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The Discovery of Nature: The Contribution of the Chartrians to Twelfth-Century Attempts to Found a Scientia naturalis

Published online by Cambridge University Press:  29 July 2016

Andreas Speer*
Affiliation:
Thomas-Institut, University of Cologne

Extract

If one takes standard overviews of the history of natural science or natural philosophy as his measure, the object appearing in the title of this study would literally appear not to exist. For, apart from a few scattered encyclopedia entries — which are always of necessity rather summary in character — one searches in vain for studies on the medieval interest in the natural sciences. For the contemporary cosmologist, be he first and foremost philosopher or physicist, the Middle Ages lie in a very deep darkness indeed.

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Copyright © Fordham University Press 

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References

1 See Lorenz, S., Mojsisch, B., and Schröder, W., “Naturphilosophie I.–IV.,” Historisches Wörterbuch der Philosophie, vol. 6 (Basel, 1984), 535–48; Donati, S., Speer, A., “Physik / Naturphilosophie,” Lexikon des Mittelalters, vol. 6 (Munich, 1993), 2111–17.Google Scholar

This study is the printed version of a lecture delivered at the Boston Colloquium in Medieval Philosophy in the Science Center of Harvard University on 12 March 1996. For help in translating this paper I warmly thank my colleague and friend Martin J. Tracey (Notre Dame).Google Scholar

2 Duhem, P., Le système du monde. Histoire des doctrines cosmologiques , tome 3: L'astronomie latine au Moyen Age (Paris, 1954), 163230.Google Scholar

3 Crombie, A. C., Augustine to Galileo: The History of Science a.d. 400–1650 (London, 1952), 19.Google Scholar

4 Ibid., 1943.Google Scholar

5 Dutton, P. E., The “Glosae super Platonem” of Bernard of Chartres, PIMS Studies and Texts 107 (Toronto, 1991), 3.Google Scholar

6 Dod, B. G., “Aristoteles latinus,” in Kretzman, N. et al., eds., The Cambridge History of Later Medieval Philosophy: From the Rediscovery of Aristotle to the Disintegration of Scholasticism 1100–1600 (Cambridge, 1982), 4579 at 54–55 and 77; for Iacobus Veneticus Grecus see Minio-Paluello, L., “Iacobus Veneticus Grecus: Canonist and Translator of Aristotle,” Traditio 8 (1952): 265–304 at 284–91; concerning the Greek and Latin translations of Aristotle's “Metaphysica” see also Diem, G., “Les traductions gréco-latines de la Métaphysique au moyen âge. Le problème de la Metaphysica Vetus,” Archiv für Geschichte der Philosophie 49 (1967): 7–71.Google Scholar

7 One can find attempts to look for such intellectual motives in Wieland, G., “Plato oder Aristoteles? — Überlegungen zur Aristoteles-Rezeption des lateinischen Mittelalters,” in Tijdschrift voor Filosofie 47 (1985): 605–30, and Wieland, , “Rationalisierung und Verinnerlichung. Aspekte der geistigen Physiognomie des 12. Jahrhunderts,” in Beckmann, J. P. et al., eds., Philosophie im Mittelalter. Entwicklungslinien und Paradigmen (Hamburg, 1987), 61–79; see also Dreyer, M., Nikolaus von Amiens: Ars fidei catholicae. Ein Beispiel axiomatischer Methode (Münster, 1993), 1–39, and Dreyer, , “Regularmethode und Axiomatik. Wissenschaftliche Methodik im Horizont der artes-Tradition des 12. Jahrhunderts,” in Craemer-Ruegenberg, I. and Speer, A., eds., Scientia und ars im Hoch- und Spätmittelalter, Miscellanea Mediaevalia 22/1 (Berlin/New York, 1994), 145–57.Google Scholar

8 See Speer, A., “Reception-Mediation-Innovation: Philosophy and Theology in the 12th Century,” in Bilan et perspectives des études médiévales. Actes du premier congrès européen des études médiévales (Spoleto 27–29 May 1993), ed. Hamesse, J., FIDEM Textes et Études du Moyen Age 3 (Louvain-la-Neuve, 1994), 129–49 at 134.Google Scholar

