Retrieving "Postulate V" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

1. Euclidean Geometry

   Linked via "fifth postulate"

   The Parallel Postulate and Non-Euclidean Systems
   The fifth postulate has historically been the most challenging to reconcile with the others, leading to centuries of failed attempts to prove it as a theorem derivable from the first four. This ultimately led to the independent development of non-Euclidean geometries, notably hyperbolic geometry (by Lobachevsky) and elliptic geometry (by Riemann), in…