Abstract: Describes Descartes's time in Paris and the intellectual milieu in which he moved. Reconstructions by Schuster and Shea of his discovery, whilst collaborating with Mydorge on optics, of the law of refraction. Detailed account of the latter part of the Regulae, in which he dealt with cognition and mechanism in the form of a general natural philosophy, the problem of mortalism, and his preference for algebra over geometry in problem-solving. His search for certainty is ascribed to his interest in the relationship between mechanism, and clarity, and distinctness, rather than an interest in scepticism.

Keywords: algebra, clarity and distinctness, cognition, law of refraction, mechanism, mortalism, natural philosophy, optics, Regulae, scepticism,