Th e Elements and uncertainties in Heiberg’s edition 83
as in the previously mentioned example of ix .19. 31 Contrary to Peyrard,
Heiberg does not admit that Euclid could have provided several proofs for
the same result, which would constitute what I have called above an ‘autho-
rial variation’. We will return to this important topic later. For now, let us say
simply that the criteria of Heiberg are simple. In the case of double proofs,
he retains as the sole, authentic proof that which occurs fi rst in P , whether
it is better than the other or not.
Th e limitations of this edition thus result from the adopted history of the
text and the resulting principles of selection, while the merits of the edition
derive from a more coherent observation of these choices than Peyrard
managed. Another (and not the least) of its merits is that the text as pub-
lished corresponds rather well with something which had existed, namely
manuscript P of the Vatican, 32 whereas the archetypal texts reconstituted
by the modern editors of ancient texts are sometimes nothing more than
fi ctions or philological monsters. What it represents with respect to the
ancient text is more uncertain. Th e incidental remarks of the copyist of P
already suggest a certain contamination between (at least) two branches of
the tradition.
Until the 1970s it was believed that the manuscripts resulting from the
transliteration were faithful copies of ancient models, with the only change
being the replacement of one type of writing with another. Nowadays belief
in this practice is not so sure, and there are even a number of cases in which
it may be frankly doubted. 33 We will see an argument (see below, p. 111)
which casts doubts on the two oldest witnesses of the Elements ( P and B ).
Let us assume that the copyist of P followed what was termed the ‘ancient
edition’, and that he compared the ‘ancient edition’ with the ‘new edition’
only aft er the copying. (Indeed, there is a good probability that this was the
case.) Even so, our faith in the antiquity of the text produced in this way
depends entirely on the confi dence accorded to the history of the text pro-
posed by Heiberg. In particular, the strength of the argument rests on the
validity of the interpretation he proposes for the distinction between P and
Th in connection with the re-edition by Th eon of Alexandria, around 370.
Th is history was accepted by T. L. Heath and J. Murdoch – who have
signifi cantly contributed to its diff usion – and thus by the majority of
specialists. Disconnectedly and periodically challenged, this history was
(^31) See Vitrac 2004: 10–12.
(^32) In a certain number of passages, and more generally for minor variants, Heiberg preserved the
text of the Th eonian family. Cf. the list that he gives in EHS: v, 1, xxxiv–xxxv.
(^33) See Irigoin 2003: 37–53. Th e (very illuminating) example from the Hippocratic corpus is the
object of the article reproduced on pp. 251–69 (original publication 1975).