Production Note Cornell University Library produced this volume to replace the irreparably deteriorated original. It was scanned using Xerox software and equipment at 600 dots per inch resolution and com- pressed prior to storage using CCITT Group 4 compression. The digital data were used to create Cornell’s replacement volume on paper that meets the ANSI Standard Z39.48-1984. The produc- tion of this volume was supported in part by the Commission on Preservation and Access and the Xerox Corporation. Digital file copyright by Cornell University Library 1991. 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 MATHEMATICAL SEMINARY LIBRARY ______________ THE GIFT OF LUCIEN AUGUSTUS WAIT ....................................................................... THE ELEMENTS OF EUCLID. NOW READY _______ Price 3s. A TREATISE ON ELEMENTARY TRIGONOMETRY, With Numerous Examples and Questions for Examination. ______________ Third Edition, Revised and Enlarged, Price 3s. 6d., Cloth. A SEQUEL TO THE FIRST SIX BOOKS OF THE ELEMENTS OF EUCLID, Containing an Easy Introduction to Modern Geometry: With numerous Examples. ______________ Third Edition, Price 4s. 6d.; or in two parts, each 2s. 6d. THE ELEMENTS OF EUCLID, BOOKS I.—VI., AND PROPOSITIONS I.—XXI., OF BOOK XI.; Together with an Appendix on the Cylinder, Sphere, Cone, &c.: with Copious Annotations & numerous Exercises. ______________ Price 6s. A KEY TO THE EXERCISES IN THE FIRST SIX BOOKS OF CASEY’S ELEMENTS OF EUCLID. ______________ Price 7s. 6d. A TREATISE ON THE ANALYTICAL GEOMETRY OF THE POINT, LINE, CIRCLE, & CONIC SECTIONS, Containing an Account of its most recent Extensions, With numerous Examples. ______________ DUBLIN: HODGES, FIGGIS, & CO. LONDON: LONGMANS & CO. THE FIRST SIX BOOKS OF THE ELEMENTS OF EUCLID, AND PROPOSITIONS I.-XXI. OF BOOK XI., AND AN APPENDIX ON THE CYLINDER, SPHERE, CONE, Etc. 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; MEMBER OF COUNCIL, ROYAL IRISH ACADEMY; MEMBER OF THE MATHEMATICAL SOCIETIES OF LONDON AND FRANCE; AND PROFESSOR OF THE HIGHER MATHEMATICS AND OF MATHEMATICAL PHYSICS IN THE CATHOLIC UNIVERSITY OF IRELAND. 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. ________