We consider the Swedish mathematician Torsten Brodén's article 'Om geometriens principer' from 1890. In this article Brodén gives a philosophical and pedagogical discussion on geometry and he develops an axiomatic system for Euclidean geometry. We consider in detail Brodén's view on the nature of geometry, which is influenced by Helmholtz. Brodén considers geometry to be an empirical inductive science, but at the same time he claims that geometry deals with ideal objects that are not revealed in the immediate external experience.
We discuss the criteria Brodén gives for the basic notions and axioms of a scientific system. He gives a criterion of independence of the axioms, and criteria that can be interpreted to be verions of completeness and consistency. In establishing the basic notions of geometry, Brodén considers motion, which he claims presupposes all natural sciences. Motion, he claims, can be reduced to the concept of 'point' and 'immediate equality of distance'. Finally we briefly discuss the axioms given for Euclidean geometry.