Five Axioms of Euclid
The Five Axioms (Postulates) of Euclid A straight line between two points — Any two points can be joined by a straight line segment. Extension of a line — A straight line segment may be extended indefinitely in both directions. Equality of right angles — All right angles are equal to one another. Construction of a circle — Given a centre and a radius, a circle can be drawn uniquely. The parallel postulate — Through a given point not on a line, there exists exactly one straight line parallel to the given line. The fifth postulate is historically the most significant: alternative formulations of it led, in the nineteenth century, to the development of non‑Euclidean geometries.
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Euclid’s axioms are the five fundamental assumptions upon which the ancient Greek mathematician Euclid built the geometry of his treatise Elements. They define how points, straight lines and circles behave within Euclidean geometry.