Euclid's five postulates
The foundational assumptions of plane geometry, set out in order
This text page is headed 'On the five postulates' and sets out Euclid's five postulates in order: that a straight line joins any two points; that a circle of any size may be drawn about a centre; that all right angles are equal; the parallel postulate; and that two straight lines cannot enclose a surface. It is a clean copy of the foundational assumptions of plane geometry.
On this page
The first three postulates
A straight line may be drawn from any one point to another; a circle of any desired size may be described about a centre; and all right angles are equal to one another.
The parallel postulate and the fifth
If a straight line crossing two others makes the two interior angles on one side less than two right angles, those lines, produced far enough on that side, will surely meet; and two straight lines cannot enclose a surface.