Skip to main navigation menu Skip to main content Skip to site footer
Galilæana. Studies in Renaissance and Early Modern Science

Focus

Vol. 23 No. 1 (2026)

Descartes and the law of refraction

DOI
https://doi.org/10.57617/gal-97
Submitted
22 October 2025
Published
2026-05-22

Abstract

Historical research on refraction in the modern era has often focused on the question of attributing the law of refraction to Descartes, Snel and Harriott. The discovery of Ibn Sahl’s work has put an end to the dispute over priority between these authors, leaving another problem largely unnoticed: most of the literature refers to this discovery without distinguishing the native form of the statements on refraction from the current conception of the law of refraction. This anachronism is problematic. Ancient texts do not contain a single statement of the law of refraction as we know it today. Descartes’ contribution is in line with Maurolico’s and Kepler’s work on refraction. Like them, Descartes makes no mention of sines or refractive indices, nor does he formulate a physical law of refraction. Since these ideas developed gradually between the late 17th century and the 19th century, the recognition of a “law of sines” or a “law of refraction” is not an idea native to the 16th and 17th centuries. We suggest that the work of Descartes does not fit into the modern quest for the laws of nature, but rather into the framework of the theory of proportions.

References

  1. Arago, François. “Descartes,” Oeuvres de François Arago, edited by Jean-Augustin Barral. Paris: Baudry, 1855, vol. 3, 297–309.
  2. Beeckman, Isaac. Journal tenu par Isaac Beeckman de 1604 à 1634, edited by Cornelis de Waard. Den Haag: M. Nijhoff, 1939.
  3. Belgioioso, Giulia. “Un faux de Clerselier,” Bulletin cartésien 33 (2005): iv (unpaginated).
  4. Belgioioso, Giulia, Vincent Carraud. Des éditions du XVIIe siècle aux éditions modernes (Lecce: Centro dipartimentale di studi su Descartes “Ettore Lojacono,” 2024), http://www.cartesius.net.
  5. Boyer, Carl B. “Robert Grosseteste on the rainbow,” Osiris 11 (1954): 247–258.
  6. Buchdahl, Gerd. “Methodological aspects of Kepler’s theory of refraction,” Studies in History and Philosophy of Science 3 (1972): 265–298.
  7. Burke-Gaffney, Michael Walter. Kepler and the Jesuits. Milwaukee: Bruce Publishing Co, 1944.
  8. Canguilhem, Georges. Études d’histoire et de philosophie des sciences. Paris: J. Vrin, 1968.
  9. Cardona, Carlos Alberto. “Kepler: analogies in the search for the law of refraction,” Studies in History and Philosophy of Science 59 (2016): 22–35.
  10. Correspondance de Descartes, edited by Charles Adam and Paul Tannery. Paris: Cerf, 1897, vol. 1.
  11. Correspondance du P. Marin Mersenne, edited by Cornelis de Waard et al. Paris: Beauchesne, 1933, vol. 1.
  12. Descartes, René. Dioptrique. Leiden: I. Maire, 1637.
  13. Descartes, René. Regulae ad directionem ingenii, An Early Manuscript Version, edited by Richard Serjeantson and Michael Edwards. Oxford: Oxford University Press, 2023.
  14. Descartes, René. Règles utiles et claires pour la direction de l’esprit en la recherche de la vérité, trad. J.L. Marion, notes mathématiques de P. Costabel. La Haye: M. Nijhoff, 1977.
