Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-14T23:02:27.710Z Has data issue: false hasContentIssue false
  • English
  • Français

Mathematical subtleties and scientific knowledge: Francis Bacon and mathematics, at the crossing of two traditions

Published online by Cambridge University Press:  22 November 2016

GIULIANO MORI
GIULIANO MORI*
Affiliation:
Institute for Advanced Study, School of Historical Studies, 1 Einstein Drive, Princeton, NJ 08540, USA. Email: giulianomori@yahoo.com.au; gmori@ias.edu.
Get access Rights & Permissions [Opens in a new window]

Abstract

This article engages the much-debated role of mathematics in Bacon's philosophy and inductive method at large. The many references to mathematics in Bacon's works are considered in the context of the humanist reform of the curriculum studiorum and, in particular, through a comparison with the kinds of natural and intellectual subtlety as they are defined by many sixteenth-century authors, including Cardano, Scaliger and Montaigne. Additionally, this article gives a nuanced background to the ‘subtlety’ commonly thought to have been eschewed by Bacon and by Bacon's self-proclaimed followers in the Royal Society of London. The aim of this article is ultimately to demonstrate that Bacon did not reject the use of mathematics in natural philosophy altogether. Instead, he hoped that following the Great Instauration a kind of non-abstract mathematics could be founded: a kind of mathematics which was to serve natural philosophy by enabling men to grasp the intrinsic subtlety of nature. Rather than mathematizing nature, it was mathematics that needed to be ‘naturalized’.

Type
Research Article
Information
The British Journal for the History of Science , Volume 50 , Issue 1 , March 2017 , pp. 1 - 21
Check for updates
Copyright
Copyright © British Society for the History of Science 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1 Cf. von Liebig, Justus, Über F. Bacon von Verulam und die Methode der Naturforschung, Munich: Literarisch-Artistische Anstalt, 1863 Google Scholar.

2 Cf. Koyré, Alexandre, Etudes galiléennes, Paris: Hermann, 1966, p. 12 Google Scholar; Pelseneer, Jean, ‘Gilbert, Bacon, Galilée, Képler, Harvey et Descartes: Leur relations’, Isis (1932) 17, pp. 171–208, 177Google Scholar.

3 Bacon, Francis, Essays or Counsels Civil and Moral, in The Works of Francis Bacon (subsequently WFB), ed. Spedding, James, Ellis, Robert Leslie and Denon, Douglas, 7 vols., London: Longman & Co., 1857–1874, vol. 6, pp. 365–604, 498Google Scholar.

4 Cf. Francis Bacon, Of the Proficience and Advancement of Learning Divine and Humane, in WFB, vol. 3, pp. 253–491, 360.

5 Cf. Francis Bacon, De dignitate et augmentis scientiarum, in WFB, vol. 1, pp. 413–837, 710. Cf. also Bacon, op. cit. (4), p. 360; Rees, Graham, ‘Mathematics and Francis Bacon's natural philosophy’, Revue internationale de philosophie (1986) 40, pp. 399–426, 412Google Scholar.

6 Cf. Urbach, Peter, Francis Bacon's Philosophy of Science: An Account and Reapprisal, La Salle: Open Court, 1987, p. 137 Google Scholar.

7 Giglioni, Guido, Francesco Bacone, Rome: Carocci, 2011, p. 117 Google Scholar.

8 Cf. Giglioni, op. cit. (7), pp. 15, 34, 117–118.

9 Cf. Francis Bacon, ‘A letter and discourse to Sir Henry Savill, touching helps for the intellectual powers’, in WFB, vol. 7, pp. 93–103, 95.

10 Cf. Kusukawa, Sachiko, ‘Bacon's classification of knowledge’, in Peltonen, Markku (ed.), The Cambridge Companion to Bacon, Cambridge: Cambridge University Press, 1996, pp. 47–74, 60CrossRefGoogle Scholar.

