Skip to main content
SpringerLink
Log in

The Mathematics Theses Defended at collège de Clermont (1637–1682): How to Guard a Fortress in Times of War

  • Chapter
  • First Online:
Teaching Philosophy in Early Modern Europe

Part of the book series: Archimedes ((ARIM,volume 61))

Abstract

To capture some of the early modern teaching practices while studying the interaction between ancient and new doctrines, this chapter focuses on the thesis booklets defended at the Jesuit collège de Clermont from 1637 to 1682. First, it examines what this exceptional corpus (almost one thesis in mathematics per year is available) reveals about the role that the Parisian Jesuits assigned to the defense of mathematical theses in the context of their complex relationship with the University of Paris. Then, it focuses on the optics theses that were defended under Pierre Bourdin: they borrowed from the Jesuit theoretical optics of the 1610-1620s, while making room for extraordinary devices such as the Specillum Fidei. Finally, it shows that the optics of Ignace-Gaston Pardies, who held the chair of mathematics some twenty years later, incorporated the main lesson of the novatores: it is not a theory of vision, but a theory of light, which is based on mechanics defined as the science of motion in general. While Bourdin preserved the structure of Aristotelian knowledge, Pardies overturned this structure by considering mechanics as the key to all physics.

Mathesis, République des Savoirs, ENS, Collège de France, CNRS, PSL Research University, 75005, Paris, France. This article took a very long time to complete. Above all, we would like to thank Dan Garber and Susanna Berger for their patience with us; Susanna deserves special thanks for the care with which she revised our article and helped us improve our English. We would also like to thank our colleagues in Berlin, Bologna, Brussels, Groningen, Paris, Princeton and Rome who, by their questions and comments, gave us new impetus when we were stuck in the middle of the ford.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Meyer 1993; eadem 2002; eadem 2017; and Rice 1999; eadem 2004; eadem 2007a, b.

  2. 2.

    Brockliss 1981; idem 2002; idem 2006; Gatto 1994; Ariew 1999; Hellyer 2005; Klein 2017; Raphael 2017.

  3. 3.

    Leinsle 2006.

  4. 4.

    On mathematics theses defended in Antwerp and Louvain, see Vanpaemel 2008; De Bruycker 2009; Dhombres and Radelet-de Grave 2009. According to the Ratio studiorum, the printing of theses was not compulsory. Lukács 1986, 375.

  5. 5.

    The list of these theses is given in Bibliography, section 2, which is organized by the presiding professor and for each presiding professor, listed chronologically under the name of the student defending. References to the theses in the notes are given in boldface to distinguish them from other bibliographical entries. Most of them were for the first time identified in Le Dividich 1996, xxxiii–xxxvi; see also Dupont-Ferrier 1921–1925, vol. III, Appendix I, 273–85.

  6. 6.

    Military architecture, especially Bourdin’s, is studied in d’Orgeix 2005, 91–105; Romano 2006; De Lucca 2012, 96–104, 118, 189, 217, 229, and 332. Topics in cosmology and natural philosophy in theses defended in the sixties are studied in Roux 2017. The discipline of mechanics in these theses has not yet been studied.

  7. 7.

    On the dedications and on the illustrations of theses, and on their material production, see Meyer 1993; eadem 2002; eadem 2017.

  8. 8.

    Exceptions include the thesis that Charles Potier dedicates to Claude Lestandart, holder of the abbaye du Val Secret near Château-Thierry where Potier came from (1640), the thesis that Jacques Truel de Cohon dedicates to Timoleon Le Roy, premier commis to the War Minister Michel Le Tellier (1648), and the thesis that Jules Louis Bolé de Champlay dedicates to François Michel Le Tellier, who succeeded his father as War Minister (1668).

  9. 9.

    Ariew 2014, 15–17.

  10. 10.

    On the Sorbonne copy of Anonyme 1676, the title is completed by the following manuscript annotation: “Theses mathematicae seu potius physicomathematicae” (mathematics, or rather physic-mathematics theses).

  11. 11.

    Galluzzi 1993.

  12. 12.

    When Pascal published his Expériences nouvelles touchant le vide in October 1647, the only writings to mention the Rouen experiment before were Pierius 1648 and Petit’s letter to Chanut of November 1646, which was published one year later in Petit and Magni 1647.

  13. 13.

    Compare Villette 1651, 13–4, § 37–41 and Cavalieri 1647, 3–4, § 1–5, 6, § 9. Cavalieri published his method in Cavalieri 1635; Cavalieri 1647 is an answer to the objections formulated in Guldin 1635–1641.

  14. 14.

    Tarteron 1665; Prou 1665a; and Ragayne de la Picotière 1665a.

  15. 15.

    De Vic 1643, 14, § 2. Gedoin 1644, 4.

  16. 16.

    For the quotation, see Thierry 1648, 11, § 29, and 12, § 33: “Vocetur aut a potiori parte Spiritus aërius, a communi tamen aëre distinctus.” See also Truel de Cohon 1648, 11, § 33–4. Both defend the position of Étienne Noël (1581–1659), who was then rector of the collège de Clermont, and who is now remembered for having been mocked by Pascal.

  17. 17.

    Villette 1651,14–5, § 43–6.

  18. 18.

    Prou 1665b, idem 1665c; Ragayne de la Picotière 1665b; Decombes 1665; and de la Bletonniere 1665.

  19. 19.

    Lukács 1986, 374–7, 402. The monthly disputation in mathematics was introduced in 1599. According to Cosentino (1970, 212) if no rules were formulated to regulate mathematics disputations, contrary to what Clavius had wished, it was because the enactment of rules would have obliged all colleges to create a chair of mathematics, whereas only the most important colleges could afford one. On Clavius’ fight for the teaching of mathematics through the different versions of the Ratio, see Romano 1999, 111–32; on the first chairs of mathematics in France, see ibid., 393–414.

  20. 20.

    On the rivalry between the Jesuits of Paris and the Sorbonne, see Jourdain 1862–1866, 60–7, 83–7, 94–9, 107–9, and 150–8; Dupont-Ferrier 1921–25, vol. I, 26–28. Compère and Julia 1984–2002, vol. III, 359–407 argue that the monarchy stimulated this rivalry both for motivating the two institutions to give their best and for being granted the role of an arbitrator between them.

  21. 21.

    For a similar situation in Antwerp and Louvain, see De Bruycker 2009, 139.

  22. 22.

    Bibliothèque interuniversitaire Sorbonne (Paris), OBL 32–1 (105, 130 bis); VCM 6=6680 (1–2). For an exception, see the thesis print of Coret 1661, now to be found in many European libraries. On 12 December 1661, in the midst of the Jansenist crisis, this thesis print defended the infallibility of the Pope, including on questions of fact.

  23. 23.

    Petit to Huygens, 7 August 1665, in Huygens 1888–1950, vol. V, 433; Oldenburg to Boyle, 14 July 1665, in Oldenburg 1965–1973, vol. II, 431–2. For some mathematics thesis booklets, there remain however only one copy preserved in the library of the Conservatoire des arts et métiers, where, after the Revolution, treatises on applied mathematics and on fortifications coming from the libraries of the religious orders were deposited. Romano (2006, 362–5) discusses on the circulation of manuscripts, especially those of Bourdin’s.

  24. 24.

    Bourdin himself uses the term theses only in the title of the 1640 thesis defended by Pierre Gaillard, but Paul Le Mercier introduced his manuscript transcriptions of the 1638 thesis and of the 1639 thesis respectively as “Theses mathematicae seu Musaeum mathematicum” and as “Aliae theses mathematicae … seu conclusiones mathematicae” (BNF, Ms. Lat. 17862, resp. f. 906 and 966) and Descartes speaks of the “Jesuit optical theses” (to Mersenne, 9 February 1639, in Descartes 1996, vol. II, 499). Oldenburg to Boyle, 14 July 1665, in Oldenburg 1965–1973, vol. II, 432–3 uses the terms “thesis” and “disputation” interchangeably.

  25. 25.

    The Greek term from which panegyricus derives refers to an eulogy, to the assembly in which this eulogy is pronounced, and, finally, to the festive event itself.

  26. 26.

    Similar terminological variations are noted in Leinsle 2006, 41.

  27. 27.

    On this difference and the exercises in Jesuit establishments, see Leinsle 2006, 26–9.

  28. 28.

    Jourdain 1862–1866, 150–8, Compère and Julia 1984–2002, vol. III, 364.

  29. 29.

    For a description of the annual celebrations at the collège de Clermont and at college of La Flèche, see resp. Dupont-Ferrier 1921–25, vol. I, 245–6; and de Rochemonteix 1889, vol. IV, 149–56. For a description of the public, see Meyer 2002, 38–42; and Dhombres and Radelet-de Grave 2009, 27; it should be noted, however, that the testimonies of ceremonies available to us concern the defenses of important people, like the eldest sons of a Minister and of the President of the Parlement de Paris, and that we do not know how an ordinary defense was conducted. For the place of mathematics in these celebrations during the late sixteenth and early seventeenth century, see Romano 1999, 491–511.

  30. 30.

    In our corpus, there are several exceptions to this rule. First, there were Sunday exercises; as we argued in Collacciani and Roux (2017b, 92–93), they probably corresponded to monthly disputations that were not public, but involved only the small group of mathematics students gathered in the aula mathematica. Second, there were theses that were defended in unusual times of the year because of extraordinary events such as the passage of a comet (Tarteron 1665 and Prou 1665a, both defended on 29 January 1665; Vernon to Oldenburg, 10 April 1672, in Oldenburg 1965–1973, vol. IX, 14). Last, for some unknown reasons, some defenses took place during the week, such as Guillaume Benard de Rezay’s defense (Benard de Rezay 1666) on Thursday 29 July 1666, Jean-Baptiste and Pierre-Antoine de Castagnere de Chasteauneuf’s defense (Castagnere de Chasteauneuf 1667) on Wednesday 13 July 1667, Jean-Baptiste Colbert de Seignelay’s defense (Colbert de Seignelay 1668) on Thursday 30 August 1668, or Alexandre Milon’s (Milon 1671) defense on Monday 6 July 1671.

  31. 31.

    Le Dividich 2003, 56–61 for leaflets announcing courses in mathematics; Rochemonteix 1889, vol. IV, 153; Meyer 2002, 38–9; and eadem 2017, 36–8 for leaflets announcing the defense of theses.

  32. 32.

    The strategy of sharing the costs of printing is noted by Leinsle 2006, 37; Dhombres and Radelet-de Grave 2009, 26; Meyer 2017, 20. How the time was shared when there were several defendants is not known.

  33. 33.

    We follow the indications given in Dainville 1954, 110–11.

  34. 34.

    On the 1664–65 comets, see Roux 2017. On the observatory of the collège de Clermont, see Bigourdan 1918; Dupont-Ferrier 1921–25, vol. I, 189–90; and Dainville 1954, 44. Nicolas d’Harouys built machines for teaching the different astronomical systems that are alluded to in Ragayne de la Picottière 1665b, 4, § 7. Garnier (1678, 118) describes these machines and explains that, because of their number and magnitude, they could not be stored in the rooms of the Library, but had to be kept in a large room of their own, where they could be seen by eminent travelers; see for example Huygens’ Journal, in Huygens (1888–1950, vol. XXII, 545), André de Graindorge to Huet, 9 May 1665 and 5 August 1665, in Graindorge 1942, resp. 267 and 303; and Brice 1685, vol. II, 51.

  35. 35.

