The law was rediscovered by Thomas Harriot in 1602, who however did not publish his results although he had corresponded with Kepler on this very subject. In 1621, the Dutch astronomer Willebrord Snellius (1580–1626)—Snell—derived a mathematically equivalent form, that remained unpublished during his lifetime. René Descartes independently derived the law using heuristic momentum conservation arguments in terms of sines in his 1637 essay Dioptrique, and used it to solve a range of optical problems. Rejecting Descartes' solution, Pierre de Fermat arrived at the same solution based solely on his principle of least time. Descartes assumed the speed of light was infinite, yet in his derivation of Snell's law he also assumed the denser the medium, the greater the speed of light. Fermat supported the opposing assumptions, i.e., the speed of light is finite, and his derivation depended upon the speed of light being slower in a denser medium. Fermat's derivation also utilized his invention of adequality, a mathematical procedure equivalent to differential calculus, for finding maxima, minima, and tangents.