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Euclid

Little is known about Euclid's actual life. He was living in Alexandria about 300 B.C.E. based on a passage in Proclus' Commentary on the First Book of Euclid's Elements. Indeed, much of what is known or conjectured is based on what Proclus says. After mentioning two students of Plato, Proclus writes

All those who have written histories bring to this point their account of the development of this science. Not long after these men came Euclid, who brought together the Elements, systematizing many of the theorems of Eudoxus, perfecting many of those of Theatetus, and putting in irrefutable demonstrable form propositions that had been rather loosely established by his predecessors. He lived in the time of Ptolemy the First, for Archimedes, who lived after the time of the first Ptolemy, mentions Euclid. It is also reported that Ptolemy once asked Euclid if there was not a shorter road to geometry that through the Elements, and Euclid replied that there was no royal road to geometry. He was therefore later than Plato's group but earlier than Eratosthenes and Archimedes, for these two men were contemporaries, as Eratosthenes somewhere says. Euclid belonged to the persuasion of Plato and was at home in this philosophy; and this is why he thought the goal of the Elements as a whole to be the construction of the so-called Platonic figures. (Proclus, ed. Friedlein, p. 68, tr. Morrow)

It is apparent that Proclus had no direct evidence for when Euclid lived, but managed to place him between Plato's students and Archimedes, putting him, very roughly, about 300 B.C.E. Proclus lived about 800 years later, in the fifth century C.E.

There are a few other historical comments about Euclid. The most important being Pappus' (fourth century C.E.) comment that Apollonius (third century B.C.E.) studied "with the students of Euclid at Alexandria."

Thus, we know almost nothing about Euclid's life. But we have more of his writings than any other ancient mathematician. Besides the Elements, there are the Data, On Divisions of Figures, the Phaenomena, and the Optics. All are included in the Euclidis opera omnia of Heiberg and Menge (see below) in Greek and translated into Latin. Other translations are listed below. Euclid also wrote other books which no longer exist but were mentioned by later writers. They include Surface Loci, Porisms, Conics, and the Pseudaria (that is, the Book of Fallacies).

- Archibald, Raymond Clare (1875-1957).
  Euclid's book on division of figures. Cambridge University Press, Cambridge, 1915.

- Berggren, J. L. Euclid's Phaenomena: a translation and study of a Hellenistic treatise in spherical astronomy. Garland, 1996?

- Bretschneider, Karl Anton. Die Geometrie und die Geometer vor Eukleides; ein historischer Versuch. Teubner, Leipzig, 1870.

- Busard, H.L.L. First Latin translation of Euclid's "Elements" commonly ascribe to Adelard of Bath. Pontifical Institute.

- Chasles, M. (Michel) (1793-1880)
  Les trois livres de porismes d'Euclide, rétablis ... d'aprés la notice ... de Pappus. Mallet-Bachelier, Paris, 1860.

- Frankland, William Barrett. The first book of Euclid's Elements with a commentary based principally upon that of Proclus Diadochus. Cambridge Univ Press, New York, 1905.

- Heath, Sir Thomas Little (1861-1940)
  The thirteen books of Euclid's Elements translated from the text of Heiberg with introduction and commentary. Three volumes. University Press, Cambridge, 1908. Second edition: University Press, Cambridge, 1925. Reprint: Dover Publ., New York, 1956. Reviewed: Isis 10 (1928),60-62.

  The text of Heath's translation of Euclid's Elements is also available on-line at the Perseus Project at Tuft's University starting with the first definition of book I.

- Heiberg, J. L. (Johan Ludwig) (1854-1928)
  Euclidis opera omnia. 8 vol. & supplement. 1883-1916. Edited by J. L. Heiberg and H. Menge.

- Kayas, G. J. Les Eléments. CNRS, 1978.

- Knorr, Wilbur Richard The evolution of the Euclidean elements. A study of the theory of incommensurable magnitudes and its significance for Greek geometry. Synthese Historical Library, vol. 15. Reidel, Dordrecht-Boston, 1975. Reviewed: MR 57#12003.

- Morrow, Glenn R. Proclus: A commentary on the first book of Euclid's elements. Translated by G. R. Morrow. Princeton Univ Press, Princeton, 1970.

- Mueller, Ian. Philosophy of mathematics and deductive structure in Euclid's Elements. MIT Press, Cambridge, Mass., 1981.

- Schmidt, Robert. Euclid's Recipients, commonly called the Data. Golden Hind Press, 1988.

- Taisbak, C. M. Colored quadrangles. A guide to the tenth book of Euclid's Elements. Opuscula Graecolatina, 24. Museum Tusculanum Press, Copenhagen, 1982. Reviewed: MR 84i:01022.

- Thomas-Stanford, Charles Early editions of Euclid's Elements. Bibliographical Society, London, 1926. Reviewed: Isis 10 (1928), 59-60.

- Thomson, William. Pappus' commentary on Euclid's Elements. Cambridge, 1930. Review: Isis 16 (1931), 132-136.

Table of Contents

Copyright © 1998.
D.E.Joyce
Clark University

These pages are located at http://aleph0.clarku.edu/~djoyce/java/elements/elements.html.