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Trinity College Dublin

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

The Greeks were the first mathematicians who are still ‘real’ to us to-day. 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: Non-European 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: 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 re-use it under the terms of the Project Gutenberg License included with this eBook or online at
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 well-known 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. 330--355 (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 (Adrien-Marie Legendre, 12th edition of 1823, Internet Archive
Elements of Geometry (Adrien-Marie 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)

Non-Euclidean Geometry

New Principles of Geometry (Nicolai Lobachevski, translated G.B. Halsted, Yale Digital Library

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Dr. David R. Wilkins, School of Mathematics, Trinity College Dublin.