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THE ELEMENTS OF EUCLID.

NOW READY, A SEQUEL TO THE FIRST SIX BOOKS OF THE

ELEMENTS OF EUCLID, Containing an Easy Introduction to Modern Geometry:

With numerous Examples.

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 Kopious Annotations & numerous Exercises.

A KEY TO THE EXERCISES IN THE FIRST SIX

BOOKS OF CASEY'S ELEMENTS OF EUCLID.

DUBLIN: HODGES, FIGGIS, & Co.

LONDON : LONGMANS & ICO.

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

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

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DUBLIN: HODGES, FIGGIS, & CO., GRAFTON-ST.
LONDON: LONGMANS, GREEN, & CO.

1885.

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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

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