  15. De Waard, Cornelis. “Le manuscrit perdu de Snellius sur la réfraction,” Janus 39 (1935): 51–73.
  16. Dijksterhuis, Eduard Jan. The Mechanization of the World Picture. Oxford: Clarendon Press, 1961.
  17. Dijksterhuis, Fokko Jan. Lenses and Waves. Christiaan Huygens and the Mathematical Science of Optics in the Seventeenth Century. Dordrecht: Kluwer, 2004.
  18. Dika, Tarek R. Descartes’s Method. The Formation of the Subject of Science. Oxford: Oxford University Press, 2023.
  19. Duhem, Pierre. “Les théories de l’optique,” Revue des deux mondes 123 (1894): 94–125.
  20. Eastwood, Bruce S. “Descartes on refraction,” Isis 75 (1984): 481–502.
  21. Euclide. Les Eléments, trad. B. Vitrac. Paris, PUF, 1994.
  22. Fermat, Pierre de. Synthesis ad refractiones (1662), Oeuvres de Fermat, edited by Paul Tannery and Charles Henry. Paris: Gauthier‑Villars, 1896, vol. 3: 151–152.
  23. Field, Judith V. Kepler’s Geometrical Cosmology. London: Bloomsbury, 1988.
  24. Fraunhofer, Joseph. “Bestimmung des Brechungs- und Farbenzerstreuungs- Vermögens verschiedener Glasarten, in Bezug auf die Vervollkommnung achromatischer Fernröhre,” Denkschriften der königlichen Akademie der Wissenschaften zu München 5 (1814): 193–226.
  25. Galison, Peter. “Descartes’s comparisons: from the visible to the invisible,” Isis 75 (1984): 311–326.
  26. Gaukroger, Stephen et al., eds. Descartes’ Natural Philosophy. London; New York: Routledge, 2000.
  27. Goulding, Robert. “The harvest of optics: Descartes, Mydorge, and their paths to a theory of refraction,” Annals of Science 79 (2022): 164–214.
  28. Guicciardini, Niccolò. Reading the Principia. The debate on Newton’s mathematical methods for natural philosophy from 1687 to 1736. Cambridge: Cambridge University Press, 1999, 118–135.
  29. Heeffer, Albert. “Data-driven induction in scientific discovery: a critical assessment based on Kepler’s discoveries,” E. Weber et al., eds., Logic, Reasoning and Rationality. Dordrecht: Springer, 2014, 59–76.
  30. Hentschel, Klaus. “Das Brechungsgesetz in der Fassung von Snellius,” Archive for History of Exact Sciences 55 (2001): 297–344.
  31. Huygens, Christiaan. Oeuvres complètes de Christiaan Huygens, edited by Diederik J. Korteweg. La Haye: M. Nijhoff, 1916.
  32. Itard, Jean. “Les lois de la réfraction de la lumière chez Kepler,” Revue d’histoire des sciences 10 (1957): 59–68.
  33. Jullien, Vincent. Descartes, La Géométrie de 1637. Paris: PUF, 1996.
  34. Kepler, Johannes. Ad Vitellionem Paralipomena, quibus Astronomiae pars optica traditur…. Frankfurt: C. Marnius, 1604.
  35. Kepler, Johannes. Dioptrice. Augsburg: D. Franck, 1611.
  36. Kepler, Johannes. Harmonice mundi libri V. Linz: G. Tamach, 1619.
  37. Kepler, Johannes. Optics. Paralipomena to Witelo & Optical Part of Astronomy, trans. W. H. Donahue. Santa Fe: Green Lion Press, 2000.
  38. Kuhn, Thomas. The Structure of Scientific Revolutions. Chicago: University of Chicago Press, 1962.
  39. Lettres de M. Descartes, edited by Charles Clerselier, 3 vols. Paris: Angot, 1657–1659.
  40. Lohne, Johannes. “Zur Geschichte des Brechungsgesetzes,” Sudhoffs Archiv 47 (1963): 152–172.
  41. Malet, Antoni. “Gregorie, Descartes, Kepler, and the law of refraction,” Archives internationales d’histoire des sciences 40 (1990): 278–304.
