Method and mathematics: Peter Ramus's histories of the sciences

Journal of the History of Ideas

Volumn 67, Issue 1, 2006, Pages 63-85

  Goulding, Robert ^a  

^a UNIVERSITY OF NOTRE DAME   (United States)

Author keywords

[No Author keywords available]

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EID: 31644443218     PISSN: 00225037     EISSN: None     Source Type: Journal    
DOI: 10.1353/jhi.2006.0005     Document Type: Review

References (85)

1. Peter Sharratt, "Nicolaus Nancelius, Petri Kami vita., Edited with an English Translation," Humanistica Lovaniensia 24 (1975): 161-277, at 198-200.
2. See Timothy J. Reiss, Knowledge, Discovery and Imagination in Early Modern Europe: The Rise of Aesthetic Rationalism (Cambridge: Cambridge University Press, 1997)
3. and Timothy J. Reiss, "From Trivium to Quadrivium: Ramus, Method and Mathematical Technology," in The Renaissance Computer: Knowledge Technology in the First Age of Print, ed. Neil Rhodes and Jonathan Sawday (London and New York: Routledge, 2000), 45-58.
4. On Ramus's mathematics, see Isabelle Pantin, "Ramus et l'enseignement des mathématiques," in Ramus et l'Université, ed. Kees Meerhoff and Michel Magnien (Paris: Presses de l'Ecole normale supérieur, 2004), 71-86.
5. v: ". . . nam si res constantes sunt et aeternae, earum disputatio, explicatioque firmis, perspicuis, necessariis argumentis addici debet."
6. See Brian P. Copenhaver and Charles B. Schmitt, Renaissance Philosophy, A History of Western Philosophy, 3 (Oxford: Oxford University Press, 1992), 29-30, and especially 223-25 on Valla's rhetoricizing of philosophy.
7. r: "Comparatur igitur dialectica, sicuti vis artium reliquarum, natura, doctrina, exercitatione. . . . Doctrina (cui perpaululum loci reliquum est) sola extrinsecus a magistris assumenda est."
8. Petrus Ramus, Aristotelicae animadversiones (Paris, 1543).
9. v: ". . . turn ex eorum ingeniis veluti speculis imago naturae resultabit."
10. v: ". . . ut hoc artificioso quasi speculo natura formae suae dignitatem perspicere, et si qua macula sit aspersa, delere atque eluere possit."
11. See Walter J. Ong, Ramus, Method, and the Decay of Dialogue: From the Art of Discourse to the Art of Reason (Cambridge, Mass.: Harvard University Press, 1958), 45-47 for Ramus's use of this term, beginning with his infamous master's thesis "Quaecumque ab Aristotele dicta essent, commentitia esse."
12. v.
13. This image first appeared in the Dialectici commentarii tres, issued under Omer Talon's name in 1546 while Ramus was banned from teaching philosophy. The relevant passage is translated in Ong, Ramus, 245-46.
14. v. Having described the affinity of his "second judgment" with the Platonic notion of individuals emanating from ideas, he writes: "Haec artis est cum naturae sapientia, pulcherrima contentio."
15. r).
16. This point is made at length - based on a study of Ramus's Dialectique - in Craig Walton, "Ramus and Socrates," Proceedings of the American Philosophical Society 114 (1970): 119-39.
17. r: "Postremus superest dialectici iudicii gradus in perspicienda scientiarum humanarum virtute ad supremum rerum omnium finem refer enda positus, ut laboris humani fructus possit aestimari, et optimus rerum omnium parens, atque author agnosci."
18. r-v: "Sed cum haec omnia dialectica libenter admirabitur, turn in seipsam conversa vehementius incipiet admirari, et divinae mentis imaginem non divinam non poterit arbitrari."
19. Plato, Republic 514A-517B.
20. V: "Imagines medio interiectae spatio, genera rerum, speciesque disciplinis et artibus comprehensae, quarum tenues, levissimoque motu nutantes umbrae, sunt haec omnia, quae tangi, audiri, cerni, caeterisque sensibus percipi possunt."
21. r.
22. v: "Itaque cum has disciplinas lumine suo dialectica lustraverit, quanto iam plenius naturalium principia rerum, et umbrarum illarum causae cernentur."
23. v: "Hominem corporis exigui, velut carceris angusti custodia constrictum querimur? Mathesis liberat, seu potius hominem hac mundi universitate maiorem reddit."
24. v: "Hactenus veritas dialectica, veritatisque utilitas simplex et nuda fuit, quae deinceps turbari et corrumpi coepit."
25. r: "Primus igitur Aristoteles (quod ex veterum monumentis intelligi possit) simplicem antiquorum veritatem et exercitationem libris suis depravavit."
26. Ramus, Aristotelicae animadversiones, Ibid.
27. See Charles Waddington, Ramus: Sa vie, ses écrits et ses opinions (Paris, 1855), 40-52.
28. In an oration of November 1544, he announced his intention to devote himself to mathematics, leaving the teaching of rhetoric and grammar to his colleagues Talon and Alexandre. See Petrus Ramus, Collectaneae praefationes, epistolae, orationes (Marburg, 1599), 229-39.