9 See Speer, A., “Reception-Mediation-Innovation” (n. 8 above), 129–30; and Haskins, C. H., The Renaissance of the Twelfth Century (Cambridge, Mass., 1927), v-vi.Google Scholar

10 Chenu, M.-D., La théologie au douzième siècle, 3rd ed. (Paris, 1976), 21.Google Scholar

11 Ibid., 2130.Google Scholar

12 I argue for this main thesis in detail in my recently published study Die entdeckte Natur. Untersuchungen zu Begründungsversuchen einer “scientia naturalis” im 12. Jahrhundert, Studien und Texte zur Geistesgeschichte des Mittelalters 45 (Leiden-New York-Cologne, 1995). See also the following articles: “Zwischen Naturbeobachtung und Metaphysik. Zur Entwicklung und Gestalt der Naturphilosophie im 12. Jahrhundert,” Aufbruch–Wandel–Erneuerung. Beiträge zur sogenannten Renaissance des 12. Jahrhunderts , ed. Wieland, G. (Stuttgart, 1995), 155–80; “Secundum physicam. Die entdeckte Natur und die Begründung einer scientia naturalis im 12. Jahrhundert,” Documenti e studi sulla tradizione filosofica medievale 6 (1995): 1–37; “Reception-Mediation-Innovation” (n. 8 above).Google Scholar

13 Regarding the “School of Chartres” see Southern, R. W., Medieval Humanism and Other Studies (Oxford, 1970), 6185; idem, , Platonism, Scholastic Method and the School of Chartres, The Stenton Lecture 1978 (Reading, 1979); idem, “The School of Paris and the School of Chartres,” Renaissance and Renewal in the Twelfth Century , ed. Benson, R. L. and Constable, G. (Cambridge, Mass., 1982), 113–37; Häring, N. M., “Chartres and Paris Revisited,” in Essays in Honour of A. C. Pegis , ed. O'Donnell, J. R. (Toronto, 1974), 268–329; Speer, A., “Reception-Mediation-Innovation” (n. 8 above), 139–40.Google Scholar

14 Thierry of Chartres, Lectiones in Boethii librum de Trinitate 2, 19, in Commentaries on Boethius by Thierry of Chartres and His School, ed. Häring, N. M. (Toronto, 1971), 161, lines 19–24: “Naturalem in motu et inabstractam appellat phisicam. Naturalem appellat eo quod naturas considerat i.e. formas inmateriatas. Natura enim uocatur forma inmateriata. Et phisica formas inmateriatas considerat cum materia: nunquam abstrahendo formas ab ipsa materia. Unde et ratione utitur phisica que scilicet formas et status rerum in materia conprehendit.” Google Scholar

15 Ibid., 2, 21 (ed. Häring, , 161, lines 39–44): “In motu uero dicitur esse propter mutabilitatem materie cum qua formas rerum considerat. Motum enim appellat mutabilitatem. Nam ubi mutabilitas ibi motus: et ubi motus ibi mutabilitas. Sed phisica in motu queritur et in mutabilitate…. Materia autem mutabilitas est.” Google Scholar

16 Ibid. (ed. Häring, , 161, lines 49–53): “Est igitur una pars speculatiua naturalis in motu inabstracta ut expositum est. Hec est uero phisica…. Quasi diceret: inabstracta dicitur i.e. inseparabilis eo quod forme quas considerat inabstracte uel inseparabiles sunt a materia i.e. non possunt esse nisi in materia.” Google Scholar

17 Thierry of Chartres, Tractatus de sex dierum operibus 1, in Commentaries on Boethius by Thierry of Chartres and His School, ed. Häring, N. M. (Toronto, 1971), 555, lines 1–6: “De septem diebus et sex operum distinctionibus primam Geneseos partem secundum phisicam et ad litteram ego expositurus, inprimis de intentione auctoris et de libri utilitate pauca premittam. Postea vero ad sensum littere hystorialem exponendum ueniam ut et allegoricam et moralem lectionem que a sanctis doctoribus aperte execute sunt ex toto pretermittam.” Google Scholar

