Euclid’s Axioms

Euclid’s book Elements is the earliest known systematic discussion on geometry. In it he laid the foundations and rules to what is now known as Euclidean geometry. In Elements, Euclid assumed a small set of axioms, from which theorems could be deduced. So what are these axioms?

Given any two points, you can draw a straight line between them, forming a line segment.



Any line segment can be extended indefinitely in a straight line.

Given a point and a line segment starting at the point, you can draw a circle centred on the given point with the given line segment as its radius.


All right angles are equal to each other.

Read more about this axiom here.


If you draw a line segment across two straight lines and it creates two angles on the same side which add to less than two right angles, then those two straight lines intersect.

This axiom is equivalent to saying that the angles in a triangle add up to 180 degrees.

Sources: 1 | 2

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