29. Euclides, Elementa, ed. P. Ramus (Paris, 1549).
30. On Ramus and the roles and identities of Euclid and Theon, see Robert Goulding, Studies on the Mathematical and Astronomical Papers of Sir Henry Savile (unpublished PhD dissertation, London: University of London [Warburg Institute], 1999), ch. 3.
31. Ramus, Collectaneae praefationes, 121: "semotis interpretum et commentis et figuris."
32. Ramus, Collectaneae praefationes, 121 Ibid.
33. Ramus, Collectaneae praefationes, 121 Ibid.: "Si quid autem obscurum fuerit, longe commodius viva praeceptoris intelligentis oratio, quam picta in libris interpretum manus explicabit."
34. Ramus, Collectaneae praefationes, 120: "Hic enim prima mediis, media postremis, omniaque inter se, velut aurea quadam Homeri catena . . . vincta colligataque sunt. . . ." ("For here the first are connected and linked to middles, middles to final like some golden chain of Homer"). For Ramus's use of this image with reference to dialectic,
35. see Nelly Bruyère, Méthode et dialectique dans l'œuvre de La Ramée: Renaissance et ǎge classique (Paris: J. Vrin, 1984), 124.
36. He very briefly makes the same point in the 1544 oration on mathematics, where he describes the mathematical arts as the mind's "free thoughts." Ramus, Collectaneae praefationes, 231: "mathematicas artes invisamus, et animis (quorum sunt liberae cogitationes) velut praesentes et expositas intueamur" ("let us look upon the mathematical arts, and let us contemplate them as though they were present and put before our minds [of which they are the free thoughts]").
37. He does refer to "demonstrationes" at the conclusion of the passage quoted in the previous note, but this refers to his own notion of "demonstration" - synonymous with proper, methodical ordering. The actual proofs found in the Elements are, as we have seen, merely elucidations and can be omitted without injury to the mathematical structure of the work.
38. Ramus, Collectaneae praefationes, 120.
39. Ramus, Collectaneae praefationes, 120. Ibid.: "quasi tanta scientia non ab homine inventa, sed divinitus in animis nostris impressa, recordatione animadversarum rerum paulatim recrearetur. Verumenimvero quam longa oblivio, quam tarda recordatio ista fuit?" For other examples of Ramus's assimilation of Platonic metaphysics to his own theory of knowledge,
40. see Bruyère, 262-64.
41. For a full description of Josephus's popular narrative, see Nick Popper's article in this forum.
42. Ramus, Collectaneae praefationes, 120: "Primi illi homines (ut Josephus antiquitatis Judaicae scriptor ait) Adamus, Sethus, Enus, Noeus vitae et longissimae et contemplationi deditissimae beneficio, in hanc recordationem incubuerunt."
43. Ramus, Collectaneae praefationes, 120. Ibid.: "ne alia novae oblivionis caligine circumfusa teneretur. . . ."
44. Ramus, Collectaneae praefationes, 120-21: "Hinc tot, tamque excellentia ingenia excitari . . . coeperunt, videlicet ad huius mathematicae recordationis opus exaedificandum, tot fabros, tot architectes adhiberi oportuit. . . ."
45. Ramus records that he had spent 8 years of his career teaching the trivium, followed by four years of teaching mathematics (Ramus, Collectaneae praefationes, 409). He is most likely dating the beginning of his career from the 1543 publications.
46. Pierre de Mondoré, Euclidis Elementorum liber decimus (Paris, 1552).
47. Ramus, Collectaneae praefationes, 409: "Quindecim Euclidis libri sunt, quos (ut omnes omnino artes) sicut uno Logicae organo contextos esse primum, sic eodem postea retexi posse cogitabam. Organum autem illud una imprimis mathematum causa diu multumque praecultum nobis ac praeparatum est. Quare persuasione hac inductus nihil reputans quot et quantae mathematum per se obscuritates essent, prompto atque alacri animo ad decimum usque librum penetravi, sed immensa subtilitate operis illius, licet eruditissimis P. Montaurei vigiliis explicati et illustrati, tarnen sic exercitatus sum . . . ut quodam die cum binomii et residui cuiusdam demonstrationem summa animi intentione, corpore horam integram idem vestigium premente nondum conclusissem, senserim collo nervos obriguisse: turn vero abacum radiumque abieci, indignatusque mathematis succensui, quod sui studiosos et amatores tam acerbe cruciarent."
48. See also Waddington, Ramus, 108.
49. Ramus, Collectaneae praefationes, 121: "Haec enim primorum generis humani parentum, Adami, Sethi, Noëi divina contemplandis optimi maximique Dei mathematicis operibus otia fuerunt."
50. Ramus, Collectaneae praefationes, 122.
51. Ramus, Collectaneae praefationes, 122: "sed opinantur prodesse has artes non caeterarum more, cum perceptae fuerint, sed cum percipiuntur."
