Projective geometry has always been called the geometry of joining and intersecting to contrast it with Euclidean, affine and other geometries which besides consider congruency, perpendicularity and parallelism. When preparing a course on projective geometry at the University of Vienna in 1927/28 I therefore looked for an axiomatic foundation that would reflect this principal feature of the theory, in other words, for a development based on assumptions about joining and intersecting. But nowhere in the immense literature could I find what I was looking for. So I formulated such a foundation myself.¹