- #1
diogo_sg
Hello people. I've been reading some papers online (if any links are needed, please let me know) regarding the foundation of the non-euclidean geometries, but i just can't figure out one or two details about Saccheri's contribution to said matter. In his attempts to prove the Parallel Postulate using the reductio ad absurdum method, according to which he designed the Saccheri Quadrilateral, he disposed of two of the three hypotheses: the acute angle and obtuse angle ones. I understand the basis of the Quadrilateral and "how it works" and why the right angle hypothesis is equivalent to the Parallel Postulate. My question is about how Saccheri proved the other two hypotheses wrong. All the papers i find on the subject don't go too deep into it and provide almost no mathematical proof, only focusing on the "theoretical part" of the proofs. Plus, the only edition of Saccheri's original paper that's available online is in latin and my latin skills are, well, inexistent. So if anyone is willing to share their knowledge or some obscure paper on the matter, please be my guest; i'd be extremely grateful for it, because this has been troubling my mind for several weeks as of now. Thank you all.
P. S. I'd like to point out that Saccheri never actually proved the Parallel Postulate, although the title of this post may make it seem like he did.
P. S. I'd like to point out that Saccheri never actually proved the Parallel Postulate, although the title of this post may make it seem like he did.