The mathematical basis for the line geometry, with the line as its basic element, is presented in the paper because the forces that act on a body in space-whether we are interested in conditions of movement or immobility (balance) of that body-are vectorial values related to specific lines of action, so that the system of forces can be linked to the set of lines in space. The application of line geometry has proven the known claim that the system of forces in space, provided the forces are in a general position, can be reduced to two forces on reciprocal lines. The visualisation of this claim via the 3D graphic statics is also presented.