Thus the fourth postulate asserts homogeneity of the plane: in whatever directions and through whatever point two perpendicular lines are drawn, the angle they form is one and the same and is called right. By the Definition 10, an angle is right if it equals its adjacent angle. The second postulate gives an expression to a commonly held belief that straight lines may not terminate and that the space is unbounded. They may be said to be based on man's practical experience. Postulates 1 and 3 set up the 'ruler and compass' framework that was a standard for geometric constructions until the middle of the 19th century. If the sum of two angles A and B formed by a line L and another two lines L 1 and L 2 sum up to less than two right angles then lines L 1 and L 2 meet on the side of angles A and B if continued indefinitely. The fifth postulate refers to the diagram on the right. 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.

A circle may be drawn with any given radius and an arbitrary center.

A piece of straight line may be extended indefinitely.

A straight line may be drawn between any two points.

Besides 23 definitions and several implicit assumptions, Euclid derived much of the planar geometry from five postulates.

Parallel postulate definition geometry