CAMBRIDGE UNIVERSITY PRESS C. F. CLAY, MANAGER LONDON : FETTER LANE, E. C. 4 NEW YORK: G. P. PUTNAM'S SONS ALL RIGHTS RESERVED BOOK I WITH INTRODUCTION AND NOTES BY SIR THOMAS L. HEATH K.C. B., K.C. V.O., F.R.S. SC,D. CAMB. HON. D.SC. OXFORD CAMBRIDGE AT THE UNIVERSITY PRESS 1920 239306 NOV 18 320 LBDA • EUR . PREFACE I N these days when Greek is supposed to be on its trial and Euclid happily defunct, it may well seem a wildly reactionary proceeding to suggest to teachers a combination of the two, a piling (so it might be thought) of one inutility on another. But, first, we must bear in mind that it is only compulsory Greek that is threatened: when that is gone, the study of Greek will be no whit less necessary to a complete education. Generation after generation of men and women will still have to go to school to the Greeks for the things in which they are our masters; and for this purpose they must continue to learn Greek. Again, Euclid can never at any time be more than apparently in abeyance; he is immortal. Elementary geometry will also continue to form part of a complete education; and elementary geometry is Euclid, however much the editors of text-books may try to obscure the fact. But I am not here concerned to argue the case of Euclid against other text-books of geometry. The aim of this book is to maintain an opinion which I have long held that, if the study of Greek and Euclid be combined by reading at least part of Euclid in the original, the two elements will help each other enormously. In the first place, boys learning Greek in the higher Forms in schools will generally have some knowledge of elementary geometry. Even if this is read in some text-book other than Euclid, all the technical terms and phrases will be the same, and in any proposition of Euclid that may be taken up the course of the proof will be easily divined, almost by simple inspection. Hence, in translating the Greek, the student will really be translating something quite familiar. Now every one knows that, when beginning the study of a foreign language, it is quite a good plan to read familiar chapters of the Bible in a translation into the particular tongue. The advantage to the student of Greek of reading in Greek the familiar propositions of Euclid's first book will hardly be less. Secondly, from the point of view of learning geometry, much advantage will be gained by having, as it were, to spell out the Greek. The beginner in geometry needs to learn a good many things by heart, especially technical terms, many of which, being reflections of the Greek, will be the better understood if the Greek forms are known. How can any person who has only had such words as theorem, problem, isosceles, parallelepiped explained to him in English apart from their derivation get any such clear idea of their significance as the person who knows them as θεώρημα, πρόβλημα, ισοσκελές, παραλindenitredov? Again, persons with no particular aptitude for mathematics find a difficulty in memorising the course of the proofs and avoiding confusion |