Newton's first law revisited

The formulations of Newton's first law in Newton's Principia and in modern textbooks are examined critically. A special effort is made to differentiate clearly between definitions and nontrivial. facts of nature, and this is done in as primitive terms as possible, with emphasis on the projective structure. A somewhat novel characterization of the term 'free particle' is proposed, and a new, coordinate-independent definition of the term 'straight line' is provided. The analysis is performed in 4-dimensional spacetime, and separately for the idealized case of the absence of gravity and for the dynamics in the presence of gravity.