The five postulates, which together with 23 definitions and five "common
notions" form the basis of Euclid's great work
on geometry, Elements. The postulates are:
The last postulate is not as obvious as the other four, and Euclid himself
was reluctant to use it. Later mathematicians, finding the fifth postulate
to be complicated, thought it might be possible to derive it from the other
four. However, they only succeeded in replacing it with equivalent statements.
The most common of these is the parallel
- A straight line may be drawn from any one point to any other point.
- A finite straight line may be produced to any length in a straight
- A circle may be described with any center at any distance from that
- All right angles are equal.
- If a straight line meets two other lines, so as to make the two interior
angles on one side of it together less than two right angles, the other
straight lines will meet if produced on that side on which the angles
are less than two right angles.