    On Bourdin, see Sommervogel 1890–1932, vol. II, 29–30; on his career, see Dainville 1954, 110; and Romano 1999, 563–4. On his relations with Descartes, see Ariew 1995; idem 1997; idem 1999, 5, 24–9, 156, 173, 193–6, and 203–4; and Collacciani and Roux 2017b. On his treatise on fortifications, see d’Orgeix 2005, 91–105; Romano 2006; De Lucca 2012, 96–104, 118, 189, 217, 229, and 332. On his theses and more generally his teaching at the collège de Clermont, see Le Dividich 1996, 39–44, 47–8, 180–8, 234–43, and 272–6; and Collacciani and Roux 2017b.

  36. 36.

    Leinsle (2006, 20) notes that some theses are a series of exercises independent of each other, while others constitute small treatises on a given subject.

  37. 37.

    Potier 1640, 3, § 4, and 7, § 1–2.

  38. 38.

    Leurochon 1622; and idem 1629. On the diversity of these theses, see Romano 1999, 501–3. See also (ibid., 618–21) on the reproduction of mathematics thesis booklets defended in Paris in 1622. Concerning mathematical recreations, see Chabaud 1994.

  39. 39.

    Jones (1947, 119–20) and Ariew 1995, 212; idem 2014, 21, date Boudan’s engravings in Bourdin’s thesis booklets back to 1631, but Collacciani and Roux (2017b, 110–11) prove that they were made in 1637, at the time when Bourdin was beginning to teach mathematics in Paris.

  40. 40.

    Petit 1639, in BNF, Ms. Lat. 17861, p. 879; Culant 1639, in BNF, Ms. Lat. 17861, p. 881; Bourdin 1641; idem 1645; idem 1661. Le Dividich (1996, 41; and 2003, 61–3) mention the use of these engravings in Bourdin’s classes.

  41. 41.

    Collacciani and Roux 2017b, 106–11.

  42. 42.

    Henri 1639, 6 § 3, 7 § 1, and 6 § 1. The machine to display books is certainly a book wheel similar to the one presented in Ramelli 1588.

  43. 43.

    Henri 1639, 7 § 1–4; and Cornouaille and Manchon 1638, 7 § 4–5.

  44. 44.

    Henri 1639, 2. The programs of 1640, 1648 and 1651 also mention real experiments.

  45. 45.

    Henri 1639, 6. It is also mentioned in Foucquet 1646, 6 and, 11 § 4.

  46. 46.

    Collacciani and Roux 2017b, 99–100. The most complete article on this device is Malcolm 1998; concerning Niceron, see Truci 1976; and Bessot 2005; concerning Bourdin, see Collacciani and Roux 2017b, 95–100.

  47. 47.

    Niceron 1638, 101 and du Breuil 1649, “Instruction sur le traite VII,” sigs. Zz1v–2r. On Charles du Lieu, see Malcolm 1998, 219–21.

  48. 48.

    Du Breuil 1649, 161–2; Forest-Duchesne 1650, 226–7; Schott 1657, 470–1 and pl. 23, fig. 7, 453.

  49. 49.

    For a photograph of the Florentine apparatus, see Bonelli 1959, 38; the optical tube was lost in the 1966 Arno flood, see Righini-Bonelli 1976, 197–96; for its present state, see https://catalogue.museogalileo.it/object/OpticalToy.html. Only the optical tube remains in the Teyler Museum, see https://www.teylersmuseum.nl/en/collection/instruments/fk-0316-1-5-anamorphoscopes-5. Hunt and Sharp 2011 propose a reconstruction of the apparatus.

  50. 50.

    Niceron 1638, 106, 115–8; and Du Breuil 1649, 162 and 165.

  51. 51.

    Kepler 1604, 37–56, 168. On Kepler’s optics, see Lindberg 1976, 178–208; Sabra (1981); Simon 1988 and idem 2019; Smith 2015, 322–75.

  52. 52.

    Scheiner 1619, 124–5, 137–8, and 197–9. See also Scheiner 1630, 106a30–116b9. On Scheiner’s compromise, see Pantin 2008, 263–7; Gal and Chen-Morris 2010 203–6; and Smith 2015, 374–5.

  53. 53.

    Scheiner 1619, 17–18; and Scheiner 1630, 110b39–112a3.

  54. 54.

    Scheiner 1619, 128–38; Pantin 2008, 263–7.

  55. 55.

    Scheiner 1619, 73–4.

  56. 56.

    Aguilón and Scheiner are among the very few authors to be named, see Bouthier 1647, 12 § 1–2.

  57. 57.

    Cornouaille and Manchon 1638, 15 § 2, 4–5; Henri 1639, 14 § 1; Culant 1639, [ 1] § 2; Potier 1640, 9 § 1–2 and 4; Gaillard 1640, [1] § 1–2; de Vic 1643, 11 § 4–5; Gedoin 1644, 13 § 29; Bouthier 1647, 12 § 2; Thierry 1648, 8 § 19–20; and de Bourneuf, 1650, 10–11 § 27, and § 30. See also BNF, Ms. Lat. 17861, f. 900 and 905 and Ms. Lat. 17862, f. 906–9.

  58. 58.

    Culant 1639, [3] § 1; Henri 1639, 14 § 2; Potier 1640, 7 § 5; Gaillard 1640, [1] § 6; Bouthier 1647, 12 § 2. On the arguments against the emission of visual rays, see Lindberg 1976, 66–7, 178-85; Smith 2015, 185–8, 256–75; and Simon 2019, 43–44, and 127–28.

  59. 59.

    De Bourneuf 1650, 10 § 15–16.

  60. 60.

    Despont 1642, 10 § 1–2: “Ad explicandam visionem necessariæ sunt species in medio. Hæ non sunt, ut vulgo creditor, (nisi forte metonymice) imagines obiectorum, sed entitas quædam simplicissima, et uniusmodi respectu omnium omnino visilium, cuius sit munus Aspectabilia potentiis distantibus coniugere ad agendum, ut de lumine censent Peripatetici, quo veluti vehiculo, cœlestia in sublunaribus varios producunt effectus… II Species rerum visilium impressæ potentiis et ab iisdem expressæ sunt vere similes obiectis, et illorum imagines naturales, ac præter eas nullæ sunt aliæ rerum imagines, aut species formales, ne in speculis quidem, sed nec in charta dum clauso in conclavi per foramen externa obiecta apparent.” For other mentions of species, see Thierry 1648, 8 § 17–18; and de Bourneuf 1650, 10 § 25–6. de Vic 1643, 10 § 1 is discussed infra, p. XXX.

  61. 61.

    Potier 1640, 5 § 5: “… cùm essent privati oculorum usu, naso viderent, et obiectos colores naribus aptè discernerent, ut referunt probatae fidei Platerus, Rungius, Smetius, Vagerus, Keplerus, et Fortunatus Vopiscus Plempius.” This is the last problem discussed in Plempius 1632, 310–12, who refers exactly to the same group of authors.

  62. 62.

    We would like to thank Tawrin Baker for the clues on anatomical representations of the eye that he shared with us. For more, see Baker 2016.

  63. 63.

    Scheiner 1619, 17–18. The inclination of the optic nerve with respect to the central axis of the eyeball is also taken into account in Descartes’ Dioptrique, see Descartes 1996, vol. VI, 106.

  64. 64.

    On these conventions, see Shapiro 2008, 282–6. Concerning pictures in Descartes’ natural philosophy, see Lüthy 2006; Zittel 2009; and idem 2011.

  65. 65.

    Collacciani and Roux 2017a, 59–65. According to Bourdin, the law of reflection and the law of refraction are the same, insofar as the less inclined a light ray is, the less reflected or refracted it is, see Pallu and Touchelée 1635, 10 § 7; Potier 1640, 9 § 6; and BNF, Ms. Lat. 17861, f. 908. His conflict with Descartes was linked to the fact that they were not referring to the same angles by the terms “angle of incidence” and “angle of refraction.”

  66. 66.

    Potier 1640, 11 § 3.

  67. 67.

    Potier 1640, 15 § 3: “Lucis et colorum actionem in oculos explicare per motum materiæ cuiusdam subtilis fusæ per aëris, et transparentium corporum poros, quàm lucida corpora moveant, eáque tangant oculos modis variis, atque omnino aliter, quam per species intentionales, est cicatricem curare novo vulnere, et gratis implicare sese iisdem, et insuper novis difficultatibus. Has afferre, et inanitatem subtilis illius materiæ demonstrare.”

  68. 68.

    De Vic 1643, 10 § 1: “Ad visionem necesse est ut à visili in medio diaphano producatur aliquid, sive illud sit species, ut placet Peripateticis; sive motio medii subtilis ad instar baculi, ut Aristoteli affingit Simplicius; sive aliquid aliud transmissum per poros, aut vacuum, ut innuit Democritus.” Matton (2018) argued against Collacciani and Roux (2017a, 71–2) that this passage does not contain any allusion to Descartes, but is only an allusion to Simplicius’ exposition of Aristotle’s doctrine, that Bourdin might have known through Gassendi (1642, 173–4). This seems improbable to us, because Bourdin never discusses Gassendi, while he had been involved in a long controversy with Descartes. In 1644, Bourdin’s and Descartes’ reconciliation was so complete that Bourdin was entrusted with the task of distributing copies of Principia philosophiae to the French Jesuits (Descartes 1996, vol. IV, 143 and 160).

  69. 69.

    De Bourneuf 1650, 8, § 17–8: “Luminis naturam varii vario modo exponunt: alii per corpusculorum perpetuum fluxum et eiaculationem à lucido: alii per corpusculorum perspicuo in medio positorum motum factum à lucido, vel colorato. Ingeniosè quidem utrique; at minus commodè, singula si spectes. Nobis igitur via restat, communis et regia. Quare lumen dicimus esse formam in subiecto apto, sine tamen subiecti penetratione. Subiectum illud perspicuum est, et aliud quidem alio magis. Lumine vero indoles ea quæ percipitur satis ab oculato, à cæco nato minimé.” See also Villette 1651, 12 § 34–5. The mention of a blind person is probably an allusion to Dioptrique, in Descartes 1996, vol. VI, 85–6.

  70. 70.

    Pardies 1665a; idem 1665b.

  71. 71.

    On Pardies’s life and works, see Anonymous 1726; Sommervogel 1890–1932, vol. VI, 201–8; and Ziggelaar 1971.

  72. 72.

    The thesis booklets on military architecture that the catalogue of the Bibliothèque municipale de Lyon dates from 1671 without giving any reason for such a date are left aside.

  73. 73.

    The section on optics of de Mesrigny 1670, 7–14 is borrowed from Anonymous 1666, 3–13; Lamoignon de Basville 1666, 3–13; or Benard de Rezay 1666, 3–13; its section on military architecture is borrowed from Bolé de Champlay 1668, 10–11 or from Anonymous 1669, 14–15 § 3–6. We were not able to see Hervé 1670 but our guess is that it is identical to Mesrigny 1670.

  74. 74.

    Concerning paradoxes in Lamoignon (1663) and Ragayne de la Picottiere 1665b, 15–16, see Roux 2017 114–5. The 1665 theses were defended by many students, see Ragayne de la Picottiere 1665a; Prou 1665b; Ragayne de la Picottiere 1665b; Prou 1665c; Decombes 1665; and de la Bletonniere 1665: in what follows, we only give reference to Ragayne de la Picottiere.

  75. 75.

    For a study of Renaissance paradoxes, see Colie 1966. That thesis booklets presented paradoxes is noted in Leinsle 2006, 40, 45–6; and Dhombres and Radelet-de Grave 2009, 173.

  76. 76.

    On this polarization of the French natural philosophy, see Roux 2013a.

