Hippocratesʹ lunes and transcendence

Hippocrates gave the first examples of circular lunes that can be squared by means of ruler and compass only. By its nature, the problem of classifying all these lunes consists of two parts. The algebraic part was solved in 1947, whereas the transcendental part was neglected by most authors, with the effect that its final solution in 1966 remained unnoticed. The aim of this note is to fill this gap.