The History of Mathematical Proof in Ancient Traditions

(Elle) #1

Th e Elements and uncertainties in Heiberg’s edition 81


site was the case for Proposition xi .38 vulgo. Heiberg considered that the
manuscript – which he would call P in homage to Peyrard – had been pro-
duced beginning with at least two models, one of which was pre-Th eonian,
and the other was Th eonian. His edition was thus founded on the compari-
son of P with Th and on an examination of the total or partial agreement
or disagreement between the two families. 29 From there, he claimed he
had determined the editorial actions of Th eon of Alexandria, and passed
severe judgement on the changes. Th eon’s re-edition of the Elements did not
compare favourably with the editions of the great poetical texts produced
by the Alexandrian philologists of the second and third centuries before the
modern era. 30
If we return to the terms of our previous line of reasoning and if
we accept this history of the text, we ought to distinguish two textual
archetypal manuscripts: the fi rst representing the re-edition of Th eon and
realized in the 370s, and the second corresponding to the pre-Th eonine
model called P. However, the alterations which Th eon is supposed to have
eff ected on the text, as deduced by a comparison with the manuscript P , are
so limited that with a few exceptions (which are listed in the Appendices),
Heiberg believed he could combine the two versions in one text with a
single apparatus criticus.
For the divergent Greek text ( b xi .36– xii .17), his solution was somewhat
diff erent. It seems that the discovery of this manuscript must be attributed
to Heiberg in the context of the previously mentioned debate. In an 1884
article, he presented this new Greek evidence, taking the opportunity
to respond to the arguments presented by Klamroth. Th e reason for his
approach was that this ‘dissenting’ Greek text and the Arabic translations
are incontestably related in this portion of the text. Precisely this incom-
plete but incontestable structural agreement in opposition to the tradition
in P + Th constitutes the principal argument in the article by W. Knorr.
However, noting that the text of b , copied in the eleventh century and
also Th eonine, is particularly defi cient in section xi .36– xii .17, Heiberg
introduced into the history of the text a Byzantine redactor, the author
of an abridged version of the Elements , in order to explain the diff erence.
From this abbreviated work was derived b xi .36– xii .17 and the models
used by the Arabic translators. Th e consequences for the edition of the text
were clear. Aside from some specifi c references to the Latin recension of
Campanus, the indirect medieval tradition which had been connected from


(^29) See EHS: v, 1, xxv–xxxvi.
(^30) lviii. Th e comparison is irrelevant: see Rommevaux, Djebbar and Vitrac 2001: 246–7.

Free download pdf