The algebra of geometry

pp. 220-224

in: Karl Menger, Selected papers in logic and foundations, didactics, economics, Berlin, Springer, 1979

Abstract

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