Researches in the non-Euclidean geometries of Bolyai-Lobach vski and Riemann, while renewing the traditional admiration for Euclid, yet emphasize the advantages of a comparative study of pure spherics and plane geometry before similar figures. Putting pure spherics as Book II is thus a beginning toward comparative geometry.Again, the non-Euclidean geometry has given the key to the artificiality in Euclid's order of propositions. But it is approaching...