It is well known that Euclid 's twelfth axiom, even in Playfair 's form of it, has been considered as needing demonstration: and that Lobachevsky constructed a perfectly consistent theory, wherein this axiom was assumed not to hold good, or say a system of non-Euclidean plane geometry.
Ito ay din na kilala na Euclid 's ikalabindalawa axiom, kahit na sa Playfair' s form ng mga ito, ay itinuturing bilang pangangailangan ng pagpapatotoo: at na Lobachevsky na itinayo ng isang ganap na ganap pabago-bagong kuru-kuro, kung saan ito axiom ay assumed na hindi paniwalaan, o sabihin ng isang system ng mga di-Euclidean eroplano geometry.