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Axioms


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

P1) The line is infinite, ie it contains infinite points.

P2) For one point infinite straight lines can be drawn.

P3) Two distinct points pass a single line.

P4) Any point on a line divides it into two straight lines.

Postulates about plane and space

P5) Three non-collinear points pass a single plane.

P6) The plan is infinite, that is, unlimited.

P7) A line can be drawn by a multitude of planes.

P8) Every line belonging to a plane divides it into two regions called semiplanes.

P9) Any plane divides space into two regions called semi-spaces.

Next: Relative Positions of Two Lines