Euclid's Fifth Postulate . Besides 23 definitions and several implicit assumptions, Euclid derived much of the planar geometry from five postulates. A straight line may be drawn between any two points. A piece of straight line may be extended indefinitely. A circle may be drawn with any given radius and an arbitrary center.
All right angles are equal.
If a straight line crossing two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if extended indefinitely, meet on that side on which are the angles less than the two right angles. The fifth postulate refers to the diagram on the right. A and B if continued indefinitely. They may be said to be based on man's practical experience. The second postulate gives an expression to a commonly held belief that straight lines may not terminate and that the space is unbounded.