11 Cf. Rossi, Paolo, Francesco Bacone: Dalla magia alla scienza, repr., Bologna: il Mulino, 2004, p. 408 Google Scholar. Petrus Ramus was perhaps one of the most influential humanists of the sixteenth century. Ramist logic became extremely widespread in the seventeenth century, particularly so in the field of sciences. For a general introduction to his works and influence see, inter alia, Feingold, Mordechai, Freedman, Joseph S. and Rother, Wolfgang (eds.), The Influence of Petrus Ramus: Studies in Sixteenth and Seventeenth Century Philosophy and Sciences, Basle: Schwabe, 2001 Google Scholar; Goulding, Robert, Defending Hypatia: Ramus, Savile, and the Renaissance Rediscovery of Mathematical History, Dordrecht: Springer, 2010 CrossRefGoogle Scholar; Hotson, Howard, Commonplace Learning: Ramism and Its German Ramifications 1543–1630, Oxford: Oxford University Press, 2007 Google Scholar; Ong, Walter J., Ramus: Method and the Decay of Dialogue, Cambridge, MA: Harvard University Press, 1958 Google Scholar; Reid, Steven J. and Wilson, Emma Annette, Ramus, Pedagogy and the Liberal Arts: Ramism in Britain and the Wider World, Farnham: Ashgate, 2011 Google Scholar.

12 Cf. Johnston, Stephen, ‘The identity of the mathematical practitioner in 16th-century England’, in Hantsche, Irmgard (ed.), Der ‘Mathematicus’: Zur Entwicklung und Bedeutung einer neuen Berufsgruppe in der Zeit Gerhard Mercators, Bochum: Brockmeyer, 1996, pp. 93–120, 110–111Google Scholar.

13 Cf. Reiss, Timothy J., Knowledge, Discovery and Imagination in Early Modern Europe: The Rise of Aesthetic Rationalism, Cambridge: Cambridge University Press, 1997, pp. 139–142 CrossRefGoogle Scholar.

14 During the sixteenth and seventeenth centuries a number of diverse disciplines were raised to the status of mathematicae mixtae. Cf. [Girolamo Cardano], Encomium Geometriae, recitatum anno 1535 in Academia Platina [sic] Mediolani, in Carolus Sponius (ed.), Hieronymi Cardani Mediolanensis Philosophi ac Medici Celeberrimi Opera Omnia … (subsequently HCO), 10 vols., Lyon: Sumptibus Ioannis Antonii Huguetan & Marci Antonii Ravaud, 1663, vol. 4, pp. 440–445, 441; [Girolamo Cardano], Artis Arithmeticae Tractatus de Integris, in HCO, vol. 10, pp. 117–128, 117; Clavius, Christoph, Euclidis Elementorum libri XV …, Rome: Apud Vincentium Accoltum, 1574, n.p. [Prolegomena]Google Scholar; Petrus Ramus, … Scholarum Mathematicarum libri unus et triginta … Frankfurt: Typis & Sumptibus Wechelianorum, apud Danielem & Davidem Aubrios & Clementem Schleichium, 1627, n.p. [Index in secundum librum], pp. 42–62; [Juan Luis Vives], De Disciplinis, in Gregorius Majansius (ed.), Joannis Ludovici Vivis Opera Omnia, 8 vols., Valencia: In officina Benedicti Monfort, 1782–1790, vol. 6, pp. 1–437, 203. This tendency was continued in the seventeenth century by authors such as Savile, and it can also be witnessed in Bacon's own works. Cf. Bacon, op. cit. (5), pp. 577–578; [Savile, Henry], Praelectiones tresdecim in principium elementorum Euclidis Oxonii habitae , Oxford: Iohannis Lichfield, & Iacobus Short, 1621, p. 20 Google Scholar. The importance of the early modern debate on mathematicae mixtae and of the consequent expansion of the canon of mathematics is so great that it has led some scholars to hold it responsible for the seventeenth-century mathematization of nature, which is more traditionally explained by the set of Platonic theories analysed by Koyré and others. Cf. Gingras, Yves, ‘What did mathematics do to physics?’, History of Science (2001) 39, pp. 383–416, 383CrossRefGoogle Scholar.

15 Cf. Oosterhoff, Richard J., ‘Idiotae, mathematics, and artisans: the untutored mind and the discovery of nature in the Fabrist circle’, Intellectual History Review (2014) 24, pp. 301–319, 310CrossRefGoogle Scholar; Pantin, Isabelle, ‘Oronce Fine's role as royal lecturer’, in Marr, Alexander (ed.), The Worlds of Oronce Fine: Mathematics, Instruments and Print in Renaissance France, Donington: Shaun Tyas, 2009, pp. 13–30, 24Google Scholar.

16 Cf. Pantin, op. cit. (15); Oronce Fine, Protomathesis: Opus varium, ac scitu non minus utile, quam iucunum, nunc primum in lucem foeliciter emissum, Paris: 1532, fols. 157r–209r.

17 Cf. [Melanchthon, Philipp], Mathematicarum disciplinarum tum etiam Astrologiae Encomia, Strasbourg: 1537, fol. B 2r–vGoogle Scholar.

