"Descartes's theory of light rapidly displaced the conceptions which had held sway in the Middle Ages. The validity of his explanation of was, however, called in question by his fellow-countryman Pierre de Fermat... and a controversy ensued which was kept up by the Cartesians long after the death of their master. Fermat eventually introduced a new fundamental law, from which he proposed to deduce the paths of rays of light. This was the celebrated Principle of Least Time, enunciated in the form, "Nature always acts by the shortest course." From it the law of reflection can readily be derived, since the path described by light between a point on the incident ray and a point on the reflected ray is the shortest possible consistent with the condition of meeting the reflecting surfaces. In order to obtain the law of refraction, Fermat assumed that "the resistance of the media is different," and applied his "method of maxima and minima" to find the paths which would be described in the least time from a point of one medium to a point of the other. In 1661 he arrived at the solution. "The result of my work," he writes, "has been the most extraordinary, the most unforeseen and the happiest, that ever was; for, after having performed all the equations, multiplications, antitheses and other operations of my method, and having finally finished the problem, I have found that my principle gives exactly and precisely the same proportion for the refractions which Monsieur Descartes has established." His surprise was all the greater, as he had supposed light to move more slowly in dense than in rare media, whereas Descartes had... been obliged to make the contrary supposition."