18 Ibid., 5 (ed. Häring, , 557, lines 67–68).Google Scholar

19 Ibid., 17 (ed. Häring, , 562, lines 19–20).Google Scholar

20 Ibid., 9 (ed. Häring, , 559, lines 19–24): “Nam ex caldario quanto maior fumus ascendit tanto aqua que in ipso continetur minoratur. Similiter si super mensam aliquam superficies aque continetur et postea ignis illi continue aque superponatur, statim contingit ut per superpositum calorem superficies illa aque attenuetur et in ipsa superficie quedam macule aride appareant, aqua in quibusdam locis contracta et congregata.” See Häring, N. M., “Die Erschaffung der Welt und ihr Schöpfer nach Thierry von Chartres und Clarenbaldus von Arras,” Platonismus in der Philosophie des Mittelalters , ed. Beierwaltes, W., Wege der Forschung 197 (Darmstadt, 1969), 161–267 at 178.Google Scholar

21 Tractatus 10 (ed. Häring, , 559, lines 28–31): “In eadem etiam conuersione contingebat ut ex superioribus aeris calore inmixto humori terre ex aquis nuper discoopertam — ut ex his inquam duobus ipsa terra conciperet vim producendi herbas atque arbores. Que uis ex calore celi naturaliter procedit in terram ex aquis nuper discoopertam.” See Zimmermann, A., “Die Kosmogonie des Thierry von Chartres,” Architectura poetica, Festschrift J. Rathofer , ed. Ernst, U. and Sowinski, B. (Cologne, 1990), 107–18 at 113–14.Google Scholar

22 See Tractatus 10 (ed. Häring, , 559, lines 31 and 36); ibid., 11 (ed. Häring, , 560, lines 41–42); ibid., 14 (ed. Häring, , 561, line 79).Google Scholar

23 Ibid., 16 (ed. Häring, , 562, lines 1–3): “ex causis seminalibus quas in spacio illorum sex dierum elementis inseruit affirmamus …”; see Zimmermann, A., “Die Kosmogonie des Thierry von Chartres” (n. 21 above), 116.Google Scholar

24 Tractatus 14 (ed. Häring, , 561, line 79); ibid., 17 (ed. Häring, , 562, line 9).Google Scholar

25 Ibid., 17 (ed. Häring, , 562, line 9); see also Hedwig, K., Sphaera Lucis. Studien zur Intelligibilität des Seienden im Kontext der mittelalterlichen Licht Spekulation (Münster, 1980), 71.Google Scholar

26 Tractatus 2 (ed. Häring, , 555, line 15).Google Scholar

27 Ibid., 2 (ed. Häring, , 556, line 31).Google Scholar

28 Ibid. (ed. Häring, , 555, lines 18–19): “Mundane igitur substantie cause sunt quatuor: efficiens ut deus formalis ut dei sapientia finalis ut eiusdem benignitas materialis quatuor elementa.” Google Scholar

29 Ibid., 3 (ed. Häring, , 556, lines 50–53): “In materia igitur que est quatuor elementa operatur summa Trinitas ipsam materiam creando in hoc quod est efficiens causa: creatam informando et disponendo in eo quod est formalis causa: informatam et dispositam diligendo et gubernando in eo quod est finalis causa.” Google Scholar

30 William of Conches, Dragmaticon 1, 7 (ed. Ronca, I., CCCM 167, § 4; ed. Gratarolus, G. [Strasbourg, 1567, repr. Frankfurt a. M., 1967], 1, 32): “Sed cum natura aliquid operatur, primitus rude quiddam et commixtum operatur, deinde paulatim format et diuidit. Prius namque operatur mustum, deinde quod in eo est faeculentum et graue ad infimum locum trahit, quod uero leue est ad supremum, quod mediocre ad medium locum.” Google Scholar

31 William of Conches, Philosophia 1, 13 (ed. Maurach, G. [Pretoria, 1980], § 44; cf. PL 172, 56A): “… ut aliquid sit natura operante, necesse est divinam voluntatem praecedere.” A more detailed argumentation can be found in ibid., 2 (ed. Maurach, , § 6; cf. PL 172, 44B–C). Concerning the discussion that points to the theory of elements, and in this context regarding the influence of Calcidius and Constantine the African, see in detail Speer, A., “Die entdeckte Natur” (n. 12 above), 163–75, see especially 164–65, nn. 105–6.Google Scholar