18 Fine, Oronce, ‘Epitre touchant la dignité, perfection, et utilité des sciences mathematiques …’, in Le sphere du monde, proprement ditte cosmographie …, Paris: Michel de Vascosan, 1551, fols. 59r–64v, 59v–60rGoogle Scholar. Cf. also [d'Etaples, Jacques Lefèvre], Arithmetica decem libris demonstrata …, Paris: J. Higman, W. Hopyl, 1496, n.p.Google Scholar; Ramus, op. cit. (14), p. 12; Valla, Giorgio, De expetendis, et fugiendis rebus opus …, Venice: In aedibus Aldi, 1501, fols. a vv–a viiiv Google Scholar. Concerning Fine's Epitre, cf. inter alia Heninger, S.K. Jr , ‘Oronce Finé and the English textbooks for the mathematical sciences’, in Randall, Dale B.J. and Williams, George Walton (eds.), Studies in the Continental Background of Renaissance English Literature: Essays Presented to John L. Lievsay, Durham, NC: Duke University Press, 1977, pp. 171–185, 179–180Google Scholar.

19 Cf. [Jacques Lèfevre d'Etaples], Epitome compendiosaque introductio in libros Arithmeticos divi Severnini Boethij …, [Paris: 1510], fol. 1v; Fine, op. cit. (16), fol. 1r; Valla, op. cit. (18), fol. a vir. Cf. also Angela Axworthy, ‘The epistemological foundations of the propaedeutic status of mathematics according to the epistolary and prefatory writings of Or once Fine’, in Marr, op. cit. (15), pp. 31–51, 33–34, 49; Oosterhoff, Richard J., ‘From pious to polite: Pythagoras in the res publica litterarum of French Renaissance mathematics’, Journal of the History of Ideas (2013) 74, pp. 531–552, 541–542; Oosterhoff, op. cit. (15), pp. 309, 312CrossRefGoogle Scholar; Pantin, op. cit. (15), pp. 19–20; Reiss, op. cit. (13), p. 160; Kusukawa, Sachiko, ‘Petrus Ramus (1515–1572): method and reform’, in Blum, Paul Richard (ed.), Philosophers of the Renaissance, Washington: Catholic University of America Press, 2010, pp. 163–167, 165CrossRefGoogle Scholar. Concerning Boethius’ Platonic interpretation of the propaedeutic role of mathematics cf. Guillaumin, Jean-Yves, ‘Boethius's De institutione arithmetica and its influence on posterity’, in Kaylor, Noel Harold Jr and Phillips, Philip Edward (eds.), A Companion to Boethius in the Middle Ages, Leiden: Brill, 2012, pp. 135–161, 137–138CrossRefGoogle Scholar.

20 Cf. Johnston, op. cit. (12), p. 108; Romano, Antonella, La Contre-Réforme mathématique: Constitution et diffusion d'une culture mathématique Jésuite à la Renaissance (1540–1640), Rome: Ecole Française de Rome, 1999, pp. 97, 469CrossRefGoogle Scholar; Williams, Travis D., ‘The dialogue of early modern mathematical subjectivity’, Configurations (2013) 21, pp. 53–84, 58–59CrossRefGoogle Scholar.

21 [Vives], op. cit. (14), p. 370.

22 Cf. [Vives], op. cit. (14), p. 369.

23 Cf. Ramus, op. cit. (14), p. 43.

24 Cf. [Cardano], Encomium Geometriae, op. cit. (14), p. 441; Clavius, Christoph, Algebra Christophori Clavii Bambergensis e Societate Iesu, Rome: Apud Bartholomaeum Zannettum, 1608, fol. a 2v Google Scholar.

25 Cf. [Vives], op. cit. (14), p. 370; Fine, op. cit. (18), fol. 61r; Ramus, op. cit. (14), p. 48; [Melanchthon], op. cit. (17), fol. B 1r.

26 Cf. inter alia Romano, op. cit. (20), pp. 132, 159; Williams, op. cit. (20), p. 60.

27 Cf. Bacon, op. cit. (5), pp. 540–541; Francis Bacon, Novum Organum, in WFB, vol. 1, pp. 70–365, 281.

28 Cf. Bacon, op. cit. (5), pp. 576–577.

29 Cf. Boethius, , ‘De Sancta Trinitate’, in Moreschini, Claudio (ed.), De consolatione philosophiae, Opuscula theologica, Munich: K.G. Saur, 2000, pp. 165–181, esp. 168–169CrossRefGoogle Scholar.