52. See Ong, Ramus, 258-62.
53. Ramus, Collectaneae praefationes, 123: "Itaque arithmetica arithmetice, geometrica geometrice doceantur."
54. Ramus, Collectaneae praefationes, 123-24.
55. Ramus, Collectaneae praefationes, 124-26: "Atque haec elementa licet a primis usque hominibus repetita, tarnen hunc in modum et proposita et collocata ab Euclide existimantur; quern virum mathematica singularum propositionum scientia tanquam singularem et prope divinum suscipio . . . at logica recte et ex ordine docendi prudentia parem efficere nequeo. . . . Quare licet Theonem mathematicarum rerum intelligentia non inferiorem putemus, attamen videmus adhuc quam demonstrationibus suis elementa mathematica non illustret, sed obscuret."
56. Ramus, Collectaneae praefationes, 123: "quibus perfecte et absolute rudis et imperitus institui possit."
57. Ramus, Collectaneae praefationes, 126-27: "Denique mathematica elementa logicis legibus illis institue; propositiones singulae loco et ordine collocatae, ipsaemet suae veritatis non tantum propositiones, sed etiam demonstrationes erunt."
58. See Walter J. Ong, "Christianus Ursitius and Ramus' New Mathematics," Bibliothèque d'humanisme et renaissance 36 (1974): 603-10 for Ramus's continuous emendation of his mathematical texts.
59. Ramus, Collectaneae praefationes, 126: "non Aristotelis commentitia illa quidem, sed certe naturali et aperta demonstratione singulariter et eximie demonstrari."
60. Waddington, Ramus, 136, 149-50.
61. Ramus, Collectaneae praefationes, 410.
62. Petrus Ramus, Prooemium mathematicum (Paris, 1567).
63. Petrus Ramus, Scholarum mathematicarum libri unus et triginta (Basel, 1569).
64. Ramus, Scholae mathematicae, 109: "Ergo artes mathematicae divinitus vel oblatae vel inventae, quae Dei potentiam in mundi creatione, sapientiam in administratione, pietatem ex infinita bonorum omnium erga genus humanum largitate demonstrarent."
65. Ramus, Scholae mathematicae, 54-55. See also 82-83, where he criticizes the Aristotelian conception of the mind as a "tabula nuda."
66. Compare also Ramus's conception of theology in Petrus Ramus, De religione christiana libri quatuor (Frankfurt a.M., 1576), 2, where he states that theology consists in the methodical arrangement of scriptural quotations; the material is God-given, while the form is in accordance with human reason, so that the practice of theology is easy and open to all human beings.
67. Based on the history of geometry by the Peripatetic Eudemus of Rhodes. See Proclus, A Commentary on the First Book of Euclid's Elements, trans. Glenn R. Morrow (Princeton: Princeton University Press, 1992), 52-56.
68. Proclus's commentary was first printed in Basel in 1533 by Simon Grynaeus, and in Latin in 1560 by Francesco Barozzi (A Commentary on the First Book of Euclid's Elements, ibid., Ixviii).
69. Ramus, Scholae mathematicae, 77 and 100.
70. Ramus, Scholae mathematicae, 39: "ut Euclidi praeter inane nomen nihil admodum relinquatur."
71. Ramus, Scholae mathematicae, 12.
72. Ramus, Scholae mathematicae, 18: "ista pene muliebris zelotypia."
73. Ramus, Scholae mathematicae, 30: "caeca ambitio."
74. Ramus, Scholae mathematicae, 89 and 92: "studium demonstrandi . . . insanum."
75. Ramus, Scholae mathematicae, 110.
76. See James Byrne's article in this forum.
77. v.
78. Savile's personal copy of Euclid is in the Bodleian Library with shelfmark Savile W.9(1) (Euclid, Stoicheia, ed. Simon Grynaeus, Basel, 1533). The volume is heavily annotated, but offers no support for Savile's account. Note that Savile makes no mention of the arithmetical books of the Elements; his own copy of Euclid, however, suggests that he read them continuously with the geometrical ones.
79. Republic 528A-B.
80. See Robert Goulding, "Testimonia humanitatis: The Early Lectures of Henry Savile" in Sir Thomas Gresham and Gresham College: Studies in the Intellectual History of London in the Sixteenth and Seventeenth Centuries, ed. F. Ames-Lewis (Aldershot: Ashgate, 1999), 125-45, especially 139, 142.
81. See Goulding, Studies, chaps. 1 and 2.
82. V: "Mathematicam illam intelligo puram, castam, incorruptam, non physicis coniecturis, aut praedictionibus Chaldaicis contaminatam."
83. Ibid.: "Turcica barbaries crudelitasque non solum homines suis sedibus expulit, sed ipsas etiam humaniores disciplinas et omnium sanctissimam mathesim nova domicilia conquirere coegit."
84. Ibid.: "Verum earn querimoniam deponamus. Illud potius agamus, quomodo possit Oxonium Alexandria transferri, aut si illud maius est, quam ut optari debeat, certe quomodo possit Alexandrinus Ptolemaeus ab Oxoniensibus intelligi." This passage is underlined for emphasis in the manuscript.
85. v.