The time has long passed when the teacher of elementary geometry, however elementary, can efficiently exercise his individuality in devising improved methods of exposition without taking some cognisance, however small, of the study of non-Euclidean geometry which has grown up out of the failure to prove what may be described as “Euclid’s Parallel Postulate.”

A paper has recently been published in the Proceedings of the Edinburgh Mathematical Society by Prof. Carslaw, of Sydney, N.S.W., containing an elementary interpretation of the Bolyai-Lobatschewsky geometry, which is so simple and so easily intelligible that I strongly recommend every teacher of mathematics or science to read it. It does away altogether with the necessity of forming conceptions of space which appear contradictory to experience, and shows the possibility of constructing a non-Euclidean geometry in ordinary Euclidean space.