The geometry of Euclid was based on a number of a axioms and postulates of which we quote the first five postulates. Euclid makes a distinction between the words axiom and postulate. Modern mathematics tend to use the word axiom, except when referring to Euclid's postulates. Any terminated straight line may be extended indefinitely. A circle may be drawn with any given point as center and any given radius.
All right angles are equal.
If two straight lines lying in a plane are met by another line, and if the sum of the internal angles on one side is less than two right angles, then the straight lines will meet if extended sufficiently on the side on which the sum of the angles is less than two right angles. In other words, referring to Figure 4.5.1, if the sum of angles at A and B is less than 180 degrees, then the lines L 1 and L 2 will intersect at some point on the rights hand side of L 3 . Within deductive geometry, the axiom functions as a cornerstone on which further conclusions are based. Within descriptive geometry, the axiom functions as a true and accurate statement of the world of spatial experiences. Postulate 5 is different.