There is no Euclidean proof of the fourth postulate

Viktor Blåsjö

doi:10.1016/j.hm.2025.06.001

There is no Euclidean proof of the fourth postulate

Viktor Blåsjö^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

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.

Original language	English
Article number	103171
Journal	Historia Mathematica
Volume	73
Early online date	3 Jul 2025
DOIs	https://doi.org/10.1016/j.hm.2025.06.001
Publication status	Published - Dec 2025

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There is no Euclidean proof of the fourth postulate

Abstract

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