On the axioms of the forces in the mechanics of rigid bodies

Newton summarised knowledge related to forces in three axioms. The first and second ones define the mechanical state and motion of the examined body when there is no force or when force is exerted on the body. The third defines the law of action and reaction. Newton did not define it as separate axiom but assumed that forces are completely independent from each other. The statics applies four axioms. The first applies to the balance of two forces while the second one applies of three forces. The third axiom defines the relationships inside an equilibrium force system. The fourth one is the axiom of action and reaction. The two axiom systems are independent from each other. Further the independent axioms are applied in case of constraint forces: frictionless reaction force orthogonal on the forced surface, friction force acts in the direction of the motion, the deformation can be elastic, plastic and viscous