70 bernard vitrac
Euclid or the Euclid of the sixteenth century. Rather, this Euclid indicates
the third-century Hellenistic geometer and author of the Elements. To speak
about the Hellenistic Euclid, to describe the contents of his composition with
precision – which certainly implies the fact that it qualifi es as a ‘classic’ –
and to adopt or reject its approach towards proof presumes a reasonably
certain knowledge of the text of the Elements. Precisely this knowledge,
however, is in doubt.
To examine these assumptions, in the fi rst part I revisit some informa-
tion (or hypotheses) concerning the transmission of ancient Greek texts,
particularly the text of the Elements. I emphasize there the indirect char-
acter of our knowledge about this subject, and I review the history of the
text proposed by the Danish philologist J. L. Heiberg, at the time when he
produced, in the 1880s, the critical edition of the Greek text to which the
majority of modern studies on Euclid still refer. 2 I raise some uncertainties
and mention the recent criticism of W. Knorr. 3 In the second part , I give
examples of diff erences between preserved versions of the text, illustrating
the uncertainties which dismantle our knowledge about the Euclidean text,
notably the texts of certain proofs.Refl ections on the History of the Text of the Elements
A brief history of the ancient Greek texts
Lest the present study become too complicated, 4 let us admit that there
existed in thirteen books a Hellenistic edition (ἔκδοσις) of the Elements
(τὰ Στοικεῖα), corresponding, at least in rough outline, to that which has
come down to us and produced by Euclid or one of his closest students. 5 I n(^2) Heiberg and Menge, 1883–1916. It has been partially re-edited and (seemingly) revised by E. S.
Stamatis: Heiberg and Stamatis, 1969–77. In the following, I will designate these editions by
the EHM and EHS respectively.
(^3) Knorr 1996.
(^4) Th e literature on this subject is immense. I have consulted Pasquali 1952, Dain 1975, Reynolds
and Wilson 1988, Dorandi 2000 (which contains extensive information about papyri)
and Irigoin 2003 (a collection of articles published between 1954 and 2001, plus several
unpublished studies).
(^5) At least two other possibilities are conceivable, by analogy with some known cases of ancient
scholarly editions:
- Euclid had produced two versions of his text: the fi rst, a provisional copy, for a restricted
circle of students, correspondents or friends; the other, revised and authorized. Th is
corresponds with the composition of the Conics of Apollonius, as described by the author
himself in the introduction of Book i (of his revised version). Consequently, this hypothesis