82 bernard vitrac
the beginning to a lower-quality model was not taken into account by the
Danish editor. Th e portion b xi .36– xii .17 was relegated to Appendix II of
Volume 4 of the edition, together with portions of the text which Heiberg
deemed inauthentic.
In other words, his decisions (or rather his non-decisions) resulted in
a critical edition that can be described as ‘conservative’. In order to clarify
the meaning of this term, let us recall that the Greek text had undergone
fi ve editions in recent times: the editio princeps by S. Grynée (Bâle, 1533),
the edition by D. Gregory (Oxford, 1703), the edition by F. Peyrard (Paris,
1814 –18), that of E. F. August (Berlin, 1826–29) and fi nally Heiberg’s own
edition. I do not intend to examine in detail their respective merits, but
two or three facts are clear. Th e fi rst two editions were produced from
manuscripts belonging to the family later characterized as ‘Th eonine’.
Despite the many discussions of the sixteenth century, 170 years had
passed before the appearance of a new edition, which Peyrard judged to be
no better than the preceding!
At any rate, Peyrard’s edition scarcely agrees with his history of the text.
Aft er he affi rmed that the Vatican manuscript contained the text of Euclid,
he continued to follow the text of the editio princeps of 1533 (and thus
the Th eonine family of texts) in several passages where the divergences
are especially well-marked. Th e quest for authenticity was not of primary
importance. It was more important to present a mathematically correct
Euclid. We may suppose that it is for this reason that Peyrard continued to
follow the Th eonine family which is more correct in the case of ix .19 and
more general in the case of xi .38, but privileged P which is (apparently) less
faulty in the case of iii .24 and more complete in the case of xiii .6. Peyrard
also wanted his edition to be easy to use. Quite bluntly, Peyrard admits to
having retained what is now designated as Proposition x .13 vulgo lest he
introduce a shift in the enumeration of the Propositions of the book with
respect to the previous editions – even though this proposition is omitted
in P and is clearly an interpolation! More generally, he preserves most of
the additional material (various additions, lemmas, alternate proofs) which
P would have been able to dismiss as inauthentic had it been taken into
account.
It was not until the edition of Heiberg that the primacy of manuscript P
was truly assumed. A large part (but not all!) of the material thereaft er con-
sidered additional was added to the Appendices inserted at the end of each
of the four volumes. Whenever the textual divergence is marked and the
result (in Th ) is identifi ed as the product of a voluntary modifi cation, the
reading of P is retained, even if this destroys the mathematical coherence,