“The first law is the same for both light and material bodies; they both move in a straight line, as long as they are not deflected by an outside force.
The second law is also the same as that governing the reflection of an elastic ball from an impenetrable surface. Mechanics shows that such a ball is reflected from such a surface so that its angle of reflection equals its angle of incidence, as observed for light.
But the third law still requires a plausible explanation. The passage of light from one medium to another exhibits behavior that is totally different from a ball moving through different media.”

— Pierre Louis Maupertuis

Accord de différentes loix de la nature qui avoient jusqu’ici paru incompatibles (1744)

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Pierre Louis Maupertuis 24

French mathematician, philosopher and man of letters 1698–1759

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Source: Sayings of Sri Ramakrishna (1960), p. 649

“The refraction of light agrees with the grand principle that Nature always uses the simplest means to accomplish its effects. From this principle, can be derived whenever light passes from one medium to another, the ratio of the sine of the angle of refraction to the sine of the angle of refraction equals the inverse ratio of the speeds at which light moves in each medium.
But this "budget", this expense of action that Nature minimizes in the refraction of light, is it also minimized in the direct propagation and reflection of light? Yes, it always has the smallest possible value.”

Pierre Louis Maupertuis (1698–1759) French mathematician, philosopher and man of letters

Accord de différentes loix de la nature qui avoient jusqu’ici paru incompatibles (1744)

“The most beautiful discoveries since the Renaissance, indeed since the beginnings of all science, are the laws governing light, whether moving through a uniform medium, or being reflected from an opaque surface, or changing direction upon entering another transparent medium.”

Pierre Louis Maupertuis (1698–1759) French mathematician, philosopher and man of letters

Accord de différentes loix de la nature qui avoient jusqu’ici paru incompatibles (1744)

“Heron and Olympiodorus had pointed out in antiquity that, in reflection, light followed the shortest possible path, thus accounting for the equality of angles. During the medieval period Alhazen and Grosseteste had suggested that in refraction some such principle was also operating, but they could not discover the law.”

Carl B. Boyer (1906–1976) American mathematician

Source: The Rainbow: From Myth to Mathematics (1959), p. 205
Context: Fermat had recourse to the principle of the economy of nature. Heron and Olympiodorus had pointed out in antiquity that, in reflection, light followed the shortest possible path, thus accounting for the equality of angles. During the medieval period Alhazen and Grosseteste had suggested that in refraction some such principle was also operating, but they could not discover the law. Fermat, however, not only knew (through Descartes) the law of refraction, but he also invented a procedure—equivalent to the differential calculus—for maximizing and minimizing a function of a single variable. … Fermat applied his method … and discovered, to his delight, that the result led to precisely the law which Descartes had enunciated. But although the law is the same, it will be noted that the hypothesis contradicts that of Descartes. Fermat assumed that the speed of light in water to be less than that in air; Descartes' explanation implied the opposite.