30 Cf. Boethius, De arithmetica, in J.-P. Migne, Patrologia latina (subsequently PL), 221 vols., Paris: Migne, 1841–, vol. 63, cols. 1079–1176, 1081–1082. Cf. also Albertson, David, Mathematical Theologies: Nicholas of Cusa and the Legacy of Thierry of Chartres, Oxford: Oxford University Press, 2014, p. 82 CrossRefGoogle Scholar.

31 Cf. Valla, op. cit. (18), fols. a iiiv, a ivr.

32 Cf. Fine, op. cit. (18), fol. 60v. Cf. also Axworthy, op. cit. (19), pp. 37, 40. The characteristic medietas of mathematical objects was also frequently underlined in contexts different from that of the quaestio de certitudine mathematicarum. Ramus, for instance, assigned mathematics an intermediate position between dialectics and the world. In this way, departing from the third dialectic judgement it would have been possible to arrive at mathematics, and through mathematics to analyse nature. Besides, at the same time, it was also possible to arrive at dialectics from mathematics since the mathematical study constituted the first stage of the process of liberation of the intellect, which was to be fully achieved only through dialectics. Cf. Goulding, op. cit. (11), pp. 23–24.

33 Cf. Fine, op. cit. (16), fol. AA 2r. Cf. also Axworthy, op. cit. (19), pp. 44–45, 49.

34 Cf. inter alia Romano, op. cit. (20), p. 155.

35 Cf. [Piccolomini, Alessandro], … Commentarium de Certitudine Mathematicarum disciplinarum…, Rome: Antonio Blado, 1547 , fol. 72rGoogle Scholar.

36 Cf. Clavius, op. cit. (14), n.p. [Prolegomena]; Dear, Peter, Discipline and Experience: The Mathematical Way in the Scientific Revolution, Chicago: The University of Chicago Press, 1995, pp. 38–39 CrossRefGoogle Scholar; Peletarius, Iacobus, In Euclidis Elementa Geometrica Demonstrationum Libri sex, Lyon: Apud Ioannem Tornaesium et Gulielmum Gazeium, 1557, n.p. [Praefatio]Google Scholar.

37 Cf. [Barozzi, Francesco], … Opusculum, in quo una oratio, & duae quaestiones: altera de certitudine, et altera de medietate Mathematicarum continentur, Padua: E.G.P., 1560, fol. 21r–vGoogle Scholar.

38 Cf. [Barozzi], op. cit. (37), fol. 24r–v; [Piccolomini], op. cit. (35), fols. 104r–107r.

39 Cf. Francesco Barozzi, Lectiones in Procli Commentarios in Primum Librum Euclidis Elementorum …, in De Pace, Anna, Le matematiche e il mondo: Ricerche su un dibattito in Italia nella seconda metà del Cinquecento, Milan: Franco Angeli, 1993, pp. 349–430, 382–383, 388–389, 406Google Scholar; [Barozzi], op. cit. (37), fols. 37r–40r. Cf. also Angelini, Annarita, ‘“Un autre ordre du monde”: Science et mathématiques d'après les commentateurs de Proclus au Cinquecento’, Revue d'histoire des sciences (2006) 59, pp. 265–283, 273Google Scholar.

40 Cf. Mancosu, Paolo, Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century, Oxford: Oxford University Press, 1996, p. 12 Google Scholar.

41 Cf. [Piccolomini], op. cit. (35), fols. 97r–v, 107v–108r. Cf. also Feldhay, Rivka, ‘The use and abuse of mathematical entities: Galileo and the Jesuits revisited’, in Machamer, Peter (ed.), The Cambridge Companion to Galileo, Cambridge: Cambridge University Press, 1998, pp. 80–145, 88CrossRefGoogle Scholar.

42 Cf. Goulding, op. cit. (11), p. 36.

43 Cf. [Piccolomini], op. cit. (35), fols. 107v–108r; Bacon, op. cit. (5), pp. 576–577.

44 Francis Bacon, Translation of the ‘De augmentis’, in WFB, vol. 4, pp. 273–498, 452 (original: Bacon, op. cit. (5), p. 666).

45 Bacon, op. cit. (44), p. 432 (original: Bacon, op. cit. (5), p. 644).

46 Cf. Francis Bacon, Translation of the ‘De principiis atque origininbus’, in WFB, vol. 5, pp. 459–500, 462 (original: Francis Bacon, De principiis atque originibus secundum fabula cupidinis et coeli …, in WFB, vol. 3, pp. 79–118, 81).

