  In this paper we propose a well-justified synthetic approach of the
projective space. We define the concepts of plane and space of incidence and
also the Gallucci's axiom as an axiom to our classical projective space. To
this purpose we prove from our space axioms, the theorems of Desargues, Pappus,
the fundamental theorem of projectivities, and the fundamental theorem of
central-axial collinearities, respectively. Our building up do not use any
information on analytical projective geometry, as the concept of cross-ratio
and the homogeneous coordinates of points.