  77. 77.

    BNF, Ms. Lat. 17862, f. 501–13.

  78. 78.

    Lamoignon 1663; Le Meilleur 1663, 12–13 § 3–8. On the political context of Lamoignon’s thesis, see Lerner 2001, 534–7. Nicolas d’Harouys was the author of the “new mathematical hypothesis of Clermont” which is also presented in Lamoignon de Basville 1666, 19 but not in Benard de Rezay 1666.

  79. 79.

    Anonymous 1664, 6 § 4: “Nimium tamen et poetica videtur esse et mechanica; quatenus est poetica, reiicitur a philosophia omnis inimica figmenti; ut mechanica nimius est, non admittitur a natura, cuius est artis humanæ legibus imperare, non subiici.”

  80. 80.

    Ragayne de la Picottière 1665a, 3 § 3, 4 § 4, 11 § 39; and Ragayne de la Picottière 1665b, 5–6 § 14–15, § 19; commented in Roux 2017, 114.

  81. 81.

    Lamoignon de Basville 1666, 17: “Si quid a Copernicæa differt, maxime quam absurda de suo multa conferat, et hypothesym cæteroquin ingeniosam labefacet. Peccat quidem contra Sapientiæ leges Copernicæa, sed multo gravius Cartesiana, quæ sic Dei potentiæ tribuit omnia, nihil ut sapientiæ videatur relinquere: mundum illa jam mole quam par era longe maiorem expresserat, hæc immensum exhibet: prohibet prima ne recta deorsum ferantur gravia; eadem sursum ire certe jubet altera. Gloriatur Copernicæa motuum simplicitate, multiplicitatem consectatur Cartesiana dum infinities infinitis partibus motus pariter infinitos imprimit…. Denique Copernicæa quamvis non vera, possibilis tamen est: Cartesiana nec vera, nec possibilis.” See also Anonymous, 1666, 15 § 6.

  82. 82.

    Castagnere de Chasteauneuf 1667 (or Bolé de Champlay 1668), 4 § 3. For other criticisms, see idem, 5 § 5, 8 § 11, 9 § 11, and 11, § 16; Anonymous 1669, 8 § 5. While the other theses present one system after another, Castagnere de Chasteauneuf 1667 and Bolé de Champlay 1668 present one celestial phenomenon after another and, for each of them, compare the different systems.

  83. 83.

    On the official condemnations of Cartesianism, see Armogathe (1969, 1977); Ariew (2013) and Roux 2019.

  84. 84.

    Pardies to Kircher, 20 August 1665 and Pardies 1673a; and Ziggelaar 1971, 30–6.

  85. 85.

    Pardies to Payen, 27 October 1666, in Journal des sçavans, 7 February 1667, 45–8.

  86. 86.

    Milon 1671, 3 § 1–2.

  87. 87.

    Milon 1671, 4 § 3: “[E]sse aliquas Species emissas ex objectis, quæ tamen non distinguantur ab ipsiis radiis reflexis, decussatis, terminatis…. Visionem fieri per receptionem, nullatenus per emissionem. Species terminatas in Retina determinare videndi facultatem ope tenuium nervi optici capillamentorum. Objecta tanto majora apparere quanto major est eorum in Retina imago: visionem eo fortiorem quo plures radii ad oculum penetrant: eo distinctiorem quo radii ex uno procedentes puncto magis ad se se accedentes colliguntur ad Retinam in angustiori loco.”

  88. 88.

    Pardies neatly summarizes the explanation of light proposed in Descartes 1996, vol. VIII-1, 108 sqq. By comparison Lamoignon de Basville 1666 and Anonymous 1666, 3 § 2 are vague.

  89. 89.

    Milon 1671, 4 § 4: “In ea hypothesi, solem lucidáque corpora etiam aversi aut intra cubiculum occlusi videremus; et radius solaris per foramen obliquè jacentis chartæ transmissus ad perpendicularem infringeretur.”

  90. 90.

    Other similar objections appear in Paradoxes 2 and 3, in Milon 1671, 7: light would be reflected as well by the earth or by a rough piece of wood, as by a mirror; the light of the Sun or of a burning torch would be as intense at large distances as at small ones.

  91. 91.

    This objection is also at the root of Paradox 12, in Milon 1671, 8. This is at the time a common criticism of Descartes 1996, vol. VI, 93–105; it is for example to be found in Grimaldi 1665, prop. 19, 173–6. There might be an echo of this criticism in Anonymous 1666 (or Benard de Rezay 1666), 6 § 10, which is identical to Lamoignon de Basville 1666, 6 § 11. Later on, it will be found in Pardies 1670, 86–7 § 37 and Ango 1682, book I, prop. 72, 85–8.

  92. 92.

    Milon 1671, 5 § 5–6: “[C]onjecturam aliquam facere fortasse possumus ex comparatione ad sonum: jure enim optimo Luminis Simius appellatus Sonus est. Manifestum autem est sonum produci et formari et propagari per certas quasdam aëris undulantis aut alterius æquivalentis corporis vibrationes: adeo ut variæ ejusmodi undulationes ex varii locis procedentes contagione quodam ulterius procedentes, se se impunè trajiciant, ac deinde in aurem illapsæ organum auditus verberent, excitentque varios sonorum sensus pro varietate commotionum seu tremorum aëris. Ita fortasse posset ut lumen excitaretur et propagaretur organumque visus afficeret, per certas quasdam et crebras, non quidem aëris, sed subtilioris alicujus substantiæ undulationes et frequentes succussiones.”

  93. 93.

    This is an allusion to the interpretation of the barometric experiments that were given in Jesuit colleges. In the case of the collège de Clermont, see Thierry 1648, 10–15 § 26–33; Truel de Cohon 1648, 10–15 § 33–44; and De Bourneuf 1650, 13 §§ 37–38. These are commented on by Collacciani and Roux 2017b, 103.

  94. 94.

    This is what Milon 1671, 6 § 7 is about.

  95. 95.

    This is what Milon 1671, 6–7 § 8–9 is about. The theory of colors advanced here by Pardies is similar to the one that he developed in his teaching in Bordeaux, on which see Ziggelaar 1971, 177–9.

  96. 96.

    Roux 1669, 9–10 § 53–60.

  97. 97.

    This image first appears in Kircher 1671, lib. II, pars I, chap, Exp. 3, p. 102. Kircher 1673, lib. I, sect. I, cap. 1 begins with a whole section entitled “Praelusio I. Sonus lucis simia est.”

  98. 98.

    On the analogy between light and sound in general, see Darrigol 2010a and idem 2010b.

  99. 99.

    Mersenne 1636, book I prop. 1, p. 1–5. The main limitation of this analogy is that, for Mersenne, intentional species are necessary in the case of light, but not in the case of sound. See as well book I, prop. 25, p. 44–8.

  100. 100.

    Potier 1640, 11 § 1, Villette 1651, 12 § 36.

  101. 101.

    Kircher 1671, lib. II, pars I, cap. 6–7, p. 96–102.

  102. 102.

    Pardies to Payen, 27 October 1666, in Journal des sçavans, 7 February 1667, p. 45; Bibliothèque municipale de Bordeaux, mss 934, f. 236v, Pardies to Newton, 21 May 1672, in Newton 1958, p. 97. Moreover, while it is known that Pardies, if he is not the author, at least got his hands on Rochon 1672; this work mentions Grimaldi 1665, 181.

  103. 103.

    Grimaldi, 1665, prop. 2, p. 12.

  104. 104.

    Grimaldi 1665, prop. 22 and 43, p. 187–90 and p. 341–70.

  105. 105.

    Grimaldi 1665, prop. 44, p. 370–95.

  106. 106.

    Shapiro 1973, 209–44.

  107. 107.

    Duhamel 1669 was sent to the Académie des sciences and examined by Huygens (Ziggelaar 1971, 17). In Pardies 1670, Preface, Sig. A4v, Pardies claimed: “… il y a déja trois ans que j’ai donné publiquement tout ce que je mets dans ce discours”; in his letter to Oldenburg, 13 January 1672, in Oldenburg 1965–1973, vol. VIII, 455, he wrote: “Il y a deja plusieurs années que j’ay enseigné publiquement tout cecy et mesme je l’ay imprimé dans des theses.”

  108. 108.

    Milon 1671, 6 § 7.

  109. 109.

    De Caelo II, chap. 7, 289 a19.

  110. 110.

    De anima II, chap. 7, 418b9-10.

  111. 111.

    See Ziggelaar 1971, 79–85 about the remarks that were added to the Discours du mouvement local, idem (95–7) about the contemporary perception of Discours de la connaissance des bêtes as a Cartesian work, idem (113–4) about the letters concerning Rochon and Pardies that the General of Jesuits Giovanni Paolo Oliva sent, and idem 118–20 about the contribution of Pardies to the Lettre d’un philosophe. Beaude 1976 criticized Ziggelaar 1971 for not having confronted more directly the problem of Pardies’ crypto-cartesianism.

  112. 112.

    Anonymous 1726, 670.

  113. 113.

    Le Gallois 1672, 59 and 66. Pardies 1670, “Avis à ceux qui veulent apprendre la geometrie,” 1st ed. (1671), Sig. a13v: “Si l’on veut se donner la peine de venir au College de Clairmont, l’Auteur de ces Elemens les y expliquera publiquement après la S. Remy,” 2nd ed. (1673), Sig. A18: “Si l’on veut se donner la peine de venir au College de Clermont, l’Auteur de ces Elemens continuera de les y expliquer publiquement les Lundis et les Vendredis.” Denis 1682, 81: “ceux qui y trouveront quelque difficulté, pourront s’en éclaircir faciclement, en allant au College de Clermont; car le R.P. Pardies, qui y professe les mathematiques, prend la peine d’en expliquer toutes les Propositions, et de répondre aux objections qu’on luy forme sur cette Matiere [motion and the rules of percussion].” Pardies 1673a, Sig. A5r: “Ceux qui auront la curiosité d’apprendre à fond la Théorie et l’usage de ces Machines, pourront le faire aisément, s’ils veulent se donner la peine de venir au College de Clermont, où l’on en fera des entretiens publics, une fois la semaine, pendant quelque temps.”

  114. 114.

    Pardies 1672 analyzed in Roux 2013a and Pardies 1665a analyzed in Roux 2017, 117–8.

  115. 115.

    Duhamel 1669, 3: “Mechanica vocetur scientia, quae motûs localis productionem, conservationem, communicationem, contensionem, impulsionem, accelerationem, extinctionem per prima principia demonstrat.” Gabbey 1992, 311–4; and idem 2004, 22–3 emphasized this new definition of mechanics, that they found in Wallis 1670-71; in France, Poisson first made it explicit in his preface to Descartes 1668, Sig. A2.

  116. 116.

    Pardies 1670, Sig. A2.

  117. 117.

    Pardies 1673b, Sig. a2r-a3v. This preface then continues to offer a history of mechanics which evokes Descartes’ letter to Plempius for Fromondus, 3 October 1637, in Descartes 1996, 420-1, and finally ends with a presentation of the mechanics in six books that Pardies had projected. While in 1669 he divided mechanics into kinetics, statics, barytonics, ballistics, hydraulics and pneumatics (Roux 1669), here he merged barytonics and ballistics on the one hand, hydraulics and pneumatics on the other, but added a part on librations and vibrations of pendulums and another part on waves of light and sound (Pardies 1673b, Sig. a6– 11r which is rehearsed in his letter to Oldenburg, 13 January 1672, in Oldenburg 1965–1973, vol. VIII, 452–5).

  118. 118.

