In a theory, a proposition that is obvious on its own and is not subject to any demonstration.
All mathematical theories are based on a set of definitions of mathematical objects and axioms that set the elementary properties of these objects.
Traditional Euclidean geometry is based on these elements:
- basic objects:
- a point is an elementary object that does not have any dimension;
- the geometric plane is an unlimited set of points;
- the lines of the plane are subsets of the points aligned in the plane
- the axioms:
- any two distinct points determine one single line;
- a line segment can be indefinitely extended in a straight line;
- given any line segment, a circle can be drawn by taking this segment as the radius and one of its end points as the centre;
- all right angles are congruent;
- in a plane, there is only one single line parallel to a given line through a point that is outside the line.