Axioms, or postulates (**P**), are propositions accepted as true without demonstration and which serve as the basis for the development of a theory. We have as fundamental axiom:* There are infinite points, lines and planes.*

## Postulates about points and lines

P_{1}) The line is infinite, ie it contains infinite points.

P_{2}) For one point infinite straight lines can be drawn.

P_{3}) Two distinct points pass a single line.

P_{4}) Any point on a line divides it into two straight lines.

## Postulates about plane and space

P_{5}) Three non-collinear points pass a single plane.

P_{6}) The plan is infinite, that is, unlimited.

P_{7}) A line can be drawn by a multitude of planes.

P_{8}) Every line belonging to a plane divides it into two regions called *semiplanes.*

P_{9}) Any plane divides space into two regions called semi-spaces.