The author wishes to thank Michael Hunter for his valuable comments and suggestions on earlier drafts of this essay and to acknowledge the support provided by the Gustav Kettel-Stiftung, Königswinter.

As far as possible, the works of Thomas Hobbes are quoted from the first editions; in addition, the locations in the editions of Sir William Molesworth, London, 1839-1845, English Works, 11 volumes, and Opera Latina, 5 volumes (subsequently quoted as: EW, respectively OL) are indicated. The Elements of Law, Natural and Politic, are quoted from the edition of Ferdinand Tonnies (2nd edn, London, 1969; subsequently quoted as: Elements).

¹ For a comprehensive survey on Hobbes and the historians of mathematics see Schuhmann, Karl, ‘Geometrie und Philosophie bei Thomas Hobbes’, Philosophisches Jahrbuch (1985), 92, 161–77Google Scholar, especially 171f, and Breidert, Wolfgang, ‘Les mathematiques et la méthode mathématique chez Hobbes’, Revue Internationale de Philosophie (1979) 33, 415–31.Google Scholar

² Cf. De Morgan, August, A Budget of Paradoxes, 2nd edn (ed. Smith, David E.), 2 vols., n.p., 1915 (reprinted Freeport, New York, 1969), i, 110Google Scholar; Hoffmann, J. C. V., ‘Zur Geschichte der Mathcmatik (Der englische Philosoph Hobbes als Mathematiker)’, Zeitschrift für mathematischen und naturwissenschaftlichen Unterricht (1902), 32, 262–7, especially 265Google Scholar; Boyer, Carl B., The History of the Calculus and Its Conceptual Development, 2nd edn, New York, 1949 (reprinted 1959 etc.), 175–8.Google Scholar

³ Scott, Joseph Frederick, The Mathematical Work of John Wallis, London, 1938 (reprinted New York, 1981), 166–72, quoted from 166Google Scholar. See also Robertson, George Croom, Hobbes, Edinburgh, 1886 (reprinted, New York, 1971), 160–85, especially 162.Google Scholar

⁴ Shapin, Steven and Schaffer, Simon, Leviathan and the Air-Pump, Princeton, 1985, especially chapter 3Google Scholar, ‘Seeing double: Hobbes's politics of plenism before 1660’, 80–109Google Scholar. Mancosu, Paolo and Vailati, Ezio, ‘Torricelli's infinitely long solid and its philosophical reception in the seventeenth century’, Isis (1991), 82, 50–70CrossRefGoogle Scholar; Giorello, Giulio, ‘Pratica geometrica e immagine della matematica in Thomas Hobbes’, in Napoli, Andrea (ed.), Hobbes oggi, Milano, 1990, 215–44.Google Scholar

⁵ The continuation of the discussion between Hobbes and Wallis will be investigated in a sequel to this paper.

⁶ Ward, Seth, A Philosophicall Essay Towards an Eviction of the Being and Attributes of God, The Immortality of the Souls of Men, The Truth and Authority of Scripture, Oxford, 1652Google Scholar, ‘To the Reader’, A3ff (subsequently quoted as: Essay).

⁷ See Hunter, Michael, ‘Science and heterodoxy: an early modern problem reconsidered’, in Lindberg, David C. and Westman, Robert S. (eds.), Reappraisals of the Scientific Revolution, Cambridge, 1990, 437–60.Google Scholar

⁸ Blackbourne, Richard, ‘Vitae Hobbianae auctarium’ in Thomae Hobbes Angli Malmesburiensis philosophi vita, London, 1681, 21–221Google Scholar, reprinted in OL, i, pp. xxii–lxxxGoogle Scholar; cf. p. lxxiii; EW, vii, p. 334, 339.Google Scholar

⁹ Robertson, , op. cit. (3), 169Google Scholar. Metzger, Hans-Dieter, Thomas Hobbes and die Englische Revolution 1640–1660, Stuttgart-Bad Cannstatt, 1991, 188Google Scholar, follows Robertson but makes the important observation that Ward's remarks in the Essay (op. cit. 6) already contain the main elements of later critiques of the Leviathan.

