Kepler: Analogies in the search for the law of refraction

•We show that Kepler used a Pythagorean methodology to discover a law of refraction.•We show why the Kepler's analogies failed.•We clarify the heuristics that led finally to the Kepler's law of refraction.

This paper examines the methodology used by Kepler to discover a quantitative law of refraction. The aim is to argue that this methodology follows a heuristic method based on the following two Pythagorean principles: (1) sameness is made known by sameness, and (2) harmony arises from establishing a limit to what is unlimited. We will analyse some of the author's proposed analogies to find the aforementioned law and argue that the investigation's heuristic pursues such principles.