more from Euclid

Single Idea 8673

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry]

Full Idea

Euclid's fifth 'parallel' postulate says if there is an infinite straight line and a point, then there is only one straight line through the point which won't intersect the first line. This axiom is independent of Euclid's first four (agreed) axioms.

Gist of Idea

Euclid's parallel postulate defines unique non-intersecting parallel lines


report of Euclid (Elements of Geometry [c.290 BCE]) by Michèle Friend - Introducing the Philosophy of Mathematics 2.2

Book Reference

Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.24

A Reaction

This postulate was challenged in the nineteenth century, which was a major landmark in the development of modern relativist views of knowledge.