A principle of least time before Fermat?

This article aims to clarify the status of two early statements concerning least time, one from Martinus Hemerl's optics (quanto natura citius potest pertingere ad suum effectum), the other from Leonardo da Vinci's notebooks (nel più breve tempo sia possibile). A comparison of these texts with Heron of Alexandria's De speculis on the one hand, and Fermat's Analysis ad refractiones on the other, shows that 15th-century statements concerning least time should not be regarded as anticipations of Fermat's principle. I submit instead that the adoption of the intromission theory of vision made it possible to conceive of the finite speed of light, which in turn enabled the formulation of a temporal variant of the principle of economy that had existed since antiquity. Medieval and Renaissance statements resembling the principle of least time thus testify not to the existence of pre-Fermatian formulations of the principle proper, but rather to the emergence of the historical conditions that made Fermat's formulation possible in the 17th century.