Part III.” Hobbes Studies 30: 59–82.

      22 Jesseph, Douglas. 2018. “Geometry, Religion, and Politics: Context and Consequences of the Hobbes-Wallis Dispute.” Notes and Records of the Royal Society 72: 469–86.

      23 Jesseph, Douglas. 2020. “The Indivisibles of the Continuum: Seventeenth-Century Adventures in Infinitesimal Mathematics.” In The History of Continua: Philosophical and Mathematical Perspectives, edited by Stewart Shapiro and Geoffrey Hellman, 104–22. Oxford: Oxford University Press.

      24 Julien, Vincent. 2016. “Roberval’s Indivisibles.” In Seventeenth-Century Indivisibles Revisited, edited by Vincent Julien, 177–210. Heidelberg, New York, Dordrecht, and London: Springer.

      25 Malcolm, Noel. 2002. “Hobbes and Roberval.” In Aspects of Hobbes, edited by Noel Malcolm, 156–99. Oxford: Oxford University Press.

      26 Mancosu, Paolo. 2008. “Descartes and Mathematics.” In A Companion to Descartes, edited by Janet Broughton and John Carriero, 103–23. Oxford: Blackwell.

      27 Mersenne, Marin. 1644. Cogitata Physico-Mathematica. Paris: Bertier.

      28 Palmieri, Paolo. 2001. “The Obscurity of the Equimultiples: Clavius’ and Galileo’s Foundational Studies of Euclid’s Theory of Proportions.” Archive for History of Exact Sciences 55: 555–97.

      29 Parkin, Jon. 2010. Taming the Leviathan: The Reception of the Political and Religious Ideas of Thomas Hobbes in England (1640–1700). Cambridge: Cambridge University Press.

      30 Peters, Richard. 1956. Hobbes. Harmondsworth: Penguin.

      31 Proclus. 1970. A Commentary on the First Book of Euclid’s “Elements”, edited by Glen R. Morrow. Princeton, NJ: Princeton University Press.

      32 Scott, Joseph F. 1938. The Mathematical Work of John Wallis. London: Taylor and Francis.

      33 Serfati, Michel. 2005. “René Descartes’ Géométrie. ” In Landmark Writings in Western Mathematics, 1640–1940, edited by Ivor Grattan-Guinness, 1–22. Amsterdam: Elsevier.

      34 Serjeanston, Richard. 2006. “Hobbes, the Universities, and the History of Philosophy.” In The Philosopher in Early Modern Europe, edited by Conal Condren, Stephen Gaukroger, and Ian Hunter, 113–39. Cambridge: Cambridge University Press.

      35 Shirley, John W. 1983. Thomas Harriot. Oxford: Oxford University Press.

      36 Viète, François. 1591. In Artem Analyticem Isagoge. Tours: Mettayer.

      37 Wallis, John. 1655. Elenchus Geometriæ Hobbianæ. Oxford: J. Crooke.

      38 Wallis, John. 1693–1699. Johannis Wallis S. T. D. … Opera Mathematica, 3 vols. Oxford: At the Sheldonian Theater.

      39 Ward, Seth. 1654. Vindiciæ Academiarum. Oxford: L. Litchfield.

4 Explanations in Hobbes’s Optics and Natural Philosophy

      MARCUS P. ADAMS

      In the Epistle Dedicatory of De corpore, Thomas Hobbes claimed that in his time natural philosophy was only in its infancy, having been born with work of Copernicus, Galileo, Harvey, Kepler, Gassendi, and Mersenne (EW I.ix). Although he portrayed himself as the progenitor of civil philosophy, Hobbes also saw himself as contributing to the (in his opinion) juvenile disciplines of optics and natural philosophy. For example, he claimed in 1646 in A Minute or First Draught of the Optiques (hereafter Minute) that he would “deserve the Reputation of having beene the first to lay the ground of two Sciences, this of Opticques, the most curious, and that other of naturall Justice, which I have done in my book De cive, the most profitable of all other” (Hobbes 1983 [1646], 622; cf. EW VII.471).

Hobbes’s bombastic appraisals of himself aside, his contemporaries took his work in optics seriously and Mersenne included an optical treatise of Hobbes’s in Ballistica (1644).¹ Hobbes’s 1641 correspondence with Descartes ended with Descartes saying that he “to have nothing more to do with [Hobbes]” because he thought that Hobbes was trying to gain reputation at Descartes’ expense (AT III.320, CSMK 173), but their correspondence shows disagreements between them concerning, for example, refraction in media and the nature of light (see Letters 29–30 and 32–4 in Hobbes 1994a).

Hobbes’s interests in optics should make sense to anyone familiar with the opening chapters of Leviathan. If one seeks to ground all ideas, and thus all knowledge, in sensation, as Hobbes declares in Leviathan chapter 1 (2012, 22; 1651, 3), then developing an optical theory is paramount. Hobbes’s aim in optics, and in natural philosophy generally, was to explain various phenomena in a way that cohered with mechanical philosophy, so, for example, no appeal to species would be permitted. However, rather than looking to Hobbes’s optics and natural philosophy in themselves, the present chapter explores these areas of Hobbes’s thought from another angle: to show that Hobbes’s explanations in optics take the same form as how he understood ideal explanations in natural philosophy. When providing an explanation in both of these disciplines Hobbes appeals both to everyday, unaided sense experience and to geometry. Hobbes explicitly identifies this form of explanation with “mixed-mathematics,” and he goes so far as to say that “true physics” depends upon geometry in this way (Hobbes 1994b [1658], 42; OL II.93).

      First, I discuss Hobbes’s statements about the structure of philosophy and suggest that a focus on these reflections – rather than on Hobbes’s explanatory practice – has led some scholars to understand Hobbes as an armchair speculative philosopher, both in his own natural-philosophy endeavors