NOW READY.

Price 38.

A TREATISE ON ELEMENTARY TRIGONOMETRY, With Numerous Examples and Questions for Examination.

Third Edition, Revised and Enlarged, Price 38. ed., 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

Eopious Annotations & numerous Exercises.

Price 68.

A KEY TO THE EXERCISES IN THE FIRST SIX BOOKS OF CASEY'S ELEMENTS OF EUCLID.

Price 78. 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

IMENT OF MATHEMAT
CORNELL UNIVERSITY

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

JOHN CASEY, 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.
P.

A.13 139.

Esposled by Prof. Han's June 21/87

-conditions, whon return of Library's ovky.

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

b

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 pos

sesses.

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