There is No Obstruction to a Euclidean Proof for the Fourth Postulate

Authors

• José Gil-Férez, Chapman UniversityFollow
• Piotr Błaszczyk, University of the National Education Commission
• M. Andrew Moshier, Chapman UniversityFollow
• Alberto Naibo, Université Paris 1 Panthéon–Sorbonne
• Jean-Michel Salanskis, Université Paris Nanterre

Document Type

Article

Publication Date

12-15-2025

Abstract

In Gil-Férez et al. (2025), we presented a proof of Postulate 4 using purely Euclidean techniques, against which Blåsjö (2025) raised several objections. In this note, we offer linguistic, textual, historical, and mathematical evidence that demonstrate that all these objections are baseless.

Comments

This article was originally published in Historia Mathematica, volume 73, in 2025. https://doi.org/10.1016/j.hm.2025.09.001

Recommended Citation

Gil-Férez, J., Błaszczyk, P., Moshier, M. A., Naibo, A., Salanskis, J.-M., 2025. There is no obstruction to a Euclidean proof for the Fourth Postulate. Hist. Math. 73, 103182. https://doi.org/10.1016/j.hm.2025.09.001

Peer Reviewed

1

Copyright

The authors

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.