  BOOK I THE DEFINITION OF MATTER CHAPTER II OUR KNOWLEDGE OF EXTERNAL OBJECTS IS ONLY SENSATIONS CHAPTER III THE MECHANICAL THEORIES OF MATTER ARE ONLY SYMBOLS CHAPTER IV ANSWERS TO SOME OBJECTIONS, AND SUMMARY BOOK II THE DEFINITION OF MIND CHAPTER I THE DISTINCTION BETWEEN COGNITION [13] AND ITS OBJECT CHAPTER II DEFINITION OF SENSATION CHAPTER III DEFINITION OF THE IMAGE CHAPTER IV DEFINITION OF THE EMOTIONS CHAPTER V DEFINITION OF THE CONSCIOUSNESS THE RELATION SUBJECT-OBJECT CHAPTER VI DEFINITION OF THE CONSCIOUSNESS CATEGORIES OF THE UNDERSTANDING CHAPTER VII DEFINITION OF THE CONSCIOUSNESS THE SEPARABILITY CHAPTER VIII DEFINITION OF THE CONSCIOUSNESS THE SEPARATION OF CHAPTER IX DEFINITIONS OF PSYCHOLOGY BOOK III THE UNION OF THE SOUL [40] AND THE BODY CHAPTER I THE MIND HAS AN INCOMPLETE LIFE CHAPTER II SPIRITUALISM [43] AND IDEALISM CHAPTER III MATERIALISM AND PARALLELISM Materialism THE INTERNATIONAL SCIENTIFIC SERIES. Each Book Complete in One Production Note Cornell University Library produced this volume to replace the Transcriber’s Note: The Index has been regenerated to fit the pagination of this edition. Despite the author’s stated hope that “few misprints have escaped detection” there were several, which have here been corrected and noted at the end of the text. CORNELL UNIVERSITY LIBRARY ______________ THE EVAN WILHELM EVANS ______________ THE GIFT OF ....................................................................... THE ELEMENTS OF EUCLID. NOW READY _______ Price 3s. A TREATISE ON ELEMENTARY TRIGONOMETRY, ______________ Third Edition, Revised and Enlarged, Price 3s. 6d., Cloth. ______________ Third Edition, Price 4s. 6d.; or in two parts, each 2s. 6d. ______________ Price 6s. ______________ Price 7s. 6d. A TREATISE ON THE ANALYTICAL GEOMETRY OF ______________ DUBLIN: HODGES, FIGGIS, & CO. THE FIRST SIX BOOKS OF THE ELEMENTS OF EUCLID, AND PROPOSITIONS I.-XXI. OF BOOK XI., AND AN APPENDIX ON THE CYLINDER, SPHERE, WITH COPIOUS ANNOTATIONS AND NUMEROUS EXERCISES. BY J O H N C A S E Y, LL. D., F. R. S., FELLOW OF THE ROYAL UNIVERSITY OF IRELAND; PIC THIRD EDITION, REVISED AND ENLARGED. DUBLIN: HODGES, FIGGIS, & CO., GRAFTON-ST. LONDON: LONGMANS, GREEN, & CO. 1885. DUBLIN PRINTED AT THE UNIVERSITY PRESS, BY PONSONBY AND WELDRICK PREFACE. ________ This edition of the Elements of Euclid, undertaken at the request of the principals of some of the leading Colleges and Schools of Ireland, is intended to supply a want much felt by teachers at the present day—the production of a work which, while giving the unrivalled original in all its integrity, would also contain the modern conceptions and developments of the portion of Geometry over which the Elements extend. A cursory examination of the work will show that the Editor has gone much further in this latter direction than any of his predecessors, for it will be found to contain, not only more actual matter than is given in any of theirs with which he is acquainted, but also much of a special character, which is not given, so far as he is aware, in any former work on the subject. The great extension of geometrical methods in recent times has made such a work a necessity for the student, to enable him not only to read with advantage, but even to understand those mathematical writings of modern times which require an accurate knowledge of Elementary Geometry, and to which it is in reality the best introduction. In compiling his work the Editor has received invaluable assistance from the late Rev. Professor Townsend, s.f.t.c.d. The book was rewritten and considerably altered in accordance with his suggestions, and to that distinguished Geometer it is largely indebted for whatever merit it possesses. The Questions for Examination in the early part of the First Book are intended as specimens, which the teacher ought to follow through the entire work. Every person who has had experience in tuition knows well the importance of such examinations in teaching Elementary Geometry. The Exercises, of which there are over eight hundred, have been all selected with great care. Those in the body of each Book are intended as applications of Euclid’s Propositions. They are for the most part of an elementary character, and may be regarded as common property, nearly every one of them having appeared already in previous collections. The Exercises at the end of each Book are more advanced; several are due to the late Professor Townsend, some are original, and a large number have been taken from two important French works—Catalan’s ThÉorÈmes et ProblÈmes de GÉomÉtrie ElÉmentaire, and the TraitÉ de GÉomÉtrie, by RouchÉ and De Comberousse. The second edition has been thoroughly revised and greatly enlarged. The new matter includes several alternative proofs, important examination questions on each of the books, an explanation of the ratio of incommensurable quantities, the first twenty-one propositions of Book XI., and an Appendix on the properties of the Prism, Pyramids, Cylinder, Sphere, and Cone. The present Edition has been very carefully read throughout, and it is hoped that few misprints have escaped detection. The Editor is glad to find from the rapid sale of former editions (each 3000 copies) of his Book, and its general adoption in schools, that it is likely to accomplish the double object with which it was written, viz. to supply students with a Manual that will impart a thorough knowledge of the immortal work of the great Greek Geometer, and introduce them, at the same time, to some of the most important conceptions and developments of the Geometry of the present day. JOHN CASEY.
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