Fermat's principle lead to the same differential equation for the ray path, and that in the case of Fermat's principle, the converse holds. De Witte also noted that "The matter seems to have escaped treatment in textbooks." See also Notes References Bibliography M. Born and E. Wolf, 2002, Principles of Optics, 7th Ed., Cambridge, 1999 (reprinted with corrections, 2002). J. Chaves, 2016, Introduction to Nonimaging Optics, 2nd Ed., Boca Raton, FL: CRC Press, . O. Darrigol, 2012, A History of Optics: From Greek Antiquity to the Nineteenth Century, Oxford, . A.J. de Witte, 1959, "Equivalence of Huygens' principle and Fermat's principle in ray geometry", American Journal of Physics, vol.27, no.5 (May 1959), pp.293–301, . Erratum: In Fig.7(b), each instance of "ray" should be "normal" (noted in vol.27, no.6, p.387). E. Frankel, 1974, "The search for a corpuscular theory of double refraction: Malus, Laplace and the competition of 1808", Centaurus, vol.18, no.3 (September 1974), pp.223–245, . A. Fresnel, 1827, "Mémoire sur la double réfraction", Mémoires de l'Académie Royale des Sciences de l'Institut de France, vol. (for 1824, printed 1827), pp.45–176; reprinted as "Second mémoire..." in Oeuvres complètes d'Augustin Fresnel, vol.2 (Paris: Imprimerie Impériale, 1868), pp.479–596; translated by A.W. Hobson as "Memoir on double refraction", in R.Taylor (ed.), Scientific Memoirs, vol. (London: Taylor & Francis, 1852), pp.238–333. (Cited page numbers are from the translation.) C. Huygens, 1690, Traité de la Lumière (Leiden: Van der Aa), translated by S.P. Thompson as Treatise on Light, University of Chicago Press, 1912; Project Gutenberg, 2005. (Cited page numbers match the 1912 edition and the Gutenberg HTML edition.) P. Mihas, 2006, "Developing ideas of refraction, lenses and rainbow through the use of historical resources", Science & Education, vol.17, no.7 (August ), pp.751–777 (online 6 September 2006), . I. Newton, 1730, Opticks: or, a Treatise of the Reflections, Refractions, Inflections, and Colours of Light, 4th Ed. (London: William Innys, 1730; Project Gutenberg, 2010); republished with Foreword by A. Einstein and Introduction by E.T. Whittaker (London: George Bell & Sons, 1931); reprinted with additional Preface by I.B. Cohen and Analytical Table of Contents by D.H.D. Roller, Mineola, NY: Dover, 1952, 1979 (with revised preface), 2012. (Cited page numbers match the Gutenberg HTML edition and the Dover editions.) A.I. Sabra, 1981, Theories of Light: From Descartes to Newton (London: Oldbourne Book Co., 1967), reprinted Cambridge University Press, 1981, . A.E. Shapiro, 1973, "Kinematic optics: A study of the wave theory