84 bernard vitrac
thoroughly called into question by W. Knorr in his article of 1996. In
particular, our late colleague there affi rms that all the preserved Greek
manuscripts depend on the edition of Th eon, that the diff erences between
the Vatican manuscript and the Th family are microscopic, and that these
diff erences are not characteristic of a re-edition. Stated diff erently, if the
opinion of Knorr is adopted, the Euclid edited by Heiberg ought to corre-
spond, at best, to the text in circulation at Alexandria in the second half of
the fourth century of our era.
Th e arguments of Knorr are not all of the same value – far from it. 34 Th e
diff erence between P and Th is real. It is not a question only of divergences
attributable to errors by the copyist which philologists try to dismiss. Th e
reader can convince himself of the extent of diff erences between P and Th
by consulting the list which I give in Table 3 of the Appendix. However,
it should also be emphasized that there is not, in this internal dichotomy
in the Greek, any substitution of proofs (!), any change in the order of the
Propositions, or any Lemma which exists in one of the two versions but not
in the other. When there are double proofs, the order is always the same as
in P and in Th.
At the present stage of my work, I see only two solutions: (i) to adopt
Knorr’s opinion, or (ii) to conclude that the goal of Th eon’s re-edition was
not a large-scale alteration. About Th eon’s motivations, we know next to
nothing. He presents us with a single indication relating to the contents (the
addition at vi .33). It is possible, for example, to conceive of the hypothesis
that Th eon’s re-edition was in fact the transcription of the edition(s) written
on scrolls into a version in the form of a codex or codices. If the text of the
previous vulgata appeared satisfactory to him, the goal would not have
been to propose a diff erent mathematical composition, but to revitalize
the treatise by adopting a new format for the old book. Th e second half of
the fourth century represents a relatively late date, but it is known that the
pagan circles sometimes resisted innovations which seemed to meet with
their fi rst successes in Christian quarters. 35 And, what is known, if not
about Th eon himself, then at least about his daughter Hypatia, suggests that
he was connected with pagan, neo-Platonic intellectual circles. Moreover,
even if this explanation is adopted, nothing guarantees that he was the
fi rst to unfold this way, nor that he was the only one. On the other hand,
it is certain that this version played an important role in the transmission
of the Elements , as is proven by the statements contained in the family of
manuscripts titled Th.(^34) See Rommevaux, Djebbar and Vitrac 2001: 233–5 and 244–50.
(^35) See van Haelst 1989: 14, 26–35.