There exist at least two points on a line.For every two points there exists no more than one line that contains them both consequently, if AB = a and AC = a, where B ≠ C, then also BC = a.If A lies upon a and at the same time upon another line b, we make use also of the expression: "The lines a and b have the point A in common", etc. Instead of "contains", we may also employ other forms of expression for example, we may say " A lies upon a", " A is a point of a", " a goes through A and through B", " a joins A to B", etc. For every two points A and B there exists a line a that contains them both.All points, straight lines, and planes in the following axioms are distinct unless otherwise stated. Line segments, angles, and triangles may each be defined in terms of points and straight lines, using the relations of betweenness and containment. Congruence, two binary relations, one linking line segments and one linking angles, each denoted by an infix ≅.Lies on (Containment), three binary relations, one linking points and straight lines, one linking points and planes, and one linking straight lines and planes.Betweenness, a ternary relation linking points.Hilbert's axiom system is constructed with six primitive notions: three primitive terms: 3 Editions and translations of Grundlagen der Geometrie.