
MA232A  Euclidean and nonEuclidean Geometry
Michaelmas Term 2015
Dr. David R. Wilkins
Resources related to Euclid

The Greeks were the first mathematicians who are still
‘real’ to us today. Oriental mathematics
may be an interesting curiosity, but Greek mathematics is
the real thing. The Greeks first spoke a language which
modern mathematicians can understand: as Littlewood
said to me once, they are not clever schoolboys or
‘scholarship candidates’, but ‘Fellows
of another college’. So Greek mathematics is
‘permanent’, more permanent even than Greek
literature. Archimedes will be remembered when Aeschylus
is forgotten, because languages die and mathematical ideas
do not. ‘Immortality’ may be a silly word, but
probably a mathematician has the best chance of whatever
it may mean.
— G.H. Hardy, A Mathematician's Apology
N.B., for a contrasting valuation of ‘oriental mathematics’,
see in particular
The Crest of the Peacock: NonEuropean Roots of Mathematics,
by George Gheverghese Joseph (Princeton University Press, ISBN 9780691135267).
Summary of Lectures
For an indication of what has been covered in lectures, consult the
Lecture Log.
Principal Texts
 The First Six Books of the Elements of Euclid by John Casey
 This eBook is available from the
Project Gutenberg
website at the following URL:
http://www.gutenberg.org/ebooks/21076.
This eBook is for the use of anyone anywhere at no
cost and with almost no restrictions whatsoever. You may
copy it, give it away or reuse it under the terms of
the Project Gutenberg License
included with this eBook or online
at www.gutenberg.org.
 Euclid's Elements of Geometry (Richard Fitzpatrick, University of Texas)
 This modern edition, translated from Heiberg's critical edition,
has parallel texts in Greek and English. This edition presents
the text of Euclid, without scholia or extensive commentary.
 The Thirteen Books of Euclid's Elements  Introduction and Books I, II (Thomas L. Heath, 1908, Internet Archive)
 The Thirteen Books of Euclid's Elements  Books III—IX (Thomas L. Heath, 1908, Internet Archive)
 This wellknown scholarly edition presents a translation into
English from Heiberg's critical edition, with introductory
chapters and substantial commentary. The edition is available,
in paperback, in three volumes, from Dover Books.
Local Resources related to Euclid

The Axiom System of Book I of Euclid's Elements of Geometry

The Theory of Parallels in Book I of Euclid's Elements of Geometry

Euclid, Book III Extracts (transcription of T.L. Heath's edition, under development)

Euclid, Book V Extracts (transcription of T.L. Heath's edition, under development)
Online Editions of Euclid
See Editions of Euclid
Other works relating to Euclid
 Euclid and his Modern Rivals (Charles Dodgson, 1879, Internet Archive)
 Review of F. Peyrard, Les Oeuvres de Euclide, en Grec, en Latin, et en Franç, d'àpres un manuscrit très ancien qui é resté inconnu jusqu'à nos jours, Dublin Review, vol.~11, 1841,
pp. 330355 (Google Books)
 Euclid, his Life and System (Thomas Smith, 1902, Internet Archive

This book, by
Thomas Smith (1817—1906)
was written for a general audience. The American philosopher,
logican and mathematician Charles Sanders Peirce published
a very critical review of this book (made available on the Internet with other published papers of C.S. Peirce as part of the Peirce Edition Project at Indiana University—Purdue University Indianapolis.
 Modern Synthetic Geometry versus Euclid (Robert J. Aley, Science Vol. 20, 1829, [Jstor, Internet Archive]
Other Systems of Euclidean Geometry
 Éléments de géométrie; avec des notes (AdrienMarie Legendre, 12th edition of 1823, Internet Archive
 Elements of Geometry (AdrienMarie Legendre, translated by Thomas Carlyle, edited by David Brewster and Charles Davies, 1837, Internet Archive)
 The Elements of Geometry (G.B. Halsted, 1889, Internet Archive)
 Foundations of Geometry (David Hilbert, translated E.J. Townsend, Internet Archive)
NonEuclidean Geometry
 New Principles of Geometry (Nicolai Lobachevski, translated G.B. Halsted, Yale Digital Library
Back to Module MA232A
Back to D.R. Wilkins: Lecture Notes
Dr. David R. Wilkins,
School of Mathematics,
Trinity College Dublin.