NOTICE. The methods of proof set forth in this Edition of Euclid's ELEMENTS OF GEOMETRY satisfy the requirements of the Cambridge Local and Schools Examinations. CONTAINING BOOKS I. TO VI. AND PORTIONS OF BOOKS XI. AND XII. OF EUCLID WITH Exercises and Notes BY J. HAMBLIN SMITH, M.A. OF GONVILLE AND CAIUS COLLEGE, AND LATE LECTURER AT ST. PETER'S COLLEGE CAMBRIDGE FIFTH EDITION RIVINGTONS WATERLOO PLACE, LONDON MDCCCLXXXIII 183.9.139 PREFACE. To preserve Euclid's order, to supply omissions, to remove defects, to give short notes of explanation and simpler methods of proof in cases of acknowledged difficulty—such are the main objects of this Edition of the Elements. The work is based on the Greek text, as it is given in the Editions of August and Peyrard. To the suggestions of the late Professor De Morgan, published in the Companion to the British Almanack for 1849, I have paid constant deference. A limited use of symbolic representation, wherein the symbols stand for words and not for operations, is generally regarded as desirable, and it is certain that the symbols employed in this book are admissible in the Examinations at Oxford and Cambridge. I have generally followed Euclid's method of proof, but not to the exclusion of other methods recommended by their simplicity, such as the demonstrations by which I propose to replace the difficult Theorems 5 and 7 in the First Book. I |