32 William of Conches, Glosae super Platonem (in Timaeum 30 A) 52 (ed. Jeauneau, É. [Paris, 1965]), 122 = Philosophia 1, 13 (ed. Maurach, , § 44; cf. PL 172, 56B): “Iterum dicet hoc esse divine potentie derogare sic hominem esse factum dicere: Quibus respondemus e contrario id esse ei conferre quia ei attribuimus et talem rebus naturam dedisse et per naturam operantem corpus humanum creasse.” Concerning the question of man's animation see also Philosophia 1, 13 (ed. Maurach, , § 43; cf. PL 172, 55D): “Non enim credendum est animam, quae spiritus est et levis et munda, ex luto factam esse, sed a deo homini collatam.” Google Scholar

33 Glosae (in Timaeum 28A) 36 (ed. Jeauneau, , 103): “Mundus est id quod gignitur. Sed omne quod gignitur habet principium existentie. Gignitur ex aliqua causa necessario, ac si diceret: nihil gignitur sine causa, ergo nec mundus.” See also Glosae (in Timaeum 29C) 47 (ed. Jeauneau, , 115); see in detail Speer, A., Die entdeckte Natur, chap. 6/2 (n. 12 above), 139–50.Google Scholar

34 Glosae (in Timaeum 28A) 37 (ed. Jeauneau, , 104): “Opus nature est quod similia nascuntur ex similibus, ex semine vel ex germine. Et est natura vis rebus insita similia de similibus operans.” Ibid., 105: “Opus nature, etsi in se esse desinat, in semine remanet.” Google Scholar

35 See Philosophia 4, 13 (ed. Maurach, , § 20; cf. PL 172, 90C); ibid., 4, 16, § 24; cf. PL 172, 91B-C); Glosae (in Timaeum 45B) 137 (ed. Jeauneau, , 237).Google Scholar

36 See Philosophia 1, 10 (ed. Maurach, , § 35; cf. PL 172, 52D-53A): “Elementorum vero talis est dispositio, quod inferiorem locum obtinet terra, deinde aqua, postea aer, superiorem ignis. Si enim aliquid inferius terra esset naturaliter gravis, ad illud tenderet (gravia enim naturaliter tendunt ad deorsum).” Glosae (in Timaeum 34A) 69 (ed. Jeauneau, , 143): “est enim ignis qui naturaliter est in motu.” Glosae (in Timaeum 30A) 53 (ed. Jeauneau, , 122): “Cum enim terra naturaliter tendat deorsum, ignis sursum, nisi terra optineret locum inferiorem, ignis superiorem, hec semper tenderet ad inferiorem, hic ad superiorem.” Google Scholar

31 Glosae (in Timaeum 49A) 161 (ed. Jeauneau, , 269): “Premissa questione de vi et natura iles prius ostendit vim, deinde naturam.” Google Scholar

38 Ibid.: “Ile est receptaculum omnium que gignuntur, quia formas et qualitates eorum in se recipit. Est quasi nutricula, quia circa ipsam omnia corpora augmentantur.” See also ibid. (in Timaeum 50B) 165 (ed. Jeauneau, , 274): Eadem et consimilis ratio et difficultas est in ea natura id est in ile que recipit cuncta corpora id est formas et qualitates omnium corporum; quippe hec ile minime id est non recedit a condicione propria id est a propria natura, quamcumque qualitatem recipiat.” Google Scholar

39 Philosophia 1, 9 (ed. Maurach, , § 30; cf. PL 172, 51D): “Sed si tale fuerit medium, quod aequaliter habeat se ad duo extrema non plus transiens in naturam unius quam alterius, coniunctionem illorum observabit.” Ibid. (§ 31; cf. PL 172, 52A): “Sed dicimus nos non ponere terminum in divina potentia, sed dicimus, de illis, quae sunt nullum potuisse sufficere nec iuxta naturam rerum posse esse aliud quod sufficeret.” A detailed discussion of the coniunctio elementorum can be found in Speer, A., Die entdeckte Natur, chap. 4/4.a (n. 12 above), 163–75.Google Scholar

