Were all the five Euclid's postulates from the first book discarded to give rise to hyperbolic and elliptical geometry or only the Parallel Postulate was discarded?

Were all the 23 definitions and 48 prepositions from the first book incorporated in these non-Euclidean geometries?

  • 2
    $\begingroup$ only the fifth (and there are more than five postulates in Euclid's work). $\endgroup$ – Ittay Weiss Apr 12 '13 at 19:25
  • $\begingroup$ +1 Damn...beat me to it :-) but I should point out in addition that the definition of a "straight line" also changes. A straight line is the shortest distance between two points and they look very different in different geometries. $\endgroup$ – Fixed Point Apr 12 '13 at 19:25
  • $\begingroup$ All the 23 definitions ( and maybe the 48 prepositions ) from the first book are also encorporated in hyperbolic and eliptical geometry or just the four postulates ? $\endgroup$ – nerdy Apr 12 '13 at 19:27
  • $\begingroup$ Definitions yes, propositions no, the parallel postulate is essential for many of the propositions of Book I. $\endgroup$ – André Nicolas Apr 12 '13 at 19:29
  • $\begingroup$ I know, but only few of them used the fifth paralel.Can i say the ones that didn't use were encorporated ? $\endgroup$ – nerdy Apr 12 '13 at 19:35

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.