    Leibniz to Des Bosses, 2 February 1706, in Leibniz 1875–1890, vol. II, p294.

  119. 119.

    Ango 1682, 2.

  120. 120.

    Ango 1682, 3–4.

  121. 121.

    La Forest 1682, 3 § 1.

  122. 122.

    Lecture notes by Paul Mercier of Bourdin’s mathematics course at the collège de Clermont in 1636–1638.

  123. 123.

    Lecture notes by an anonymous hand of Bourdin’s course in mathematics.

  124. 124.

    Lecture notes by doctor Raymond Dufour of a philosophy course given by Ignace–Gaston Pardies in Bordeaux in 1669.

  125. 125.

    The list is organized by the presiding professor who wrote the theses, and under each professor organized chronologically. The names of the professors of mathematics who wrote the theses are not mentioned in the thesis booklets, but are known through the Jesuit archives. We follow the list given in Dainville 1954, 110–111.

  126. 126.

    According to the dates we know, Bourdin had already left La Flèche for Paris when Pallu and Touchelée 1635 was defended, we include it as the earliest existing thesis booklet written by Bourdin.

  127. 127.

    Yves Henri is mentioned only in the BNF copy, which begins with a frontispiece in which the rectangles and circles are printed while the images inside them are drawn by hand. The Lyon copy includes printed figures of the three cosmological systems at the section “Stadium cosmographiæ,” of optics and the physiology of the eye at the section “Gymnasium opticæ,” and of military fortifications with the manuscript annotation “propugnaculum Le Bastion” at the section “Ænigma geometricomilitare.”

  128. 128.

    The BNF copy does not mention the year of the defense, the CNAM copy mentions neither the year nor the day. We argued that this exercise dates from 1640 in Collacciani and Roux 2017a, 55–6.

  129. 129.

    There are two copies at the Bibliothèque centrale du conservatoire national des arts et métiers, one of which does not mention the name of the defendant.

  130. 130.

    The BSG copy does not mention the name of the defendant.

  131. 131.

    According to the title-page, the disputation took place on 20 June only, but, according to the program, it took place on 20 and 21 June.

  132. 132.

    De Bourneuf 1650 and Villette 1651 have an identical introductory page introduced by the title “Dissertatio generalis.”

  133. 133.

    Due to the Covid-19 pandemic we were not able to compare Villette 1651 and d’Herbelot 1651, but our suspicion is that they are identical..

  134. 134.

    According to the title-page, the disputation took place on 8 June 1663, but according to handwritten annotations in some copies, it took place on 15 June.

  135. 135.

    Tarteron 1665 and Prou 1665a are identical.

  136. 136.

    Ragayne de la Picottiere 1665a and Prou 1665b are identical.

  137. 137.

    Ragayne de la Picottiere 1665b, Prou 1665c, Decombes 1665, and de la Bletonniere 1665 are identical.

  138. 138.

    Due to the Covid-19 pandemic we were not able to compare Anonymous 1666 and de Maupeou 1666, but our suspicion is that they are identical..

  139. 139.

    The section on optics is identical in Benard de Rezay 1666 and Lamoignon de Basville 1666, but the latter adds § 8. The section on optics in Anomymous 1666 and Lamoignon de Basville 1666 are identical, except that the latter omits § 8 and § 22, but adds § 29. The section on astronomy which is mentioned in the titles (ex astronomica) of Benard de Rezay 1666 and Lamoignon de Basville 1666 includes fairly similar comparisons of the systems of the world, but the later adds a section on eclipses [or: “on the eclipse”]. Anomymous 1666 does not include the comparison of the systems of the world present in Benard de Rezay 1666 and Lamoignon de Basville 1666, but includes the section on eclipses of Lamoignon de Basville 1666.

  140. 140.

    Castagnere de Chasteauneuf 1667, Bole de Champlay 1668, and perhaps Anonymous 1667 are identical. Bole de Champlay originally bore the date “20 January” but this is corrected by hand to “20 March.”

  141. 141.

    The last page indicates that the thesis booklet was defended in August 1668: Renaudot, “Gazette du 1 Septembre 1668,” in Renaudot 1669, 914, gives the precision that it was on 30 August, Colbert having defended his philosophy thesis on 29 August.

  142. 142.

    The section on optics in Mesgrigny 1670, 7–14 is borrowed from Anonymous 1666, its section on military architecture is borrowed from Anonymous 1668, 10–11, § 21–4, and from Anonymous 1669,14–15, § 3–6. The problems to be solved at the end of each paragraph are sometimes, but not always, different. A few developments of Anonymous 1666 do not figure in Mesgrigny 1670, for example the condemnation of Descartes’ subtle matter expressed in Anonymous 1666, 4, § 6.

  143. 143.

    Due to the Covid-19 pandemic we were not able to compare De Mesgrigny 1670 and Hervé 1670, but our suspicion is that they are identical.

  144. 144.

    As a manuscript note indicates, this copy was sent by Pardies to Huygens, through the intermediary of Galois.

  145. 145.

    Roux 1669 and Duhamel 1669 are identical. According to the dates we know, Pardies was still in Bordeaux when these theses were defended. We include them here as the earliest known theses written by Pardies.

  146. 146.

    Anonymous 1671a and Milon 1671 are identical.

  147. 147.

    Anonymous 1671b has no title-page. The King’s College copy is bound with Milon 1671. The same printing matrices were used.

  148. 148.

    Godley 1674 and de Geldrop 1674 are identical.

  149. 149.

    Anonymous 1676 and de Geldrop 1674 are identical except for one page added in the former (p. 6, “de meteororum æquilibrium”).

References

  • Ango, Pierre. 1682. L’optique divisée en trois livres. Paris: Michallet.

    Google Scholar 

  • Anonymous. 1726. Review of Pardies. Œvres complètes. Journal de Trévoux ou Mémoires pour l’histoire des sciences et des beaux–arts. Avril 1726: 664–693.

    Google Scholar 

  • Ariew, Roger. 1995. Pierre Bourdin and the Seventh Objections. In Descartes and his Contemporaries: Meditations, Objections, and Replies, ed. Roger Ariew and Marjorie Greene, 208–225. Chicago: University of Chicago Press.

    Google Scholar 

  • ———. 1997. Critiques scolastiques de Descartes: le cogito. Laval théologique et philosophique 53 (3): 587–603.

    Article  Google Scholar 

  • ———. 1999. Descartes and the Last Scholastics. Ithaca: Cornell University Press.

    Google Scholar 

  • ———. 2013. Censorship, Condemnations and the Spread of Cartesianism. In Cartesian Empiricism, ed. Mihnea Dobre and Tammy Nyden, 25–46. Dordrecht/Heidelberg/New York/London: Springer.

    Chapter  Google Scholar 

  • ———. 2014. Descartes and the First Cartesians. Oxford: Oxford University Press.

    Book  Google Scholar 

  • Armogathe, Jean-Robert. 1969. Dom Desgabets et Port–Royal. Chroniques de Port–Royal 17 (18): 68–87.

    Google Scholar 

  • ———. 1977. Theologia cartesiana: L’explication physique de l’eucharistie chez Descartes et Dom Robert Desgabets. The Hague: Martinus Nijhoff.

    Book  Google Scholar 

  • Baker, Tawrin. 2016. Why All This Jelly? Jacopo Zabarella and Hieronymus Fabricius ab Aquapendente on the Usefulness of the Vitreous Humor. In Early Modern Medicine and Natural Philosophy, ed. Peter Distelzweig, Benjamin Goldberg, and Evan Ragland, 59–90. Dordrecht: Springer.

    Chapter  Google Scholar 

  • Beaude, Joseph. 1976. Sur le cartésianisme d’Ignace-Gaston Pardies. A propos de l’ouvrage du Père A. Ziggelaar. Revue d’histoire des sciences 29–33: 261–267.

    Article  Google Scholar 

  • Bessot, Didier. 2005. Synthèse et développement de techniques d’anamorphoses au xviie siècle: les traités du père Jean-François Niceron. Mélanges de l’École Française de Rome. Italie et Méditerranée 117 (1): 91–129.

    Article  Google Scholar 

  • Bigourdan, Guillaume. 1918. La station astronomique du collège de Clermont (première période) et la mission astronomique de Siam. Comptes rendus hebdomadaires des séances de l’Académie des sciences 166: 833–840 and 871–875.

    Google Scholar 

  • Bonelli, Maria Luisa. 1959. Una lettera di Evangelista Torricelli a Jean-François Niceron. In Convegno di studi Torricelliani in occasione del 350o anniversario della nascita di Evangelista Torricelli (19–20 ottobre 1958), 37–41. Faenza: Fratelli Lega.

    Google Scholar 

  • Bourdin, Pierre. 1641. Le Cours de mathématique, representé par figures, et cartes, et clairement expliqué dans toutes ses parties, avec quantité de connoissances et pratiques nouvelles, Le tout en faveur de ceux qui veulent apprendre les mathematiques en peu de temps. Paris: François Pelican.

    Google Scholar 

  • ———. 1645. Le Cours de mathématique, representé par figures, et clairement expliqué, avec quantité de connoissances et pratiques nouvelles. Le tout en faveur de la Noblesse, et de ceux qui veulent apprendre en bref la Mathematique du temps rapportée à la Milice. Paris: François Pelican.

    Google Scholar 

  • ———. 1661. Le Cours de mathématique contenant en cent figures une idée generale de toutes les parties de cette Science. Paris: Sébastien Bernard.

    Google Scholar 

  • Brice, Germain. 1685. Description nouvelle de ce qu’il y a de plus remarquable dans la ville de Paris. 2 vols. La Haye: Abraham Arondeus.

    Google Scholar 

  • Brockliss, Laurence. 1981. Aristotle, Descartes and the New Science: Natural Philosophy at the University of Paris 1600–1740. Annals of Science 38: 33–69.

    Article  Google Scholar 

  • ———. 2002. Harvey, Torricelli and the institutionalization of new ideas in seventeenth–century France. In Wissensideale und Wissenskulturen in der Frühen Neuzeit Ideals and Cultures of Knowledge in Early Modern Europe, ed. Wolfgang Detel and Claus Zittel, 115–134. Berlin: Walter de Gruyter.

    Chapter  Google Scholar 

  • ———. 2006. The Moment of No Return: The University of Paris and the Death of Aristotelianism. Science and Education 15: 259–278.

    Article  Google Scholar 

  • Cavalieri, Bonaventura. 1635. Geometria indivisibilibus continuorum nova quadam ratione promota. Bologna: de Ducis.

    Google Scholar 

  • ———. 1647. Exercitationes Geometricæ Sex. Bologna: J. Monti.

    Google Scholar 

  • Chabaud, Gilles. 1994. Sciences en jeux: les récréations mathématiques et physiques en France du xviie au xviiie siècle. Unpublished PhD, École des hautes études en sciences sociales (Paris).

    Google Scholar 

  • Colie, Rosalie L. 1966. Paradoxia epidemica. The Renaissance tradition of Paradox. Princeton: Princeton University Press.

    Google Scholar 

  • Collacciani, Domenico, and Sophie Roux. 2017a. La querelle optique de Bourdin et de Descartes à la lumière des thèses mathématiques soutenues au collège de Clermont. In Chemins du cartésianisme, ed. Antonella Del Prete and Raffaele Carbone, 51–84. Paris: Garnier.

    Google Scholar 

  • ———. 2017b. Pierre Bourdin, anti–cartésien ou jésuite ordinaire? Historia Philosophica 15: 89–113.

    Google Scholar 

  • Compère, Marie-Madeleine and Dominique Julia. 1984–2002. Les collèges français (xvie—xviiie siècles), 3 vols. Paris: INRP/Éditions du CNRS.