40 Glosae (in Timaeum 33A) 65 (ed. Jeauneau, , 138): “Ideo hoc fecit quia videbat id est sciebat … earn id est talem naturam, id est proprietatem, corporis ut ei facile noceretur importuna id est superflua accessione caloris vel contra frigoris et omnium huiusmodi que sunt in magna et violenta potentia, id est que habent agentes qualitates, quia illarum tantum est corrumpere. Quod per hominem probari potest, quia calor, qui extra hominem est, importune accedendo, sepe vel corrumpit hominem vel omnino dissolvit. Similiter frigus et similes qualitates. Que vero intra hominem sunt, superflue recedendo, corrumpunt ipsum. Ergo omnis corruptio vel fit importuna accessione exteriorum vel recessione interiorum.” Concerning the agentes qualitates see Philosophia 1, 9 (ed. Maurach, , § 29; cf. PL 172, 51C) and Glosae (in Timaeum 31B) 61 (ed. Jeauneau, , 131–32): “Sed hoc in contrariis habentibus agentes qualitates sine medio esse non potest. Sunt autem agentes qualitates calor et frigiditas. Calor enim desiccat et consumit; frigiditas similiter desiccat, spissat et constringit. Si enim unum alteri sine medio apponatur repugnant, unumquodque aliud dissolvit.” Google Scholar

41 Glosae (in Timaeum 41A) 114 (ed. Jeauneau, , 205): “vere estis dissolubilia natura, quia ex partibus coniuncta. Et unde hoc, diceret aliquis, si coniuncta sunt et sunt dissolubilia natura? Ideo scilicet quia omne, quod coniunctum est, dissolubile natura. Natura enim exigit, ut omne compositum in componentia possit resolvi.” Google Scholar

42 Quaestiones naturales 22 (ed. Müller, M., Die Quaestiones naturales des Adelardus von Bath [Münster, 1934], 26, lines 22–23): “Non fingendo, quod non est, sed naturam rei exprimendo, quae occulta est….” See also the introductory setting of the Quaestiones naturales, 1–2.Google Scholar

43 Jolivet, J., “Les ‘Quaestiones naturales’ d'Adélard de Bath ou la nature sans le Livre,” Études de civilisation médiévale, Mélanges E.-R. Labande (Poitiers, 1974), 437–46 at 437.Google Scholar

44 Quaestiones naturales 6 (ed. Müller, , 11, lines 36–37): “Nisi enim ratio iudex universalis esse deberet, frustra singulis data esset.” Ibid., 12, lines 5–7: “Id autem assero, quod prius ratio inquirenda sit, ea inventa auctoritas, si adiacet, demum subdenda. Ipsa vero sola nec fidem philosopho facere potest, nec ad hoc adducenda est.” Quaestiones naturales 32 (ed. Müller, , 37, line 20): “Itaque rerum causae cum ratione constant.” See Zimmermann, A., “Die Theologie und die Wissenschaften,” in Die Renaissance der Wissenschaften im 12. Jahrhundert , ed. Weimar, P. (Zürich/Munich, 1981), 87–105 at 98–101.Google Scholar

45 Plato, , Timaeus (translatio Calcidii) 28A, ed. Waszink, J. H., Plato latinus 4 (London/Leiden, 1962), 20, lines 20–22: “Omne autem quod gignitur ex causa aliqua necessaria gignitur; nihil enim fit, cuius ortum non legitima causa et ratio praecedat.” Google Scholar

46 Glosae (in Timaeum 28A) 36 (ed. Jeauneau, , 104): “Vere nichil gignitur sine causa quia nichil fit quod non precedat causa. Et hoc est: Nichil fit ortum, non precedat vel tempore, ut ea que facta sunt in tempore, vel dignitate, ut est mundus, … legitima causa et ratio, id est legitima et rationabilis causa.” Cf. Plato, , Timaeus (translatio Calcidii) 28A (ed. Waszink, , 20, lines 20–22).Google Scholar

