Euclid's  rst 28 propositions are true in all of, for ten points, what constructs formed by negating the parallel postulate, which include hyperbolic and elliptical kinds?
Saccheri proved a number of results about one of these constructs, but believed that his results demonstrated the impossibility of that construct's ex- istence. One of these constructs was modeled by Eugenio Beltrami using the Klein model, and the Cayley-Klein metric was used to describe these constructs. One of these constructs is also known as   Bolyai-Lobachevskian after the two mathematicians who independently discovered it. The pseudosphere models a section of one of these constructs. Euclid's  rst 28 propositions are true in all of, for ten points, what constructs formed by negating the parallel postulate, which include hyperbolic and elliptical kinds?
Saccheri proved a number of results about one of these constructs, but believed that his results demonstrated the impossibility of that construct's ex- istence.
non-Euclidean geometry [prompt on partial answers, prompt on hyperbolic geometry, prompt on elliptical geometry, prompt on geometry, prompt on quadrilateral and accept non-Euclidean quadrilateral until  Beltrami , do NOT accept or prompt on  Euclidean geometry ]