    Google Scholar 

  • Coret, Jacques. 1662. Theses propugnatæ a jesuitis, die 12. decembris an. 1661. In Collegio Claromontano Parisiens. In quarum decimâ nonâ appendice manifesta continetur hæresis qua fidei catholicæ fundamentum & Ecclesiæ gallicanæ doctrina concutiuntur. [Paris]: s.n.

    Google Scholar 

  • Cosentino, Giuseppe. 1970. Le matematiche nella Ratio studiorum della Compagnia di Gesù. Miscellanea storica ligure 2: 169–213.

    Google Scholar 

  • D’Orgeix, Émilie. 2005. Fortification et perspective militaire au xviie siècle en France. Les Cahiers de la recherche architecturale et urbaine 17: 91–105.

    Google Scholar 

  • Darrigol, Olivier. 2010a. The Analogy between Light and Sound in the History of Optics from the ancient Greeks to Isaac Newton. Centaurus 52 (2): 117–155.

    Article  Google Scholar 

  • ———. 2010b. The Analogy between Light and Sound in the History of Optics from the ancient Greeks to Isaac Newton. Part 2. Centaurus 52 (3): 206–257.

    Article  Google Scholar 

  • De Bruycker, Angelo. 2009. To the adornment and honour of the city’: the mathematics course of the Flemish Jesuits in the seventeenth century. British Society for the History of Mathematics Bulletin 24: 135–146.

    Article  Google Scholar 

  • de Dainville, François. 1954. L’enseignement des mathématiques dans les Collèges jésuites de France du XVIe au XVIIIe siècle. Revue d’histoire des sciences 7–1: 6–21 and 7–2: 109–123.

    Google Scholar 

  • De Lucca, Denis. 2012. Jesuits and Fortifications: The Contribution of the Jesuits to Military Architecture in the Baroque Age. Leiden-Boston: Brill.

    Book  Google Scholar 

  • de Rochemonteix, Camille. 1889. Un collège de Jésuites aux xviie et xviiie siècles: Le Collège Henri IV de La Flèche, 4 vols. Le Mans: Leguicheux.

    Google Scholar 

  • Denis, Jean–Baptiste. 1682. Mémoires, conférences et observations sur les arts et les sciences présentées à Monseigneur Le Dauphin. 2nd ed. Paris: Laurent d’Houry.

    Google Scholar 

  • Descartes, René. 1668. Traité de la Mécanique, composé par Monsieur Descartes: de plus l’Abrégé de Musique du même auteur, mis en français avec les éclaircissements nécessaires par N. P. P. D. L. [Nicolas Poisson], Paris: Charles Angot.

    Google Scholar 

  • ———. 1996. Œuvres de Descartes, ed. Charles Adam and Paul Tannery, revised ed. ed., 11 vols. Paris: Vrin.

    Google Scholar 

  • Dhombres, Jean, and Patricia Radelet-de Grave. 2009. Une mécanique donnée à voir. Les thèses illustrées défendues à Louvain en juillet 1624 par Grégoire de Saint-Vincent S.J. Turnhout: Brepols.

    Google Scholar 

  • Du Breuil, Jacques. 1649. Troisième et dernière partie de la perspective pratique où se voient les beautez et les Raretez de cette Science […] et les effets admirables des trois rayons. Droit, reflechi et brisé. Paris: Vve F. Langlois.

    Google Scholar 

  • Dupont-Ferrier, Gustave. 1921–25. Du collège de Clermont au lycée Louis-le-Grand, 2 vols. Paris: De Boccard.

    Google Scholar 

  • Forest–Duchesne, Nicolas. 1650. Florilegium universale liberalium artium et scientiarum, philologicum, mathematicum, philosophicum ac theologicum. Paris: Lesselin.

    Google Scholar 

  • Gabbey, Alan. 1992. Newton’s Mathematical Principles of Natural Philosophy: A Treatise in Mechanics? In The Investigation of Difficult Things: Essays on Newton and the History of Exact Sciences in Honour of D.T. Whiteside, ed. Peter M. Harman and Alan E. Shapiro, 305–322. Cambridge: Cambridge University Press.

    Google Scholar 

  • ———. 2004. What was ‘Mechanical’ About ‘The Mechanical Philosophy’? In The Reception of the Galilean Science of Motion in Seventeenth-Century Europe, ed. Carla Rita Palmerino and J.M.M.H. Thijssen, 11–24. Dordrecht: Springer.

    Chapter  Google Scholar 

  • Gal, Ofer, and Raz Chen-Morris. 2010. Baroque Optics and the Disappearance of the Observer: From Kepler’s Optics to Descartes’ Doubt. Journal of the History of Ideas 71-2: 191–217.

    Google Scholar 

  • Galluzzi, Paolo. 1993. Gassendi e l’affaire Galilée delle leggi del moto. Giornale Critico Della Filosofia Italiana 72: 86–119.

    Google Scholar 

  • Garnier, Jean. 1678. Systema bibliothecae collegii parisiensis Societatis Jesu. Paris: Sébastien Marbre-Cramoisy.

    Google Scholar 

  • Gassendi, Pierre. 1642. De apparente magnitudine solis humilis et sublimis epistolæ quatuor, in quibus complura physica, opticaque problemata proponuntur, et explicantur. Paris: Louis de Heuqueville.

    Google Scholar 

  • Gatto, Romano. 1994. Tra scienza e immaginazione. Le matematiche presso il collegio gesuitico napoletano (1552–1670 ca.). Florence: Olschki.

    Google Scholar 

  • Graindorge, André. 1942. Une page d’histoire des sciences. Vingt-deux lettres inédites d’André de Graindorge à P.-D. Huet. Mémoires de l’Académie nationale des sciences, arts et belles-lettres de Caen. N.S. 10: 245–337.

    Google Scholar 

  • Grimaldi, Francesco Maria. 1665. Physico-mathesis de lumine, coloribus et iride. Bologna: V. Benatiis.

    Google Scholar 

  • Guldin, Paul. 1635–1641. De centro gravitatis trium specierum quantitatis continuae. Vienna: Formis Gregorii Gelbhaar.

    Google Scholar 

  • Hellyer, Marcus. 2005. Catholic Physics: Jesuit Natural Philosophy in Early Modern Germany. Notre-Dame: University of Notre Dame Press.

    Google Scholar 

  • Hunt, James L., and John Sharp. 2011. The refractive anamorphic viewer of J.-F. Niceron: Reconstructing a 17th century optical toy. American Journal of Physics 79: 2023–2029.

    Article  Google Scholar 

  • Huygens, Christiaan. 1888–1950. Œuvres complètes de Christian Huygens, Société Hollandaise des Sciences, ed., 22 vols. The Hague: Martinus Nijhoff.

    Google Scholar 

  • Jones, Phillip S. 1947. The Identity of the Author of a Hitherto Anonymous Work. Scripta Mathematica 13: 119–120.

    Google Scholar 

  • Jourdain, Charles. 1862–1866. Histoire de l’université de Paris aux xviie et xviiie siècles. Paris: Hachette.

    Google Scholar 

  • Kepler, Johannes. 1604. Ad Vitellionem Paralipomena Quibus Astronomiae Pars Optica Traditur. Frankfurt: Claudius Manius et Haeredes Joanni Aubri.

    Google Scholar 

  • Kircher, Athanasius. 1671. Ars Magna Lucis et Umbræ in decem libros digesta quibus admirandæ Lucis et Umbrae in mundo, atque adeo universa natura, vir effectusque uti nova, ita varia novorum reconditiorumque spcciminum exhibitione, ad varios mortalium usus, panduntur. 2nd ed. Amsterdam: Janssonius a Waesberge Weyerstraet. (1st ed. 1645).

    Google Scholar 

  • ———. 1673. Phonurgia nova sive Conjugium mechanico-physicum Artis et naturae Paranympha Phonosophia Concinnatum qua universa sonorum natura, proprietas, vires effectuumq prodigiosorum Causae…. Describitur. Campidoniae: per Rudolphum Dreherr.

    Google Scholar 

  • Klein, Boris. 2017. Les chaires et l’esprit. Organisation et transmission des savoirs au sein d’une université germanique au xviie siècle. Lyon: Presses universitaires de Lyon.

    Book  Google Scholar 

  • Le Dividich, Aude. 1996. L’enseignement des mathématiques en France (1600–1670), Unpublished PhD. École des Chartes (Paris).

    Google Scholar 

  • ———. 2003. Afficher, distribuer: usages éphémères de l’imprimé dans l’enseignement des sciences mathématiques en France au xviie siècle. Revue de la Bibiothèque nationale de France 14: 56–63.

    Google Scholar 

  • Le Gallois, Pierre. 1672. Conversations de l’Académie de Monsieur l’abbé Bourdelot, contenant diverses recherches, observations, expériences et raisonnements de physique, médecine, chymie et mathématique. Le tout recueilli par le Sr Le Gallois. Et le parallèle de la physique d’Aristote et de celle de Mons. Descartes, leu dans ladite Académie. Paris: Thomas Moette.

    Google Scholar 

  • Leibniz, Gottfried Wilhelm. 1875–1890. Die philosophischen Schriften. Carl Immanuel Gerhardt, ed. 7 vols. Berlin: A. Asher & Comp.

    Google Scholar 

  • Leinsle, Ulrich. 2006. Dilinganae Disputationes. Der Lehrinhalt der gedruckten Disputationen an der Philosophischen Fakultät der Universität Dillingen 1555–1648. Regensburg: Schnell & Steiner.

    Google Scholar 

  • Lerner, Michel-Pierre. 2001. La réception de la condamnation de Galilée en France au xviie siècle. In Largo Campo di Filosofare. Eurosymposium Galileo 2001, ed. José Montesinos and Carlos Solís Santos, 513–548. La Orotava: Fundación Canaria Orotava de Historia de la Ciencia.

    Google Scholar 

  • Leurochon, Jean. 1622. Selectæ propositiones in tota sparsim mathematica pulcherrimæ. Quas in solemni festo sanctorum Ignatii et Xaverii et anniversaria colegii Mussipontani celebritate literaria propugnabunt Mathematicarum auditores. Pont-à-Moussson: S. Cramoisy.

    Google Scholar 

  • ———. 1629. Selectæ propositiones in tota sparsim mathematica pulcherrimæ ad usum et exercitationem cerebrium academiarum. Propositiones arithmeticæ, Geometricae, Mechanicae, Cosmographicae, Musicae, Opticae. Pont-à-Moussson: G. Bernard.

    Google Scholar 

  • Lindberg, David C. 1976. Theories of Vision from Al-Kindi to Kepler. Chicago: University of Chicago Press.

    Google Scholar 

  • Lukács, Ladislao, ed. 1986. Ratio atque institutio sudiorum Societatis Iesu (1586 1591 1599), Monumenta paedagogica Societatis Iesu. Vol. 5. Rome: Institutum historicum Societatis Iesu.

    Google Scholar 

  • Lüthy, Christoph. 2006. Where Logical Necessity Becomes Visual Persuasion: Descartes’ Clear and Distinct Illustrations. In Transmitting Knowledge: Words, Images and Instruments in Early Modern Europe, ed. Ian Maclean and Sachiko Kusukawa, 97–133. Oxford: Oxford University Press.

    Google Scholar 

  • Malcolm, Noel. 1998. The Title Page of Leviathan Seen in a Curious Perspective. The Seventeenth Century 13: 124–155.

