Between Euclid's time and 1829, the conviction that Postulate V depends on I- IV Axioms was so strong that no one recognized the basis for new geometry.
     

"The assumption that the sum of three angles is less than 180° leads to some curious geometry, quite different than ours, but thoroughly consistent"
                          

  Carl Friedrich Gauss on 8Nov 1824

      In order to present some of this "new", "curious" geometry we have created Mathematica package "L2Primitives".