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Vol . 1( BooksIa ndI I ) EUCLI D THETHI RTEENBOOKSOF THEELEMENTS Tr a n s l a t e dwi t hi n t r o d u c t i o na n d c o mme n t a r yb ySi rTh o ma sL. He a t h Se c o n dEd i t i o nUn a b r i d g e d THE THIRTEEN BOOKS OF EUCLID'S ELEMENTS TRANSLATED FROM THE TEXT OF HEIBERG WITH iNTRODUCTION AND COMMENTARY BY T. L. HEATH, C.B., Sc.D., SOMETIME FELLOW OF TRINITY COLLEGE, CAMBRIDGE VOLUME I INTRODUCTION AND BOOKS I, II CAMBRIDGE: at the University Press 19 68 I~n~11~lm1I11111111111~'llllllllllllt 80047429 QI:ambribge: PRINTED BY JOHN CLAY, M.A. AT THE UNIVERSITY PRESS. ERRATA Vol. Vol. Vol. Vol. Vol. Vol. Vol. I. p. 19, line 17 ,jor " but not a platform and sixpence" read" but not a figure and sixpence" p. 105, line 10 } p. +15, :01. z, line 17 for Christoph Schllissel read Christoph Klan II. p. +1, lme z7 III. p. 539, col. I, line +5 I. p. I06'l' line I } p. +15, col. I. li~e ZI for Giacomo "ead Giovanni III. p. 538, col. z, lme z5 I. p. 18z, line ZI, for Opos read"Opos III. p. +99, In the figure, CV should be a thick line. H!:ATH~S EUCLID PREFACE "THERE never has been, and till we see it we never shall believe that there can be, a system of geometry worthy of the name, which has any material departures (we do not speak of corrections or extensi(Jns or developments) from the plan laid down by Euclid." De Morgan wrote thus in October 1848 (Short supplementary remarks on "the first six . Books 0.1 Euclid's Elements in the Companion to the Almanac for 1849); and I do not .think that, if he had been living to-day, he would have seen reason to revise the opinion so deliberately pronounced sixty years ago. I t is true that in the interval much valuable work has been done on the continent in the investigat