  42. Manning, Gideon. “Analogy and falsification in Descartes’ physics,” Studies in History and Philosophy of Science 43 (2012): 402–411.
  43. Maurolico, Francesco. Diaphana (1554), Photismi de lumine & umbra… Diaphanorum partes, seu libri tres… Naples: T. Longo, 1611.
  44. Maurolico, Francesco. Francisci Maurolyci Optica, edited by Riccardo Bellè and Ken’ichi Takahashi. Pisa: F. Serra, 2017.
  45. Maurolico, Francesco. De proportione sermo noster (1554). edited by P. D. Napolitani, Francisci Maurolyci Opera Mathematica, http://www.dm.unipi.it/pages/maurolic/intro.htm
  46. Maurolico, Francesco. Compendium (1567), edited by J. P. Sutto, “Le compendium du 5e livre des Éléments d’Euclide de Francesco Maurolico,” Revue d’histoire des mathématiques 6 (2000): 59–94.
  47. Mersenne, Marin. Quaestiones celeberrimae in Genesim. Paris: S. Cramoisy, 1623.
  48. Mersenne, Marin. Harmonie universelle. Paris: S. Cramoisy, 1636.
  49. Milhaud, Gaston. “Descartes et la loi des sinus,” Revue générale des sciences pures et appliquées 18 (1907): 223–228.
  50. Mydorge, Claude. L’inclination et la refraction de quelconque rayon (1626), MS: Paris, BnF, naf 5176, fol. 15r, edited by Cornelis de Waard, Correspondance de Mersenne, vol. 1, 404–415.
  51. Mydorge, Claude. Examen du livre des recreations mathematiques. Paris: R. Boutonné, 1630.
  52. Newton, Isaac. “A new theory about light and colors,” Philosophical Transactions 80 (1672): 3075–3087.
  53. Proclus, A Commentary in the First Book of Euclid’s Elements, trad. G. R. Morrow. Princeton: Princeton University Press, 1970.
  54. Rashed, Roshdi. “A pioneer in anaclastics: Ibn Sahl on burning mirrors and lenses,” Isis 81 (1990): 464–491.
  55. Rashed, Roshdi. Geometry and Dioptrics in Classical Islam. London: al-Furqān, 2005.
  56. Rhodius, Ambrosius. Optica Ambrosii Rhodii, Kembergensis. Wittenberg: L. Seuberlich, 1611.
  57. Schuster, John A. Descartes and the Scientific Revolution: 1618–1634, Doctoral Dissertation. Princeton: Princeton University, 1977.
  58. Schuster, Descartes–Agonistes: Physico-mathematics, Method and Corpuscular-Mechanism 1618–33. Dordrecht: Springer, 2013.
  59. Schuster, John A. “Descartes opticien,” S. Gaukroger et al., eds., Descartes’ Natural Philosophy. London; New York: Routledge, 2000, 258–312.
  60. Simon, Gérard. Kepler, rénovateur de l’optique. Paris: Garnier, 2019.
  61. Smith, A. Mark. “Descartes’s theory of light and refraction,” Transactions of the American Philosophical Society 77 (1987): 1–92.
  62. Stephenson, Bruce. The Music of the Heavens. Kepler’s Harmonic Astronomy. Princeton, NJ: Princeton University Press, 1994.
  63. Sutto, Jean-Pierre. “Le compendium du 5e livre des Éléments d’Euclide de Francesco Maurolico,” Revue d’histoire des mathématiques 6 (2000): 59–94.
  64. Vollgraff, Johan Adriaan. “Snellius’ notes on the reflection and refraction of rays,” Osiris 1 (1936): 718–725.
  65. Vuillemin, Jules. Mathématiques et métaphysique chez Descartes. Paris: PUF, 1960.
  66. Wollaston, William H. “A method of examining refractive and dispersive powers by prismatic reflection,” Philosophical Transactions of the Royal Society 92 (1802): 365–380, 570–571.
  67. Young, Thomas. A Course of Lectures on Natural Philosophy and the Mechanical Arts. London: J. Johnson, 1807.