    Article  Google Scholar 

  • Matton, Sylvain. 2018. De Pierre Bourdin à Olivier Heroult: Descartes dans les collèges au XVIIe siècle. Kritikon Litterarum 45: 194–223.

    Google Scholar 

  • Mersenne, Marin. 1634. Questions inouyes, ou, Récréation des scavans: qui contiennent beaucoup de choses concernant la théologie, la philosophie, & les mathématiques. Paris: Chez Iaques Villery.

    Google Scholar 

  • Mersenne, Marin. 1636. Harmonie universelle contenant la théorie et la pratique de la musique, ou il est traité de la nature des sons, et des mouvemens, des consonances, des dissonances, des genres, des modes, de la composition, de la voix, des chants, et de toutes sortes d’instruments harmoniques. Paris: Sébastien Cramoisy.

    Google Scholar 

  • Meyer, Véronique. 1993. Les thèses, leurs soutenances et leurs illustrations dans les universités françaises sous l’Ancien Régime. Revue de la Sorbonne 12: 43–111.

    Google Scholar 

  • ———. 2002. L’illustration des thèses à Paris dans la seconde moitié du xviie siècle. Paris: Paris-Musées.

    Google Scholar 

  • ———. 2017. Pour la plus grande gloire du roi. Louis XIV en thèse. Rennes: Presse Universitaires de Rennes.

    Google Scholar 

  • Newton, Isaac. 1958. Isaac Newton’s papers & letters on natural philosophy and related documents. Cambridge: Cambridge University Press.

    Google Scholar 

  • Niceron, Jean-François. 1638. Perspective curieuse ou Magie artificielle des effets merveilleux de l’Optique par la vision directe, de la Catoptrique, par la réflexion des miroirs plats, Cylindriques et Coniques, de la Dioptrique, par la refraction des Crystaux. Paris: P. Billaine.

    Google Scholar 

  • Oldenburg, Henry. 1965–1973. The Correspondence of Henry Oldenburg, ed. and trans. Alfred Rupert Hall and Marie Boas Hall, 9 vols. Madison, Wisconsin: University of Wisconsin Press.

    Google Scholar 

  • Pantin, Isabelle. 2008. Simulacrum, Species, Forma, Imago: What Was Transported by Light into the Camera Obscura? Early Science and Medicine 13: 245–269.

    Article  Google Scholar 

  • Pardies, Ignace-Gaston. 1665a. Dissertatio de motu et natura cometarum. Bordeaux: Pierre du Coq.

    Google Scholar 

  • ———. 1665b. Remarques sur les comètes et autres phaenomènes extraordinaires de ce temps. Bordeaux: G. de la Court.

    Google Scholar 

  • ———. 1670. Discours sur le mouvement local. Paris: Edme Martin.

    Google Scholar 

  • ———. 1671. Éléments de géométrie ou par une méthode courte et aisée l’on peut apprendre ce qu’il faut sçavoir d’Euclide, d’Archimede, d’Appollonius, et les plus belles inventions des anciens et des nouveaux géomètres. Paris: Sebastien Mabre-Cramoisy.

    Google Scholar 

  • ———. 1672. Discours de la connaissance des bêtes. Paris: Sebastien Mabre-Cramoisy.

    Google Scholar 

  • ———. 1673a. Deux machines propres à faire les cadrans avec très grande facilité decrites et expliquées par le P. Ignace Gaston Pardies de la Compagnie de Jésus. Paris: Sebastien Mabre-Cramoisy.

    Google Scholar 

  • ———. 1673b. La Statique ou la science des forces mouvantes. Paris: Sebastien Mabre-Cramoisy.

    Google Scholar 

  • Pascal, Blaise. 1647. Expériences nouvelles touchant le vuide: faites dans des tuyaux, syringues, soufflets & siphons de plusieurs longueurs & figures, avec diverses liqueurs, comme vif–argent, eau, vin, huyle, air, etc. avec un discours sur le mesme sujet. Paris: Margat.

    Google Scholar 

  • Petit, Pierre and Valeriano Magni. 1647. Observation touchant le vuide, faite pour la première fois en France, contenue en une lettre écrite à Monsieur Chanut […]Par Monsieur Petit intendant des fortifications, le 10 novembre 1646. Avec le discours qui en a esté imprimé Pologne sur le mesme sujet, en juillet 1647. Paris: Sebastien Cramoisy et Gabriel Cramoisy.

    Google Scholar 

  • Pierius, Jacques. 1648. An detur vacuum in rerum natura. Paris: n.d.

    Google Scholar 

  • Platter, Felix. 1583. De corporis humani structura et usu. [Basel]: Frober.

    Google Scholar 

  • Plempius, Fortunatus Vospicus. 1632. Ophthalmographia, sive Tractatio De Oculi fabrica, actione, et usu praeter vulgatas hactenus Philosophorum ac Medicorum Opiniones. Amsterdam: Henri Laurent.

    Google Scholar 

  • Ramelli, Agostino. 1588. Le diverse et artificiose machine del Capitano Agostino Ramelli. Paris: in casa de l’autore.

    Google Scholar 

  • Raphael, Renée. 2017. Reading Galileo: Scribal technologies and the Two New Sciences. Baltimore: Johns Hopkins University Press.

    Book  Google Scholar 

  • Renaudot, Théophraste. 1669. Recüeil des gazettes nouvelles ordinaires et extraordinaires. Relations et recits des choses avenues tant en ce Royaume qu’ailleurs, pendant l’année mil six cent soixante–huit. Paris: Bureau d’Adresse.

    Google Scholar 

  • Rice, Louise. 1999. Jesuit Thesis Prints and the Festive Academic Defence at the Collegio Romano. In The Jesuits: Cultures, Sciences, and the Arts, 1540–1773, ed. John W. O’Malley, Gauvin Alexander Bailey, Steven J. Harris, and T. Frank Kennedy, 148–169. Toronto: University of Toronto Press.

    Google Scholar 

  • ———. 2007a. Apes philosophicae: Bees and the Divine Design in Barberini Thesis Prints. In I Barberini e la cultura europea del Seicento. Atti del convegno internazionale (Roma 7–11 dicembre 2004), ed. Lorenza Mochi Onori et al., 181–194. Rome: De Luca.

    Google Scholar 

  • ———. 2007b. POMIS SUA NOMINA SERVANT: The Emblematic Thesis Prints of the Roman Seminary. Journal of the Warburg and Courtauld Institutes 70: 195–246.

    Article  Google Scholar 

  • Righini-Bonelli, M.L. 1976. Il Museo di Storia della scienza a Firenze. Milano: Electa.

    Google Scholar 

  • Rochon, Antoine. 1672. Lettre d’un philosophe à un cartésien de ses amis. Paris: Thomas Jolly.

    Google Scholar 

  • Romano, Antonella. 1999. La Contre–réforme mathématique. Rome: École Française de Rome.

    Google Scholar 

  • ———. 2006. Teaching Mathematics in Jesuits Schools. Programs, Course, Content, and Classroom Practices. In The Jesuits II: Cultures, Sciences and the Arts, 1540–1773, ed. John W. O’Malley, Gauvin Alexander Bailey, Steven J. Harris, and T. Frank Kennedy, 355–370. Toronto: University of Toronto Press.

    Google Scholar 

  • Roux, Sophie. 2013a. A French Partition of the Empire of Natural Philosophy (1670–1690). In The Mechanization of Natural Philosophy, ed. Daniel Garber and Sophie Roux, 55–98. New York/Dordrecht/Boston/London: Kluwer.

    Chapter  Google Scholar 

  • ———. 2017. The Two Comets of 1664–1665: A Dispersive Prism for French Natural Philosophy Principles. In The Idea of Principles in Early Modern Thought, ed. Peter Anstey, 98–146. New York/London: Routledge.

    Chapter  Google Scholar 

  • ———. 2019. The Condemnations of Cartesian Natural Philosophy under Louis XIV (1661–1691). In Oxford Handbook to Descartes and Cartesianism, ed. Delphine Antoine-Mahut, Steven Nadler, and Tad Schmaltz, 755–779. Oxford: Oxford University Press.

    Google Scholar 

  • Sabra, Abdulhamid I. 1981. Theories of Light from Descartes to Newton. Cambridge: Cambridge University Press.

    Google Scholar 

  • Scheiner, Christoph. 1619. Oculus, hoc est: Fundamentum opticum: in quo ex accurata oculi anatome, abstrusarum experientiarum sedula pervestigatione, ex invisis specierum visibilium tam everso quam erecto situ spectaculis, nec non solidis rationum momentis, radius visualis eruitur. Innsbruck: apud Danielem Agricolam.

    Google Scholar 

  • ———. 1630. Rosa ursina, sive Sol ex admirando focularum et macularum suarum phænomenon varius. Brescia: A. Phaeum.

    Google Scholar 

  • Schott, Gaspar. 1657. Magia universalis naturae et artis, sive recondita naturalium & artificalium rerum scientia. Würzburg: Henricus Pigrin.

    Google Scholar 

  • Shapiro, Alan E. 1973. Kinematic Optics: A Study of the Wave Theory of Light in the Seventeenth Century. Archive for History of Exact Sciences 11 (2–3): 134–266.

    Article  Google Scholar 

  • ———. 2008. Images: Real and Virtual, Projected and Perceived, from Kepler to Dechales. Early Science and Medicine 13 (3): 270–312.

    Article  Google Scholar 

  • Simon, Gérard. 1988. Le Regard, l’être, l’apparence dans l’optique de l’Antiquité. Paris: Seuil.

    Google Scholar 

  • ———. 2019. In Kepler, rénovateur de l’optique, ed. Delphine Bellis and Nicolas Roudet. Paris: Classiques Garnier.

    Google Scholar 

  • Smith, A. Mark. 2015. From Sight to Light. The Passage from Ancient to Modern Optics. Chicago: University of Chicago Press.

    Google Scholar 

  • Sommervogel, Carlos. 1890–1932. Bibliothèque de la Compagnie de Jésus, nouvelle édition, 12 vols. Paris: Picard.

    Google Scholar 

  • Truci, Isabella. 1976. Le Anamorfosi di Jean François Niceron all’Istituto e Muso di Storia della Scienza di Firenze. Annali dell’Istituto e Museo di storia della scienza di Firenze 1: 57–64.

    Article  Google Scholar 

  • Vanpaemel, Geert. 2008. Mechanics and Mechanical Philosophy in Some Jesuit Mathematical Textbooks of the Early 17th Century. In Mechanics and Natural Philosophy before the Scientific Revolution, ed. Walter Roy Laird and Sophie Roux, 259–274. New York: Kluwer.

    Google Scholar 

  • Ziggelaar, August. 1971. Le physicien Ignace-Gaston Pardies S.J. (1636–1673). Odensee: Odensee University Press.

    Google Scholar 

  • Zittel, Claus. 2009. Theatrum philosophicum. Descartes und die Rolle ästhetischer Formen in der Wissenschaft. Berlin: Akademie-Verlag.

