There is no Euclidean proof of the fourth postulate

Abstract

Gil-Férez et al. (2025) claim to prove Euclid's fourth postulate by strictly Euclidean means. In fact, however, they assume a principle that is neither stated nor used by Euclid. This is all the more impermissible since this inserted assumption precludes established interpretations of the fourth postulate in terms of cone points, homogeneity of space, and line-extension uniqueness.