The teaching of mathematics has been brought to so high a pitch of excellence by the eminent teachers of the past century that it may be thought there is little scope for improvement in their methods.

Since the radical revision of our geometry text-books towards the end of the nineteenth century, when modern methods first superseded the age-old system of Euclid, we find no fundamental change of doctrine until we come to consider the place of trigonometry and of the calculus in present-day curricula.