    Book  Google Scholar 

  • ———. 2011. Conflicting Pictures: Illustrating Descartes’ Traité de l’homme. In Silent Messengers. The Circulation of Material Objects of Knowledge in the Early Modern Low Countries, ed. Sven Dupré and Christoph Lüthy, 217–260. Berlin: Lit-Verlag.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CRISES Université Paul-Valéry Montpellier 3; Mathesis, République des savoirs (USR 3608, ENS, CNRS, collège de France), École normale supérieure, PSL University, Paris, France

    Domenico Collacciani

  2. Mathesis, République des savoirs (USR 3608, ENS, CNRS, collège de France), École normale supérieure, PSL University, Paris, France

    Sophie Roux

Authors
  1. Domenico Collacciani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sophie Roux
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. USC Dornsife, Department of Art History and School of Philosophy, University of Southern California, Los Angeles, CA, USA

    Susanna Berger

  2. Department Philosophy, Princeton University, Princeton, NJ, USA

    Daniel Garber

Bibliography

Bibliography

5.1.1 Manuscripts

  • Cours de mathématiques, précédé d’un cours de théologie, 2 vols. [BnF (Paris), Latin 17861-17862].Footnote 122

  • Cursus mathematicus: breviter, et clare figuris explicatus in gratiam eorum, qui mathesim volunt addiscere cito, ac facile [Bibliothek des Max-Planck-Instituts für Wissenschaftsgeschichte (Berlin), Rara B769c].Footnote 123

  • Scientiæ contemplatricis thomus unus, quae est physiologia, sive de natura rerum corporearum… sub reverendo admodum Patre Pardies , illustrissimi Palensis senatus consiliarii filio, [Bibliothèque municipale (Bordeaux) Ms. 934].Footnote 124

5.1.2 Mathematics theses defended at the collège de Clermont (1637–1682)

5.1.2.1 1634–1653: Pierre Bourdin (1595–1653)

Pallu and Touchelée 1635

4–5 June 1635, Jacques Pallu and Jacques Touchelée, Deo hominique Jesu Christo eiusque matri Virgini Mariæ deiparæ Encyclopædiam mathematicam D.D.V. [sic] Jacobus Pallu. Jacobus Touchelée Turonenses. Iidem sedebunt propugnatores sua illius Encyclopedia pro annua celebritate Academiæ Regii Collegii Flexiensis Societatis Jesu, La Flèche: Georges Griveau [Bibliothèque municipale (Lyon), Bibliothèque Mazarine (Paris)].Footnote 125

Cornouaille and Manchon 1638

19–20 June 1638, Pierre de Cornouaille and Jacques Manchon, Deo hominique Jesu Christo eiusque matri Virgini Mariæ deiparæ Musæum mathematicum, D.D.C. [Dicant, dedicant, consecrant] Petrus de Cornouaille, Sylvanectensis, Jacobus Manchon, Parisinus, pro annua celebritate literaria collegii Claromontani Societatis Jesu, s.l.s.n. [BnF (Paris), Bibliothèque municipale (Lyon), Bibliothèque Mazarine (Paris), BL (London)].

Bussey 1638

20 June 1638, Claude Bussey, Encyclopædia mathematica Collegii Claromontani Parisiensis Societatis Jesu. Propugnator, Claudius Bussey [Public Library (New York)]

Culant 1639

27 February 1639, Jacques de Culant, Deiparæ Virgini Mariæ Propositiones ex optica et geometria militari, D.D.C. [Dicat, dedicat, consecrat] Jacobus de Cullant Molinensis…. Disputabuntur in aula mathematica collegii Claromontani Societatis Jesu, s.l.s.n. [BnF (Paris), Bibliothèque municipale (Lyon), Bibliothèque centrale du conservatoire national des arts et métiers (Paris)].

Petit 1639

22 May 1639, Antoine Petit, Deo Optimo Maximo mathematicæ Positiones, D.D.C. [Dicat, dedicat, consecrat] Antonius Petit, Meldensis…. Disputabuntur in aula mathematica collegii Claromontani Societatis Jesu, s.l.s.n. [BnF (Paris)].

Henri 1639

9–10 July 1639, Yves Henri, Augustæ cœli reginæ Mariæ Virgini Deiparæ ejusque integerrimo sponso D. Josepho Palatium mathematicum D.D.C. [Dicat, dedicat, consecrat] Yvo Henri Briocensis, pro annua celebritate literaria collegii Claromontani Societatis Jesu, s.l.s.n [BnF (Paris), Bibliothèque municipale (Lyon), Bibliothèque Mazarine (Paris)].Footnote 126

Potier 1640

30 June–1 July 1640, Charles Potier, D.O.M. [Deo Optimo Maximo] Encyclopædia mathematica, ad agones panegyricos in Claromontano Parisiensis Societatis Jesu collegio. Agonista Carolus Potier Castrotheodoricus, s.l.s.n. [Bibliothèque municipale (Auxerre), Bibliothèque municipale (Lyon), Bibliothèque Sainte Geneviève [BSG] (Paris), Bibliothèque centrale du conservatoire national des arts et métiers (Paris), Biblioteca nazionale centrale (Roma), BL (London)].

Gaillard 1640

25 November [1640], Pierre Gaillard, Soli iustitiæ omnia intuenti oculo Theses mathematicæ de optica deque mirabili oculi oeconomia D.D.C. [Dicat, dedicat, consecrat] Petrus Gaillard disputabuntur in aula mathematica collegii Claromontani Societatis Jesu, s.l.s.n. [BnF (Paris), Bibliothèque centrale du conservatoire national des arts et métiers (Paris)].Footnote 127

Despont 1642

5–6 July 1642, Philippe Despont, A.M.D.G. [Ad maiorem Dei gloriam] Encyclopædia mathematica, ad agones panegyricos in Claromontano Parisiensis Societatis Jesu collegio. Agonista Philippus Despont Parisinus, s.l.s.n. [BnF (Paris), Bibliothèque centrale du conservatoire national des arts et métiers (Paris)].Footnote 128

de Vic 1643

20–21 June 1643, Dominique de Vic, Agones mathematici in Claromontano Parisiensis Societatis Jesu collegio celebrandi. Dissertationes singulis agonibus præmittentur contra Galilæum. Agonista Dominicus de Vic Parisinus, s.l.s.n. [Bibliothèque municipale (Lyon), BnF (Paris), BSG (Paris), Bibliothèque centrale du conservatoire national des arts et métiers (Paris)].Footnote 129

Gedoin 1644

2–3 July 1644, Louis Gedoin, Agones mathematici in Claromontano Parisiensis Societatis Jesu collegio celebrandi cum Deo et B[eata] Virgini. Physico–mathematicæ prolusiones habebuntur…. Agonista Ludovicus Gedoin Parisinus, s.l.s.n. [Bibliothèque centrale du conservatoire national des arts et métiers (Paris), Bibliothèque Mazarine (Paris)].

Foucquet 1646

9 and 11 June 1646, Yves Foucquet, Exercitatio mathematica ad agones panegyricos. Cum Deo et Beata Virgini propugnator Yvo Foucquet, Parisinus, in Claromontano Parisiensis Societatis Jesu collegio, s.l.s.n. [Bibliothèque centrale du conservatoire national des arts et métiers (Paris), Bibliothèque municipale (Lyon)].

Bouthier 1647

20–21 July 1647, Blaise Bouthier, Æternæ memorie serenissimo Principis Henrici Bordoni Condæi Agones annuas D.D.C. [Dicat, dedicat, consecrat] mathematica Parisiensis collegii Claromontani Societatis Jesu. Propugnabit Deo duce et Virgine Blasius Bouthier, Parisinus, s.l.s.n. [Bibliothèque centrale du conservatoire national des arts et métiers (Paris)].

Thierry 1648

20–21 June 1648, Pierre Thierry, Exercitatio mathematica ad agones panegyricos. Cum Deo et Virgine propugnator Petrus Thierry Parisinus, in Claromontano Parisiensis Societatis Jesu collegio, s.l.s.n. [BnF (Paris), Bibliothèque centrale du conservatoire national des arts et métiers (Paris), Bibliothèque Mazarine (Paris)].Footnote 130

Truel de Cohon 1648

[Unknown] July 1648, Jacques Truel de Cohon, Positiones ex universa mathematica selectæ. Has mathematicæ positiones cum Deo et B[eata] Virgine propugnabit Jacobus Truel de Cohon, Alenconius in aula Claromontana Parisiensis, s.l.s.n. [Bibliothèque de l’Arsenal (Paris), BnF (Paris)].

de Bourneuf 1650

26–27 June 1650, Jean de Bourneuf, Agones mathematici in Claromontano Parisiensis Societatis Jesu collegio celebrandi. Cum Deo et B[eata] Virgini propugnabit Johannes de Bourneuf, Juliodunensis, s.l.s.n. [Bibliothèque centrale du conservatoire national des arts et métiers (Paris)].

Villette 1651

1–2 July 1651, Pierre de la Villette, Agones mathematici in Claromontano Parisiensis Societatis Jesu collegio celebrandi. Cum Deo et B[eata] Virgini propugnabit Petrus de la Villette, Mondiderinus, s.l.s.n. [BSG (Paris), BL (London)].Footnote 131

d’Herbelot 1651

1651, Edmond d’Herbelot, Agones mathematici in Claromontano Collegio… propugnabit Edmundus d’Herbelot, Parisinus, s.l.s.n. [Bibliothèque municipale (Grenoble)].Footnote 132

5.1.2.2 1658–1661: Georges Faultrel (Unknown–1687)

de Ruffec and Richomme 1655

3 July 1655, Hyacinthe de Ruffec and Jean Richomme, Exercitatio mathematica ad agones panegyricos, Cum Deo et B[eata] Virgine propugnabunt Hyacinthus de Ruffec, Parisinus, Ioannes Richomme, Rothomagæus, in Collegio Claromontano Societatis Iesu, s.l.s.n. [Bibliothèque municipale (Toulouse), Bibliothèque Mazarine (Paris), Bodleian Library (Oxford)].

5.1.2.3 1661–1664: Nicolas d’Harouys (1622–1698)

Lamoignon 1663

15 June 1663, Chrétien François de Lamoignon, Agones mathematici ad arcem copernicani systematis, Expugnatam in Collegio Claromontano Societatis Iesu, Paris, Antoine Vitré [Bibliothèque interuniversitaire de Santé (Paris), BnF (Paris), Bibliothèque municipale (Coutances), Bibliothèque municipale (Lyon), BSG (Paris), Bibliothèque Mazarine (Paris), BM Library (London), ETH Bibliothek (Zürich), HAB (Wolfenbüttel), Legion of Honor Museum (San Francisco), Stanford University Library (Stanford)].Footnote 133

Le Meilleur 1663

30 June 1663, Joseph Le Meilleur, Positiones mathematicæ de triplici sphæra, armillari, terrestri, cælesti, propugnabuntur in Collegio Claromontano societatis Iesu a Iosepho le Meilleur Venetensi, Paris, Edmond Martin [Bibliothèque municipale (Amiens), Bibliothèque municipale (Lyon), Bibliothèque municipale (Toulouse)].

Anonymous 1664

4 July and 6 July 1664, Positiones physico–mathematicæ, de magnetis subiecto, effectu, et usu, propugnabuntur in Collegio Claromontano Societatis Iesu, Paris, Edmond Martin, [Bibliothèque municipale (Amiens), Bibliothèque municipale (Lyon), Bibliothèque municipale (Toulouse), Bibliothèque Mazarine (Paris), Biblioteca Nacional de Portugal (Lisboa), Houghton Library (Harvard)].

5.1.2.4 1665–1669: Michel Beaussier (Unknown–Unknown)

Tarteron 1665

29 January 1665, Jérôme Tarteron, De cometa ann. 1664 et 1665 observationes mathematicæ propugnabuntur ab Hyeronymo Tarteron, Parisino, in aula Collegi Claromontani Societatis Iesu, Paris: Edmond Martin [BnF (Paris), Universiteitsbibliotheek (Ghent)].

Prou 1665a

29 January 1665, Louis Prou, De cometa ann. 1664 et 1665 observationes mathematicæ propugnabuntur a Ludovico Prou, Parisino, in aula Collegi Claromontani Societatis Iesu, s.l.s.n. [Bibliothèque d’Amiens métropole (Amiens), Bibliothèque de l’observatoire (Paris)].