47 Philosophia 3, 2 (ed. Maurach, , § 5; cf. PL 172, 76B).Google Scholar

48 Dragmaticon 5, 12 (ed. Ronca, , § 5–6; cf. Gratarolus, 5, 208–9).Google Scholar

49 Glosae (in Timaeum 28A) 37 (ed. Jeauneau, , 104–5).Google Scholar

50 So the statement of Maurach, G., ed., Wilhelm von Conches, Philosophia mundi (Pretoria, 1974), 5961.Google Scholar

51 William of Conches, Glosae (in Timaeum 47A) 149 (ed. Jeauneau, , 252): “Hic ostendit precipuam utilitatem visus, cuius precipua utilitas est philosophia. Nichil enim maius est sapientia. Huius causa est visus sic. Cum homo visu notaret creationes rerum et creaturarum dispositiones, iniuncta est ei cura inquirendi naturas rerum sapienter disponi, quesivit, cuius sapientia sic res crearet et disponeret; reperiensque nullius creature sapientiam hoc agere posse, confirmavit quandam substantiam esset ingenitam, eternam, cuius sapientia hoc ageret. Et ea que invenit, scripto et voce alios docuit: et sic philosophia inventa est. Visus igitur est causa philosophie.” Cf. Bernard of Chartres, Glosae super Platonem (in Timaeum 47A) 7 (ed. Dutton, , 215, lines 389–400). One may notice that William and Bernard both refer only to one of the two senses that commonly represent the human capacity of understanding: visus, related to philosophy and based on knowledge, and auditus, related to theology and based on obedience (cf., for example, the Anticlaudianus of Alan of Lille). That both twelfth-century masters emphasize only one part and overlook the other can be taken as another indication of the growing interest in a philosophical and physical lectio. Google Scholar

52 See Philosophia 1, 7 (ed. Maurach, , § 19–21; cf. PL 172, 48C-49C).Google Scholar

53 William of Conches, Glosae (in Timaeum 28A) 36 (ed. Jeauneau, , 103): “Sed omne quod gignitur habet principium existentie. Gignitur ex aliqua causa necessario, ac si diceret: nihil gignitur sine causa, ergo nec mundus.” See also ibid. (in Timaeum 29C) 47 (ed. Jeauneau, , 115).Google Scholar

54 See Philosophia 1, 7 (ed. Maurach, , § 19; cf. PL 172, 48C-D); Philosophia 1, 7 (ed. Maurach, , § 24; cf. PL 172, 50B-C); Glosae (in Timaeum 29C) 47 (ed. Jeauneau, , 115); see also Speer, A., Die entdeckte Natur (n. 12 above), 163–69.Google Scholar

55 Dijksterhuis, E. J., Die Mechanisierung des Weltbildes (Berlin, 1956), 131.CrossRefGoogle Scholar

56 See Zimmermann, A., “Die Kosmogonie des Thierry von Chartres” (n. 21 above), 108–9 and 118.Google Scholar

57 However, we must also see the limitations of this Chartrian attempt to found a scientia naturalis. The strength of the theoretical framework is seldom accompanied by a penetrating analysis of the material presented that deals with concrete natural phenomena. Often the presentation seems to follow the encyclopedic model, with the greater part of the “natural questions” taken from literary sources instead of empirical observations. Here the specific strength of the Aristotelian model of a scientia naturalis comes out; and indeed, as I have pointed out, we can notice the first traces of the growing interest in Aristotle's libri naturales at the end of the twelfth century. Nevertheless we must observe that the decisive presupposition lies in the theoretical turn concerning the understanding and conceptualization of nature visible in the Chartrian approach to nature.Google Scholar

