MACMILLAN AND CO., LIMITED LONDON BOMBAY CALCUTTA THE MACMILLAN COMPANY NEW YORK BOSTON CHICAGO DALLAS • SAN FRANCISCO THE MACMILLAN CO. OF CANADA, LTD. TORONTO MATHEMATICS BY DAVID BEVERIDGE MAIR, M.A. SOMETIME FELLOW OF CHRIST'S COLLEGE, CAMBRIDGE MACMILLAN AND CO., LIMITED PREFACE THE motives which give rise to mathematical activities in the human mind are classified by Dr Percy Nunn as the wonder motive, the utility motive, and the systematizing motive. The systematizing motive influences mature minds chiefly and has little concern with school education. In the school the predominant motive is that of utility. This motive must form the basis of a good school course of mathematics; while the wonder motive justifies the inclusion of an occasional striking property which has no utility value. If we held strictly to these principles we should shun all side streams, the exploration of which occupies time out of proportion to the resulting gain, and confine ourselves to the main course of mathematical development, in order that every pupilthe non-specialist included-may leave school with some real idea of the part played by mathematics in human life. In practice, however, we are not free to plan an ideal course. The school's freedom to follow the best is limited by a number of restrictions, prominent among which stands the examination syllabus. In consequence we include in this book all the branches which it is customary to teach, and at the head of each Section or Sub-section which a school free to follow the best ought to omit we place a note to that effect. The book is designed to cover the mathematical studies of the non-specialist up to the close of his school career; the mathematical pupil ought to follow the same course and then proceed to more advanced studies. Arithmetic is treated in Sections |