¹⁰ Mintz, Samuel I., The Hunting of Leviathan, Cambridge, 1962, 157.Google Scholar

¹¹ Ibid., 55.

¹² Shapiro, Barbara J., Probability and Certainty in Seventeenth-Century England, Princeton, 1983, 83fGoogle Scholar; see also Hunter, , op. cit. (7), 442.Google Scholar

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¹⁴ Vindiciae academiarum Containing, Some briefe Animadversions upon Mr. Websters Book, Stiled, The Examination of Academies. Together with an Appendix concerning what M. Hobbs, and M. Dell have published on this Argument, Oxford, 1654Google Scholar; reprinted in: Debus, Allen G., Science and Education in the Seventeenth Century. The Webster–Ward Debate, London and New York, 1970, 193–259Google Scholar. (Subsequently quoted as: Vindiciae.)

¹⁵ Although Reik, Miriam M. (The Golden Lands of Thomas Hobbes, Detroit 1977, 83 n. 12)Google Scholar stresses the point that a considerable part of the clergy had been prejudiced against Hobbes already by the publication of De cive, recent research confirms that the Leviathan was to bring about the turning point in the Anglicans' attitude to Hobbes: see Tuck, Richard, ‘The “Christian Atheism” of Thomas Hobbes’, in Hunter, Michael and Wootton, David (eds.), Atheism from the Reformation to the Enlightenment, Oxford, 1992, 111–30.CrossRefGoogle Scholar

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¹⁸ We should bear in mind that the Savilian chairs of geometry and of astronomy did not exist before 1619. The unsettled theological position of the Experimental Philosophy is delineated in chapter 7 of Shapin, and Schaffer, , op. cit. (4), 283–331Google Scholar. See also Malcolm, Noel, ‘Hobbes and the Royal Society’, in Rogers, G. A. J. and Ryan, Alan (eds.), Perspectives on Thomas Hobbes, Oxford, 1988, 43–66, especially 57f.Google Scholar

¹⁹ Essay, ‘To the Reader’, op. cit. (6), A3.Google Scholar

²⁰ Hobbes, Thomas, Humane Nature: or, The Fundamental Elements of Policie, London, 1650Google Scholar (cf. EW, iv, 1–76Google Scholar; Elements, 1–69Google Scholar; subsequently quoted as: Humane Nature). For the question of the authorship of Ward see Tönnies, Ferdinand, Studien zur Philosophie und Gesellschaftslehre im 17. Jahrhundert, Stuttgart-Bad Cannstatt, 1975, 39fGoogle Scholar; see also EW, vii, 336.Google Scholar

²¹ See Pope, Walter, The Life of the Right Reverend Father in God Seth, Lord Bishop of Salisbury, And Chancellor of the Most Noble Order of the Garter. With a Brief Account of Bishop Wilkins, Dr. Isaac Barrow, Mr. Lawrence Rooke, Dr. Turbervile, And others, London, 1697Google Scholar, and Fletcher, J. M. J., ‘Seth Ward, Bishop of Salisbury, 1667–1689’, Wiltshire Archaeological and Natural History Magazine (1940), 49, 1–16, especially 2–5Google Scholar. But see à Wood, Anthony, Athenae Oxonienses (ed. Bliss, Ph.), 3rd edn, 4 vols., London, 1813 (reprinted, 1967), iv, 246–52.Google Scholar

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²³ Ibid., 156f. See also Tuck, , op. cit. (16), p. xxv.Google Scholar

²⁴ So the English translation in the Seven Philosophical Problems (EW, vii, 5fGoogle Scholar). (Quae cum ita sint, lectores meos monitos hic vellem, ne malevolorum convitiis temere credentes aliter de me quam aequum est sentire velint: nec vitio vertant, si contra hostes tuos pugnans, et quaecunque potui tela corripiens, gladio uno usus sum ancipite. OL, iv, p. 303).Google Scholar