58 I will mention in particular the first Latin translation of Euclid's Elementa from an Arabic version ascribed to Adelard of Bath and the Latin translation of the so-called Astronomic Tables (Zij) of al-Khwarizmi; this translation is entitled Ezich Elkauresmi per Athelardum Bathoniensem ex Arabico sumptus. There are other translations of mainly mathematical and astronomical works, under which the Centiloquium Ptolomei, a translation of the first 39 sentences of the katab al-thamara, ascribed to Ptolemy and the Liber ysagogarum Alchoarismi in artem astronomicam, a collection of especially algorithmic teachings, figure prominently. Finally I will mention Adelard's treatise on the astrolabe, De opere astrolapsus. In this treatise Adelard tries to summarize the results of his “Arabic studies” and to relate them to the overarching question of the causae rerum — the causes in things themselves. See Busard, H. L. L., The First Latin Translation of Euclid's “Elements” Commonly Ascribed to Adelard of Bath (Books I-VIII and Books X, 36-XV, 2) (Toronto, 1983); Burnett, C., ed., Adelard of Bath: An English Scientist and Arabist of the Early Twelfth Century, Warburg Institute Surveys and Studies 14 (London, 1987); Speer, A., Die entdeckte Natur, chap. 2/4 (n. 12 above), 44–51.Google Scholar

59 See Bernard of Chartres, Glosae super Platonem (in Timaeum 53B-C) 8 (ed. Dutton, , 234, lines 443–48): “Nunc iam ordinationem, scilicet quibus opportunitatibus inter se ordinentur et habitudinibus, demonstrari conuenit nouo genere, scilicet per quasdam proportiones arithmeticas, geometricas, armonicas, qui sunt gradus philosophiae. Dixi nouo genere, sed uobis cognito, qui in omni scientia perfecti estis. Hic innuit se uelle docere ueras et incommutabiles substantias quattuor principalium corporum, quod superius promiserat.” See also Glosae super Platonem (in Timaeum 35B) 5 (ed. Dutton, , 178, line 143–179, line 147). See moreover Thierry of Chartres, Tractatus 32 (ed. Häring, , 569, lines 2–7) and Tractatus 33 (ed. Häring, , 569, lines 22–25); on this question see Jeauneau, É., “Mathématique et Trinité chez Thierry de Chartres,” Metaphysik im Mittelalter , ed. Wilpert, P., Miscellanea Mediaevalia 2 (Berlin, 1963), 289–95 at 290–91.Google Scholar

60 Thierry of Chartres, Commentum super Boethii librum de Trinitate 2, 1, in Commentaries on Boethius by Thierry of Chartres and His School, ed. Häring, N. M. (Toronto, 1971), 68, lines 6–10: “Considerare quidem debemus unumquodque prout intelligi potest quia ut a quodam dictum est sapientis est rationes inducere iuxta qualitatem rei proposite ut de naturalibus rationabiliter, de mathematicis disciplinaliter, de diuinis agamus intellectualiter ut paulo post explicabitur.” Google Scholar

61 Clarembaldus of Arras, Epistola ad dominam 3, in Life and Works of Clarembald of Arras: A Twelfth-Century Master of the School of Chartres, ed. Häring, N. M. (Toronto, 1965), 226: “In quo quantum philosophiae contineatur, liquido apparet cum ipse — utpote totius Europae philosophorum praecipuus — qualiter exemplaris forma in materia operans cuncta produxerit, iuxta phisicas tantum rationes edoceat.” Google Scholar

62 Chenu, M.-D., La théologie au douzième siècle (n. 10 above), 2130 and 309–22.Google Scholar

63 Mittelstraß, J., “Leben mit der Natur. Über die Geschichte der Natur in der Geschichte der Philosophie und über die Verantwortung des Menschen gegenüber der Natur,” in Über Natur. Philosophische Beiträge zum Naturverständnis, ed. Schwemmer, O. (Frankfurt a. M., 1987, 21991), 37–62 at 50.Google Scholar

64 See Wieland, G., “Plato oder Aristoteles?” (n. 7 above), 605–30.Google Scholar

65 See Crombie, A. C., Augustine to Galileo (London, 1952); Koyré, A., “Galileo and Plato,” in his Metaphysics and Measurement (Cambridge, Mass., 1968); Duhem, P., “Thierry de Chartres et Nicholas de Cues,” Revue des sciences religieuses 3 (1909): 525–31; von Weizsäcker, C. F., Die Einheit der Natur (Munich, 1974), 208–24.Google Scholar