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The law of refraction and Kepler’s heuristics. (English) Zbl 1431.01009

Johannes Kepler’s most important contribution to optics was published in 1604 as Ad vitellionem paralipomena, quibus astronomiae pars optica traditur. The aim was to provide a quantitative law for the refraction of light. He arrived at one by some analogies, but the law he arrived at was incorrect. Thomas Harriot had apparently determined the correct law of refraction, the law of sines, by 1602, which was before Kepler had even set out to find one. Willebrord Snell then arrived at the correct law at about the same time as Descartes in 1620. Descartes published it in 1637 in his La dioptrique as an appendix to his Discours de la méthode.
In a detailed work of historical reconstruction, the authors of this very interesting paper show that the analogies used by Kepler could have led him to the correct law, that there was nothing intrinsically wrong about his approach.

MSC:

01A45 History of mathematics in the 17th century
78-03 History of optics and electromagnetic theory
51-03 History of geometry

Biographic References:

Kepler, Johannes
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References:

[1] Alhacen. (trans. 2010). De Aspectibus (VII). Alhacen on Refraction, trans. and ed. Mark Smith. Philadelphia: American Philosophical Society.
[2] Borrelli, Arianna; Borrelli, Arianna; Hon, Giora; Zik, Yaakov, Optical Diagrams as “Paper Tools”: Della Porta’s Analysis of Biconvex Lenses from De refractione to De telescopio, The Optics of Giambattista Della Porta (ca. 1535-1615): A Reassessment, 57-96 (2017), New York: Springer, New York
[3] Buchdahl, Gerd, Methodological Aspects of Kepler’s Theory of Refraction, Studies in History and Philosophy of Science, 3, 265-298 (1972) · Zbl 0293.01012 · doi:10.1016/0039-3681(72)90011-8
[4] Cardona, Carlos, Neopythagoreanism in the Work of Johannes Kepler, Manuscrito, 39, 3, 91-120 (2016) · doi:10.1590/0100-6045.2016.v39n3.cs
[5] Cardona, Carlos, Kepler: Analogies in the Search for the law of refraction, Studies in History and Philosophy of Science, 59, 22-35 (2016) · doi:10.1016/j.shpsa.2016.05.004
[6] Caspar, Max. 1959/1993. Kepler. New York: Dover Publications Inc (Transl. by C. Doris Hellman). · Zbl 0118.24703
[7] de Fermat, Pierre. 1891. Synthesis ad Refractiones. In Œuvres de Fermat, vol. I, eds. Paul Tannery and Charles Henry, pp 173-179. Paris: Impremerie Gauthier-Villars et fils. · JFM 23.0013.02
[8] Descartes, René. 1897/1910. Oeuvres de Descartes, eds. Charles Adam and Paul Tannery, 12 vols. Paris: Léopold Cerf.
[9] Giardino, Valeria; Magnani, Lorenzo; Bertolotti, Tommaso, Diagrammatic Reasoning in Mathematics, Springer Handbook of Model Based Science, 499-521 (2017), New York: Springer, New York
[10] Grant, Edward, A Source Book in Medieval Science (1974), Cambridge: Harvard University Press, Cambridge
[11] Heeffer, Albrecht; Weber, E.; Wouters, D.; Meheus, J., Data-Driven Induction in Scientific Discovery: A Critical Assessment Based on Kepler´s Discoveries, Logic, Reasoning and Rationality, 59-76 (2014), Dordrecht: Springer, Dordrecht
[12] Heeffer, Albrecht, Using Invariances in Geometrical Diagrams: Della Porta, Kepler and Descartes on Refraction, Archimedes, 145-168 (2017), Cham: Springer International Publishing, Cham
[13] Huygens, Christiaan. 1690/1945. Treatise on Light. Chicago: The University of Chicago Press (Transl. by Silvanus P. Thompson). · JFM 43.0078.01
[14] Itard, Jean, Les lois de la Refraction de la lumiere chez Kepler, Revue d´histoire des sciences et de leurs applications, 10, 1, 59-68 (1957) · doi:10.3406/rhs.1957.3596
[15] Kepler, Johannes. 1601/1988. Apologia pro Tychone contra Ursus. In N. Jardine, The Birth of History and Philosophy of Science. Kepler´s A Defence of Tycho Against Ursus with Essays on its Provenance and Significance, 83-207. Cambridge: Cambridge University Press.
[16] Kepler, Johannes. 1604/2000. Optics: Paralipomena to Witelo & Optical Part of Astronomy. Santa Fe: Green Lion Press (Transl. by William H. Donahue). · Zbl 0987.01005
[17] Kepler, Johannes. 1604/1939. Ad Vitellionem Paralipomena Quibus Astronomiae pars Optica traditur. In Gesammelte Werke (GW), vol. II; München: C. H. Beck´sche Verlagsbuchhandlung; ed. and comm. Franz Hammer.
[18] Kepler, Johannes. 1604-1611/2008. In Schriften zur Optik, ed. Rolf Riecher. Frankfurt: Verlag Harri Deutch.
[19] Kepler, Johannes. 1611/2008. Dioptrice. In Schriften zur Optik (1604-1611), ed. Rolf Riekher, 441-526. Frankfurt: Verlag Harri Deutsch.
[20] Lindberg, David C., The Genesis of Kepler’s Theory of Light: Light Metaphysics from Plotinus to Kepler, Osiris, Segunda Serie, 2, 5-42 (1986)
[21] Lohne, J., Thomas Harriot (1560-1621), the Tycho Brahe of Optics, Centaurus, 6, 113-121 (1959) · Zbl 0192.32101 · doi:10.1111/j.1600-0498.1959.tb00251.x
[22] Lohne, Ja, Der Eigenartige Einfluβ Witelos auf die Entwicklung der Dioptrik, Archive for History of Exact Sciences, 4, 414-426 (1968) · doi:10.1007/BF00327698
[23] Manders, Kenneth; Mancosu, Paolo, The Euclidian Diagram, The Philosophy of Mathematical Practice, 80-133 (2008), New York: Oxford University Press, New York · Zbl 1163.03001
[24] Methuen, Charlotte, Kepler´s Tübingen. Stimulus to a Theological Mathematics (1998), Aldershot: Ashgate, Aldershot · Zbl 0982.01003
[25] Risner, Frederich, Opticae Thesaurus Alhazeni Arabis libri septem… Item Vitellonis Thuring gopoloni libri decem (1572), Basile: Per episcopios, Basile
[26] Sabra, Ai, Theories of Light from Descartes to Newton (1981), Cambridge: Cambridge University Press, Cambridge
[27] Schuster, John; Gaukroger, S., Descartes-Agonistes: Physico-mathematics, Method & Corpuscular Mechanism, Studies in History and Philosophy of Science (2013), Dordrecht: Springer, Dordrecht · Zbl 1279.01004
[28] Smith, Mark, Descartes Theory of Light and Refraction: A Discourse on Method, Transactions of the American Philosophical Society, 77, 3, 1-92 (1987) · doi:10.2307/1006537
[29] Voelkel, James R., The Composition of Kepler´s Astronomia Nova (2001), Princeton: Princeton University Press, Princeton
[30] Walker, Dp, Studies in Musical Science in the Late Renaissance (1978), London: The Warburg Institute, University of London, London
[31] Zaiser, Hedwig, Kepler als Philosoph (1932), Stuttgart: E. Suhrkamp, Stuttgart
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