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²⁹ See Controversiae de verâ circuli mensurâ anno MDCXLIV exortae, inter Christianum Severini, Longomontanum, Cimbrum, Superiorum Mathematum in Regiâ Danorum Academiâ Havniensi, professorem publicum et loannem Pellium, Coritano-regnum, Anglum, Matheseos, in illustri Amstelodamiensium Gymnasia, professorem publicum, pars prima, Amstelodami, 1647, 46Google Scholar. Three years later, Robert Boyle had informed Samuel Hartlib of the results of (probably anatomical) studies of his; Hartlib communicated the letter to Hobbes who welcomed Boyle's results. See Hartlib, to Boyle, , The Works of the Honourable Robert Boyle (ed. Birch, Thomas), London, 1772, vi, 77Google Scholar; see also Skinner, Quentin, ‘Thomas Hobbes and the nature of the early Royal Society’, The Historical Journal (1969), 12, 232.CrossRefGoogle Scholar

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³³ Vindiciae, op. cit. (14), 6f and 53f.Google Scholar

³⁴ Essay, ‘To the Reader’, op. cit. (6), A3.Google Scholar

³⁵ Vindiciae, op. cit. (14) 57f.Google Scholar

³⁶ Malcolm, , op. cit. (18), 54Google Scholar, observes that the question of the universities became suddenly topical in 1654 when their abolition was proposed in the Barebones Parliament.

³⁷ Johnston, David, ‘Hobbes's Mortalism’, History of Political Thought (1989), 10, 647–63Google Scholar, and Metzger, , op. cit. (9), 241–9, especially 244fGoogle Scholar, point to the fact that Hobbes took up the concept of the mortalism of the soul only after De cive (1642) and published his view for the first time in the Leviathan, at a moment when mortalism – after a period of liberal discussion – had been finally rejected by the presbyterian and the anglican clergy; see also Tuck, , op. cit. (15), 128.Google Scholar

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³⁹ In his subsequent discussion of the same topic with Hobbes, Wallis was quite delicately to maintain a standpoint diametrically opposed to Ward's: see Wallis, John, ‘An answer to four papers of Mr Hobs, lately published in the months of August, and this present September, 1671’, Philosophical Transactions (18 09 1671), 75, 2241–50, especially 2242f.Google Scholar

⁴⁰ Wallis will present a counter-example in his dispute with Hobbes: an infinitely produced line, starting or ending at a fixed point (ibid.).

⁴¹ Cf. North, John D., ‘One truth or more?’, in Unguru, Sabetai (ed.), Physics, Cosmology, and Astronomy, 1300–1700: Tension and Accommodation, Dordrecht, 1991, 253–93, especially 277–83.CrossRefGoogle Scholar

⁴² See OL, i, 334ffGoogle Scholar, For a profound investigation of Hobbes's related discussion of Thomas White's arguments for a creation of the world see Pacchi, Arrigo, ‘Hobbes and the problem of God’, Perspectives on Thomas Hobbes, op. cit. (18), 171–87.Google Scholar

⁴³ Ward, Seth, In Thomae Hobbii philosophiam exercitatio epistolica, Oxford, 1656, 116.Google Scholar

⁴⁴ See OL, i, 88.Google Scholar

⁴⁵ ‘For the effects we acknowledge naturally, do include a Power of their producing, before they were produced; and that Power presupposeth something existent that hath such power: And the thing so existing with power to produce, if it were not Eternal, must needs have been produced by somewhat before it, and that again by something else before that, till we come to an Eternal (that is to say the first) Power of all powers, and first Cause of all causes: And this is it which all men conceive by the Name of GOD, implying Eternity, Incomprehensibility, and Omnipotency.’ (Humane Nature, 1321Google Scholar; cf. EW, i, 591.Google Scholar, Elements, 53f.Google Scholar) It is perhaps worth noting that, from the beginning of the dispute, Hobbes tried to avoid meetings with Ward; see Malcolm, , op. cit. (18), 53, 59Google Scholar and Pope, , op. cit. (21), p. 26.Google Scholar

⁴⁶ Ward, Seth, Against Resistance of Lawful Powers: A Sermon Preached at White-Hall, Novemb. V^th 1661. By Seth Ward, D. D. Chaplain to His Majesty. Published by His Majestie's Command, London, 1661.Google Scholar

⁴⁷ Malcolm, , op. cit. (18), 57.Google Scholar

⁴⁸ Ward, , op. cit. (46), 35.Google Scholar

⁴⁹ Ibid., 2f, 4f, 35.