47 Cf. Rossi, Paolo, La nascita della scienza moderna in Europa, Rome and Bari: Laterza, 2011, p. 125 Google Scholar.

48 Cf. Rossi, Paolo, Aspetti della rivoluzione scientifica, Naples: Morano, 1971, pp. 89 ff.Google Scholar; Rossi, Paolo, Immagini della scienza, Rome: Editori Riuniti, 1977, pp. 114–117 Google Scholar.

49 Cf. Bacon, op. cit. (44), pp. 348–349 (original: Bacon, op. cit. (5), pp. 552–553).

50 Cf. Urbach, op. cit. (6), pp. 125 ff.

51 Bacon, Translation, op. cit. (46), p. 479 (original: Bacon, De principiis, op. cit. (46), p. 97). Cf. also Francis Bacon, Thema Coeli, in WFB, vol. 3, pp. 769–780, 773; Bacon, op. cit. (5), p. 644.

52 Francis Bacon, Translation of the ‘Thema Coeli’, in WFB, vol. 5, pp. 547–559, 550 (original: Bacon, op. cit. (51), p. 772).

53 Bacon, op. cit. (52), p. 556 (original: Bacon, op. cit. (51), p. 778).

54 ‘Harmonize facts with Plato's philosophy’. Angelini, op. cit. (39), p. 269.

55 Cf. De Pace, op. cit. (39), pp. 9, 341; Goulding, op. cit. (11), pp. 14–15.

56 Cf. inter alia Ramus, op. cit. (14), pp. 20, 74.

57 Cf. Gilbert, Neal W., Renaissance Concepts of Method, New York: Columbia University Press, 1963, p. 84 Google Scholar.

58 Lukács, Ladislaus (ed.), Monumenta paedagogica Societatis Iesu …, Rome: Institutum Historicum Societatis Iesu, 1986, p. 109 Google Scholar. Cf. also Dear, op. cit. (36), pp. 35–36.

59 [Melanchthon], op. cit. (17), fols. B4v–B5v.

60 Cf. Mancosu, op. cit. (40), p. 12.

61 Cf. Dasypodius, Conrad, Analyseis Geometricae sex librorum Euclidis …, [Strasbourg?]: Iosias Rihelius, 1566, fols. a2v–a3rGoogle Scholar.

62 Cf. Dasypodius, op. cit. (61), fol. D 1v; Gilbert, op. cit. (57), p. 89.

63 Cf. Ramus, op. cit. (14), p. 89, 91; Goulding, op. cit. (11), pp. 27–28.

64 Cf. Williams, op. cit. (20), p. 77.

65 Cf. Goulding, op. cit. (11), p. 170.

66 Francis Bacon, Translation of the ‘Novum organum’, in WFB, vol. 4, pp. 37–248, 167–168 (original: Bacon, op. cit. (27), p. 281).

67 Bacon, op. cit. (66), p. 24 (original: Bacon, op. cit. (27), p. 136).

68 It is interesting to remark, in this regard, that, in line with the Elizabethan suspicion towards Machiavellian subtlety, the serpent in Genesis 3:1 is described in the King James Bible as ‘more subtil than any beast of the field’, while the Vulgate simply had ‘callidior cunctis animantibus terrae’.

69 Cf. Tertullian, Adversus Hermogenem, in PL, vol. 2, cols. 219–262, 222A; Tertullian, Adversum Marcionem, in PL, vol. 2, col. 481B; Tertullian, Adversus Valentinianos, in PL, vol. 2, cols. 263–558, 543A.

70 Cf. Augustine, Contra Academicos, in PL, vol. 32, cols. 908–938, 919, 916, 937.

71 Thomas Aquinas, Scriptum super Sententiis, Book 4, d. 43, q. 1, a. 1, qc. 1 ad 2, in Corpus Thomisticum, automato translatum a Roberto Busa.

72 Cf. Boethius, op. cit. (30); Boethius, De geometria, in PL, vol. 63, cols. 1299–1364, 1353. Cf. also [Girolamo Cardano], De libris propriis eorumque ordine, et usu …, in HCO, vol. 1, pp. 55–150, 143. Such notion can also be traced in many of the humanist reformers, cf. for instance Fine, op. cit. (18), fol. 61v.

73 Cf. [Cardano, Girolamo], Hieronymi Cardani Mediolanensis medici De subtilitate libri XXI …, Basle: Per Ludovicum Lucium, 1554, p. 49 Google Scholar.

