One such model is that K is the vertices of a triangle, and L is the sides of that triangle. All A are equal. Just as for the previous system, various relations between the classes can be derived from these statements. Every straight line may be extended. Given two points, there is one and only one circle with one point a member of the circumference of the circle and the other point the centre of the circle.
All right angles are equal.
Given a straight line and a point not on the line, there exists one and only one straight line through the point which is parallel to the original line. The axioms were considered to be self-evident truths about geometry. However, the fifth axiom about parallel lines seems to some to be less simple and self-evident than the other four, and for some centuries people tried to derive the fifth axiom from the other four. The attempts all failed. In some future life, perhaps, we may have other ideas about the nature of space which, at present, are inaccessible to us.