A seventeenth-century geometrical debate

References

• Paris: Vrin et Centre national de la recherche scientifique, 1973. See Jacquot Jean Notes on an unpublished work of Thomas Hobbes Notes and Records of the Royal Society May 1952 9 B.N. fonds lat. 6566A.
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• De mundo 236 – 239 . Paris MS., fols 242–261v; Hobbes, De corpore (Latin, 1655; English, 1656), Ch. 14, Articles 7–16; Wallis, Opera mathematica, Oxford, 1693–9, vol. ii, pp. 605–630. Additional material on White, by the present writer, appeared in Notes and Queries 20, No. 10 (October 1973), 381–388. On the Hobbes-Wallis argument see his ‘Mid seventeenth century science: some polemics’, Osiris 9, 1950, 254–274.
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• Euripides Phoenissae 1372 1372
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• Barrow . 1842 . Works , edn. Vol. i , xli – xli . Edinburgh
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• Evelyn . May 1651 . Diary May , 25
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• Commercium epistolicum 3 – 3 . 11, 14, 24, 121, 155. A French translation is found in P. Tannery's and Charles Henry's edition of Fermat, Œuvres (1896), vol. iii, pp. 402–610; and the originals are reprinted in Wallis, Opera mathematica, edn. cit., vol. ii, pp. 757–860. It is perhaps unfortunate that John Collins (considered in the narrative) chose, or pitched on, an identical title for his collection of Newtoniana (1712); and at least two similar duplications of title, both occurring in 1668, are met with: Michael Angelo Ricci, Exercitatio geometrica (reviewed in Phil. Trans., 2, no. 37, pp. 736 ff.), and James Gregory, Exercitationes geometricae. That Wallis may have had direct knowledge of White's work is suggested by his referring (Hobbes, English Works, vol. vii, p. 268, Six lessons) to a humorous dictum of White's (De Mundo, pp. 175, 199): in Wallis's words, ‘the skipping of a flea is not propagated to the Indies’. But of course the instance may not be of White's invention. Wallis mentions no source.
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• 1673 . Regulae munitionum analogicae, earumque ex methodo Fritagii et Dogenii usus compendiosus Brussels Dogenius is Matthias Dögen and the work referred to is his Architechnia militaris moderna (Amsterdam, 1647). Of the others, copies are found in the Bibliothèque Nationale, Paris.
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• E.g. Physics 6 1 1 (231.b.3; 233.b.15, 32) and 6, 10 (241.a.16); Metaphysics 5, 13 (1020.a.7); De gen. et corrupt., 1, 2 (316.a.15-317.a.13). Compare Barrow's discussion in Lectio mathematica xix, p. 139, in the sectionally paginated Mathematical works, ed. Whewell (Cambridge, 1860).
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• De mundo 41 – 41 . Paris MS., fol. 18.
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• Cavalieri's method is noticed by Lect. math. Barrow xi 167 167 See also Hobbes, EW, vol vii (Three papers presented to the Royal Society against Dr. Wallis, 1671), p. 432, and Opera latina (Molesworth) vol. iv (Examinatio et emendatio mathematicae hodiernae, 1660), p. 25.
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• Galileo Two new sciences New York1914 30 52 tr. Henry Crew and Alfonso de Salvio First Day Hobbes, Paris MS., fol. 357v.
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• De mundo 9 – 17 . 295; Paris MS., fols. 8, 9v, 245, 329v; Hobbes, De corpore (EW, vol. i), Ch.7, Art. 12.
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• De mundo 108 – 108 . Paris MS., fol. 114. ‘A superficies or solid,’ says Wallis, ‘may be supposed so constituted as to be infinitely long but finitely great, the breadth continually decreasing in greater proportion than the length increaseth.’ Hobbes calls this madness (EW, vol. vii, Considerations upon the answer of Doctor Wallis to the three papers, pp. 444–445).
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• De mundo 282 – 282 . Paris MS., fol. 310v. Compare some ‘Animadversions of Dr. Wallis upon Mr. Hobbes's late book, De principiis et ratiocinatione geometrarum. Written to a friend’. (Phil. Trans. (1666), 1, no. 16, 289 ff.) Since, as has been shown, White has attacked Descartes, it may be noted that the Cartesian interpretation of the word ‘surface’ occurs in the replies made by several theologians and philosophers, excluding Hobbes, to Descartes's Méditations. The discussion will be found in Descartes, Œuvres, ed. Adam et Tannery, vol. ix (1904), p. 234 of the Réponses sixièmes section.
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• E.g. Hobbes's Opera latina Vol. iv , 74 – 75 . (Examinatio et emendatio).
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• Lect. math. 143 – 143 . no. ix
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• Lect. math. 247 247 no. xv (on incommeasurables).
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• Cf. Walker 35 37 68–71. Barrow (Lect. xv, p. 248) used the words ‘minus assignabili quavis quantitate’. See below, the Appendix on White's Tutela, and also Stigmai … or marks of the absurd geometry … of John Wallis (Hobbes, EW, vol. vii, p. 369).
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• Lect. math. 380 381 no. xxiv Torricelli's work on the rectification of curves is cited by Boulliau (1605–1694, another French mathematician among the early Fellows of the Society) in Ismael Bullialdi de lineis spiralibus (Paris, 1657), pp. 32–33. As David Eugene Smith records, however (A source book of mathematics, New York, edn. 1929, p. 90), the contents of Boulliau's huge Opus novum ad arithmeticam infinitorum (1682) were shown by Jacques Bernouilli to be expressible in a single page.
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• Hobbes . 1674 . Principia et problemata aliquot geometrica in Hobbes's Opera latina, vol. v, p. 213): Examinatio et emendatio (ib., iv, 174).
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• Guldin Centrobaryca 10 11 Bk. 2, Ch. 2. Prop. 6. pp. 46–47: Querela, 81–91.
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• De mundo 76 – 77 . 92; Paris MS., fols. 61v, 80.
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• Lectio geometrica no. xi, Appendix, Art. 37 (Mathematical works, edn. cit., Geom., p. 273).
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• E.g. in the paper ‘To find the number of the Julian period’ Phil. Trans. 1667 2 30 568 ff 568 ff
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