 Let us say that a purely synthetic geometry is one that deals with primitive concepts such as straight lines and planes in something like the above fashion. That is, it takes the straightness of the straight line and the flatness of the plane as fundamental, and appeals to the incidence properties just described. It is resistant to the idea of taking distance as a fundamental concept, or to the idea of replacing statements in geometry by statements about numbers (say, as coordinates), although it is not hostile to coordinate geometry being erected upon it.