Thing that are coincide with one another are equal to one another. The whole is greater than the part. A straight line can be drawn from any point to any point. A finite straight line can be produced continuously in a straight line. A circle may be described with any point as center and any point distance as radius.
All right angles are equal to one another.
If a transversal falls on two lines in such a way that the interior angles on one side of the transversal are less than two right angles, then the lines meet on that side on which the angles are less than two right angles. A point is on the bisector of an angle if and only if it is equidistant from the sides of the angle. We will present a modern set of axioms for Euclidean geometry as given by Hilbert later. Before we do that, we want to get more farmiliar with the axiomatic method itself. So, we now take a little break and study some simple axiomatic systems.