xviii Preface
new concepts and substantial new notation have been introduced. There is enough for
a two-semester course; a one-semester one could be made from Chapters 2-9, with
Chapter 7 trimmed back.
My object has been to give an account at once accessible and unobtrusively rig-
orous. Preparation has been in the nature of unfinished business, stemming from my
great difficulties when young in understanding the then textbooks in geometry. I hold
that the reasoning in geometry should be as convincing as that in other parts of mathe-
matics. It is too much to hope that there are no errors, mathematical or typographical.
I should be grateful to be told of any at the email [email protected].
Acknowledgements
I am grateful to students in a succession of classes who responded to this material
in its nascent stages, to departmental colleagues, especially Finbarr Holland and Des
MacHale, who attended presentations of it, and to American colleagues the late David
Rosen of Swarthmore and John Elliott of Fort Kent, Maine, who read an earlier ap-
proach of mine to geometry. I am especially grateful to Dr. P.A.J. Cronin, a colleague
in our Department of Ancient Classics, for preparing the translations from Greek and
Latin in the Glossary on pp. xix-xx.
Paddy BarryNational University of Ireland, Cork,
November, 2000.
PREFATORY NOTE TO THE REVISED EDITIONSeveral changes have taken place since the preparation of this material in the
years leading up to 2001. The original publisherHORWOODwas acquired in 2010
byWOODHEADwhich in turn was acquired in 2013 byELSEVIER.However
WOODHEADis retaining its imprint.
The reason for a revised edition was that the stock for the original edition was
exhausted. There is not a lot of alteration in this edition, some correction of errors and
the strengthening of some proofs apart from Chapter 11 in which there is considerable
alteration of detail.
There is a great alteration in the software available and required in mathemati-
cal word processing, particularly on those who have relied heavily onpstricksfor
preparing diagrams, and I owe a huge debt in this regard to my colleagues Paul Kee-
gan, Marc van Dongen, Peter Flynn, Stephen Wills, Ben McKay and Joseph Man-
ning. I also thank Ulrike Fischer, who is a troubleshooter for TeX, and without whose
involvement this project would not have been completed.
Paddy BarryNational University of Ireland, Cork,
February, 2015.