Norman Campbell

II. The elements of geometry

Summary It is maintained that the geometry of Euclid is best interpreted as an attempt to deduce as many important propositions as possible from the assumption that length, angle, area (and perhaps volume) are magnitudes universally measurable by the methods that are actually employed in experimental physics. All his chief propositions (in so far as they are true) can be deduced from that assumption without any other. This view is supported, not by a detailed analysis of the Elements, but by a very summary sketch of the laws that must be true if the assumption is to be acceptable. In a sequel it is hoped to discuss similarly the foundations of another branch of experimental geometry with which Euclid is not directly coucerned—namely the geometry of position, which involves the concept of “space.”