Ragayne de la Picottiere 1665a

12 June 1665, Louis Ragayne de la Picottiere, De duplici cometa vero et ficto positiones mathematicæ, propugnabuntur a Ludovico Ragayne de la Picottière, Sagiensi, in Collegio Claromontano Societatis Iesu, s.l.s.n. [BnF (Paris), Bibliothèque municipale (Lyon), Biblioteca nazionale centrale (Roma), BL (London), Herzog–August–Bibliothek (Wolfenbüttel)].

Prou 1665b

12 June 1665, Louis Prou, De duplici cometa vero et ficto positiones mathematicæ, propugnabuntur a Ludovico Prou, Parisino, in Collegio Claromontano Societatis Iesu, s.l.s.n. [Bibliothèque municipale (Toulouse), BSG (Paris), Bibliothèque de l’observatoire (Paris)].Footnote 134

Ragayne de la Picottiere 1665b

13–14 June 1665, Louis Ragayne de la Picottiere, De hypothesi cartesiana positiones physicomathematicæ, propugnabuntur a Ludovico Ragayne de la Picottiere, Sagiensi, in Collegio Claromontano Societatis Jesu, s.l.s.n. [BnF (Paris), Bibliothèque municipale (Lyon), Bibliothèque du Centre Sèvres (Paris), Det Kongelige Bibliotek (Copenhagen)].

Prou 1665c

13–14 June 1665, Louis Prou, De hypothesi cartesiana positiones physicomathematicæ, propugnabuntur a Ludovico Prou, Parisino, in Collegio Claromontano Societatis Jesu, s.l.s.n. [BnF (Paris), BL (London), Biblioteca nazionale universitaria (Torino)].

Decombes 1665

[13–14 June] 1665, Jean Decombes, De hypothesi cartesiana positiones physicomathematicæ, propugnabuntur a Joanne Decombes, in Collegio Claromontano Societatis Jesu, s.l.s.n. [HAB (Wolfenbüttel)].

de la Bletonniere 1665

13–14 June 1665, Louis de la Bletonniere, De hypothesi cartesiana positiones physicomathematicæ, propugnabuntur a Ludovico de La Bletonniere Burgundo, in Collegio Claromontano Societatis Jesu, s.l.s.n. [BSG (Paris)].Footnote 135

Anonymous 1666

2, 3 and 4 July 1666, Ex optica selecta mathemata, cum Deo et B. Virgine explicabuntur ac propugnabuntur in Collegio Claromontano Societ. Iesu, s.l.s.n. [Bibliothèque municipale (Lyon)].

Lamoignon de Basville 1666

10 July 1666, Nicolas de Lamoignon de Basville, Ex optica et astronomia selecta mathemata, cum Deo et B. Virgine, explicabit ac propugnabit Nicolaus de Lamoignon de Basville, Parisinus in Collegio Claromont. Societat. Iesu, s.l.s.n. [Bibliothèque d’Amiens métropole (Amiens), Bibliothèque municipale (Toulouse), BSG (Paris)].

de Maupeou 1666

23 July 1666, Pierre de Maupeou, Ex optica et astronomia selecta mathemata cum Deo et B. Virgine, explicabit ac propugnabit Petrus de Maupeou parisinus, in Collegio Claromont. Societ. Jesu [BnF (Paris), Bibliothèque d’Amiens métropole (Amiens), Bibliothèque Mazarine (Paris)].Footnote 136

Benard de Rezay 1666

29 July 1666, Guillaume Benard de Rezay, Ex optica et astronomia selecta mathemata, cum Deo et B. Virgine, explicabit ac propugnabit Guillelmus Benard de Rezay Parisinus, in Collegio Claromont. Societat. Iesu, s.l.s.n. [Bibliothèque interuniversitaire de Santé (Paris), Bibliothèque centrale du conservatoire national des arts et métiers (Paris)].Footnote 137

Castagnere de Chasteauneuf 1667

13 July 1667, Jean–Baptiste and Pierre–Antoine de Castagnere de Chasteauneuf, De corporum cælestium motibus ac phænomenis iuxta varias hypotheses astronomicas et de architectura militari propositiones mathematicæ, Deo duce, favente Deipara, propugnabunt Ioannes Baptista, et Petrus Antonius de Castagnere de Chasteauneuf, Camberienses, in Collegio Claromontano Societatis Iesu, s.l.s.n. [Bibliothèque municipale (Lyon), BSG (Paris)].

Anonymous 1667

July 1667, De corporum cælestium motibus ac phænomenis iuxta varias hypotheses astronomicas et de architectura militari Propositiones mathematicæ,… propugnabuntur in Collegio Claromontano Societatis Jesu [Bibliothèque municipale (Toulouse)]

Bolé de Champlay 1668

20 March 1668, Jules–Louis Bolé de Champlay, De corporum cælestium motibus ac phænomenis iuxta varias hypotheses astronomicas et de architectura militari Propositiones mathematicæ, Deo duce, favente Deipara, propugnabit, Iulius Ludovicus Bolé de Champlay, Parisinus, in Collegio Claromontano Societatis Iesu, s.l.s.n. [BnF (Paris), Bibliothèque municipale (Lyon)].Footnote 138

Anonymous 1668

16–17 June 1668, Propositiones mathematicæ ex statica mechanica et architectura militari, Deo duce, favente Deipara, propugnabuntur in Collegio Claromontano Societatis Iesu, s.l.s.n. [Bibliothèque municipale (Lyon)].

Colbert de Seignelay 1668

30 August 1668, Jean–Baptiste Colbert de Seignelay, Regi armis omnia expugnanti architecturam militarem sapientia omnia constituenti totius mundi constitutionem bellis pacisque arbitro bellatricem pacificamque mathesin consecrat Joannes Bapt[iste] Colbert de Seignelay, Parisinus, s.l.s.n. [Sorbonne, BnF (Paris), Bibliothèque municipale (Lyon), Bibliothèque Mazarine (Paris)].Footnote 139

Anonymous 1669

1–2 June 1669, Positiones mathematicæ de calendario Romano , mundi systemate, antiquis ac novis sideribus et architectura militari, Deo duce, favente Deipara, propugnabuntur in Collegio Claromontano Societatis Iesu, s.l.s.n. [Bibliothèque municipale (Lyon)].

de Mesgrigny 1670

14 June 1670, Jean–Baptiste Joseph–Ignace de Mesgrigny, Positiones ex variis matheseos partibus, Deo duce, favente deipara propugnabit Johannes Baptista Josephius Ignatius de Mesgrigny, Aquensis, in Collegio Claromontano Societ. Jesu, s.l.s.n. [BnF (Paris), Bibliothèque municipale (Lyon)].Footnote 140

Hervé 1670

27 June 1670, Charles–Bénigne Hervé, Positiones ex variis matheseos partibus propugnabit Car. Benig. Hervé, s.l.s.n. [Bibliothèque d’Amiens métropole (Amiens)].Footnote 141

5.1.2.5 1670–1673: Ignace–Gaston Pardies (1636–1673)

Roux 1669

1669, Étienne Roux, Theses mathematicæ et mechanicæ, Bordeaux. [Universitaire Bibliotheken (Leiden)].Footnote 142

Duhamel 1669

August 1669, André Duhamel, Clarissimmo Viro Domino D.[omino] Carolo Duhamel […] Burdegalensis Societatis Jesu primitias offert et consecrat Andreas Duhamel, Burdegalensis. Theses mathematicæ. Has theses Deo duce atque auspice Maria propugnabit Andreas Duhamel in aula Collegii Burdegalis, Bordeaux: s.n. [Bibliothèque municipale (Lyon)].Footnote 143

Anonymous 1671a

19–20 June 1671, Theses mathematicæ de optica propugnabuntur in Collegio Claromontano Societatis Iesu, s.l.s.n. [BnF (Paris), Bibliothèque municipale (Lyon)].

Milon 1671

6 July 1671, Alexandre Milon, Theses mathematicæ de optica, propugnabuntur in Collegio Claromontano Societatis Iesu ab Alexandro Milon, Turonensi, s.l.s.n. [BnF (Paris), Bibliothèque municipale (Lyon), Bibliothèque Mazarine (Paris), King’s College Library (London)].Footnote 144

Anonymous 1671b

[1671–Unknown] Theses de re militari, s.l.s.n. [Bibliothèque municipale (Lyon), King’s College Library (London)].Footnote 145

Le Mazier 1672

24–26 June 1672, Louis le Mazier and al., Theses mathematicæ de vario mundi systemate, Propugnabuntur in Collegio Claromonatno Societatis Jesu, Propugnatores Die XXIV Ludovicus le Mazier, Die XXV, Due e Societate Jesu, Die XXVI, unus a Societate Jesu, s.l.s.n. [BnF (Paris), Bibliothèque municipale (Lyon)].

5.1.2.6 1673–1676: Claude–François Millet de Chales (1621–1678)

Godley 1674

15–17 June 1674, Jean Godley and al., Theses mathematicæ de hydrostatica, architectura militari, et astronomia, Has theses, Deo duce, et auspice Deipara, propugnabuntur in Collegio Claromontano Societatis Jesu. (Propugnatores : diebus Veneris XV et Sabbati XVI, duo e Societate Jesu, Die Dominica XVII Joannes Godley, Londinensis) s.l.s.n. [BnF (Paris), Bibliothèque municipale (Lyon), Gottfried Wilhelm Leibniz Bibliothek (Hannover)].

de Geldrop 1674

20 July 1674, Embert de Geldrop, Theses mathematicæ de hydrostatica, architectura militari, et astronomia, Has theses, Deo duce, et auspice Deipara, propugnabit Embertus de Geldrop, Mechliniensis, in Collegio Claromontano Societatis Jesu, s.l.s.n. [Bibliothèque municipale (Lyon)].Footnote 146

Anonymous 1675

5, 6 and 7 July 1675, Theses mathematicæ de geometria practica, mechanica, statica, geographia, optica, Deo duce, et auspice Deipara, propugnabuntur In Collegio Claromontano Societatis Jesu, Paris: Veuve Edmond Martin [BnF (Paris)].

Anonymous 1676

19, 20 and 21 June 1676, Theses mathematicæ de hydrostatica, architectura militari, et astronomia propugnabuntur in Collegio Claromontano. [Bibliothèque interuniversitaire Sorbonne (Paris), Bodleian Library (Oxford), BL (London)].Footnote 147

5.1.2.7 1677–1682: Jean de Fontaney (1643–1710)

de La Hillière 1680

1680, François–Joseph de La Hillière, Theses mathematicæ de architectura militari. Has theses tuebitur in Collegio Claromontano La Hillière. [Public Library (New York)].

La Forest 1682

21 June 1682, Antoine–Louis de la Forest, Theses mathematicæ de mechanica et hydrostatica, Propugnabuntur in Collegio Claromontano Societatis Jesu, (Has theses, Deo duce, et auspice Virgine, tuebitur Antonius Ludovicus de La Forest Constantinopolitanus), Paris: Gabriel Martin [BnF (Paris), Public Library (New York)].

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Collacciani, D., Roux, S. (2021). The Mathematics Theses Defended at collège de Clermont (1637–1682): How to Guard a Fortress in Times of War. In: Berger, S., Garber, D. (eds) Teaching Philosophy in Early Modern Europe. Archimedes, vol 61. Springer, Cham. https://doi.org/10.1007/978-3-030-84621-3_5

Download citation

Publish with us

Policies and ethics

Search

Navigation