Euclid's postulates

Euclid's postulates are the foundation of Euclidean geometry. They are (not literally, but translated into equivalent statements or using modern vocabulary): The fifth axiom, also known as the "Parallel postulate" has several equivalent restatements and theorems in the Elements that expressly use this postulate will be noted due to it's history.
 * 1) One may draw a straight segment between any two points.
 * 2) One may extend a segment indefinitely in either direction.
 * 3) One may draw a circle with and given center and radius.
 * 4) All right angles are congruent.
 * 5) Given a line and a point not on the line, there exists exactly one line through the point that is parallel to the initial line.