The Axioms of Geometry

Abstract

SINCE the time when Riemann and Helmholtz began their investigations on the axioms of geometry so much has been written on this subject in learned papers and in a more or less popular form that it. might have appeared superfluous again to call the attention of writers on, and teachers of, elementary geometry to it, had it not been for the publication a year or two ago of a new edition of the first six books of Euclid's “Elements,” with annotations and notes, by Prof. Casey. I hope the eminent author of this in many respects excellent book will excuse me for criticising some points in it, and making them the opportunity for again returning to the question about the axioms in geometry.