Euclid' Elements Book I

Euclid as the father of geometry

Show that Euclid's first postulate holds for most pairs of points, but not all. Show that the second, third, and fourth postulates do hold in spherical geometry. Show that the fifth postulate (or equivalently Playfair's Postulate) does not hold. (Give general explanations for your answers - we do not yet have the resources to do rigorous proofs in spherical geometry) In the following exercises, experiment to determine if each statement is most likely true or false in spherical geometry. Give sho

Attempts to prove Euclid’s fifth postulate using the other postulates and axioms led to the discovery of several other geometries. - Mathematics | Shaalaa.com

Euclid's Axiomatic Geometry: Developments & Postulates

Euclid, The Father of Geometry | Biography & Contributions