The First Six Books of the Elements of Euclid
About this book
This edition of the Elements of Euclid, undertaken at the request of the prin-cipals of some of the leading Colleges and Schools of Ireland, is intended tosupply a want much felt by teachers at the present day—the production of awork which, while giving the unrivalled original in all its integrity, would alsocontain the modern conceptions and developments of the portion of Geometryover which the Elements extend. A cursory examination of the work will showthat the Editor has gone much further in this latter direction than any of hispredecessors, for it will be found to contain, not only more actual matter thanis given in any of theirs with which he is acquainted, but also much of a specialcharacter, which is not given, so far as he is aware, in any former work on thesubject. The great extension of geometrical methods in recent times has madesuch a work a necessity for the student, to enable him not only to read with ad-vantage, but even to understand those mathematical writings of modern timeswhich require an accurate knowledge of Elementary Geometry, and to which itis in reality the best introduction.In compiling his work the Editor has received invaluable assistance from thelate Rev. Professor Townsend, s.f.t.c.d. The book was rewritten and con-siderably altered in accordance with his suggestions, and to that distinguishedGeometer it is largely indebted for whatever merit it possesses.The Questions for Examination in the early part of the First Book are in-tended as specimens, which the teacher ought to follow through the entire work.Every person who has had experience in tuition knows well the importance ofsuch examinations in teaching Elementary Geometry.The Exercises, of which there are over eight hundred, have been all selectedwith great care. Those in the body of each Book are intended as applications ofEuclid’s Propositions. They are for the most part of an elementary character,and may be regarded as common property, nearly every one of them havingappeared already in previous collections. The Exercises at the end of eachBook are more advanced; several are due to the late Professor Townsend, someare original, and a large number have been taken from two important Frenchworks—Catalan’s Th´eor`emes et Probl`emes de G´eom´etrie El´ementaire, andthe Trait´e de G´eom´etrie, by Rouch´ e and De Comberousse.The second edition has been thoroughly revised and greatly enlarged. Thenew matter includes several alternative proofs, important examination questionson 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 propertiesof the Prism, Pyramids, Cylinder, Sphere, and Cone.The present Edition has been very carefully read throughout, and it is hopedthat few misprints have escaped detection.The Editor is glad to find from the rapid sale of former editions (each 3000copies) 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 studentswith a Manual that will impart a thorough knowledge of the immortal workof the great Greek Geometer, and introduce them, at the same time, to someof the most important conceptions and developments of the Geometry of thepresent day.