74 Cf. [Cardano], op. cit. (73), pp. 1–2. Concerning Cardano's notion of subtilitas cf. also Ingegno, Alfonso, Saggio sulla filosofia di Cardano, Florence: La Nuova Italia, 1980, pp. 212–213 Google Scholar; Magnard, Pierre, ‘La notion de subtilité chez Jérôme Cardan’, in Baldi, Marialuisa and Canziani, Guido (eds.), Girolamo Cardano: Le opere, le fonti, la vita, Milan: Franco Angeli, 1999, pp. 159–167, 159–160Google Scholar.

75 Cf. [Scaliger, Julius Caesar], … Exotericarum Exercitationum liber quintus decimus De subtilitate, ad Hieronymum Cardanum, Paris: Ex officina typographica Michaelis Vascosani, 1557, fols. 1v–2rGoogle Scholar.

76 Cf. [Cardano], op. cit. (73), p. 408.

77 Cf. [Cardano], op. cit. (73), p. 410.

78 Cf. [Cardano], op. cit. (73), p. 409.

79 de Montaigne, Michel, The Essays, 3 vols., New York: The Heritage Press, 1946, vol. 1, p. 414 Google Scholar (original: Montaigne, Michel de, Essais, 3 vols., Paris: Garnier-Flammarion, 1969, vol. 1, p. 369 Google Scholar).

80 Cf. Fellheimer, Jeannette, ‘The “subtlety” of the Italians’, English Miscellany (1969) 12, pp. 21–31, 21–24Google Scholar.

81 Ascham, Roger, The Schoolmaster, London: Cassel and Company, 1909, pp. 80, 84Google Scholar.

82 Fattori, Marta, Lessico del Novum organum di Francesco Bacone, 2 vols., Rome: Edizioni dell'Ateneo & Bizzarri, 1980, vol. 2, p. 292 Google Scholar.

83 Cf. Bacon, op. cit. (27), p. 228.

84 Bacon, op. cit. (66), pp. 199 (original: Bacon, op. cit. (27), p. 314).

85 Cf. Francis Bacon, Sylva Sylvarum: Or a Natural History, in WFB, vol. 2, pp. 325–680, 602–603.

86 Bacon, op. cit. (4), p. 332.

87 Francis Bacon, Translation of the ‘Cogitationes de natura rerum’, in WFB, vol. 5, pp. 419–439, 419 (original: Francis Bacon, Cogitationes de natura rerum, in WFB, vol. 3, pp. 15–35, 15).

88 Cf. [Cardano], op. cit. (73), p. 411.

89 Bacon, op. cit. (44), p. 371 (original: Bacon, op. cit. (5), pp. 577–578).

90 Bacon, op. cit. (44), p. 411 (original: Bacon, op. cit. (5), p. 621).

91 Francis Bacon, Translation of the ‘Historia vitae et mortis’, in WFB, vol. 5, pp. 213–335, 263 (original: Francis Bacon, Historia vitae et mortis …, in WFB, vol. 2, pp. 101–226, 154).

92 Bacon, op. cit. (4), p. 285.

93 Bacon, op. cit. (27), p. 191.

94 It is interesting in this regard to consider the perceived vicinity between magic and some mathematical practices in Elizabethan England. Cf. Zetterberg, J. Peter, ‘The mistaking of “the mathematicks” for magic in Tudor and Stuart England’, Sixteenth Century Journal (1980) 11, pp. 83–97, 86, 88, 95–96CrossRefGoogle Scholar.

95 Francis Bacon, Valerius Terminus of the Interpretation of Nature, in WFB, vol. 3, pp. 215–252, 242. Cf. also Bacon, op. cit. (27), p. 158.

96 Bacon, op. cit. (66), p. 49 (original: Bacon, op. cit. (27), p. 158).

97 Bacon, op. cit. (66), p. 51 (original: Bacon, op. cit. (27), pp. 160–161).

98 Bacon, op. cit. (44), p. 371 (original: Bacon, op. cit. (5), p. 578). Cf. also Rees, op. cit. (5), p. 407.

99 Bacon, op. cit. (66), p. 162 (original: Bacon, op. cit. (27), p. 275).

100 Cf. Giglioni, op. cit. (7), pp. 136–137.

101 Cf. Bacon, op. cit. (27), p. 201.

102 Bacon, op. cit. (66), p. 126 (original: Bacon, op. cit. (27), p. 235).