Elements / 原論 — Euclid
First Six Books of the Elements of Euclid | Project Gutenberg You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org . If you are not located in the United States, you will have to check the laws of the country where you are located before using this eBook. Title : The First Six Books of the Elements of Euclid Author : Euclid John Casey Release date : April 14, 2007 [eBook #21076] Most recently updated: August 5, 2025 Language : English Other information and formats : www.gutenberg.org/ebooks/21076 Credits : Joshua Hutchinson, Keith Edkins and the Online Distributed Proofreading Team at https://www.pgdp.net (This file was produced from images from the Cornell University Library: Historical Mathematics Monographs collection.) Revised by Richard Tonsing. *** START OF 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. T r a n s c r i b e r ’ s N o t e : 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. ________ 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— C a t a l a n ’ s Th éor èmes et Probl èmes de G éom étrie El émentaire , and the Trait é de G éom étrie , by R o u c h é and D e C o m b e r o u s s e . The second edition has been thoroughly revised and greatly enlarged. Th