The History of Mathematical Proof in Ancient Traditions

(Elle) #1

Th e Elements and uncertainties in Heiberg’s edition 85


Th e second scenario which might account for the limited but real varia-
tion shown between P and Th satisfi es me more than Knorr’s reconstruction.
We have only two criteria external to the text by which we can understand
the aforementioned re-edition: the glosses ‘of the edition of Th eon (ἐκ τῆς
Θέωνος ἐκδοσεως)’ and the presence or absence of the addition at vi .33. We
have so little information about the history of the text 36 that it is a little too
daring to throw out some part of our information without external support
for the decision. As for the problem discussed here, I do not believe that my
hypotheses change anything regarding the state of the texts that the Greek
manuscripts enable us to establish. It is probably approximately the text as
it circulated around the turn of the third and fourth centuries of our era. Is
it possible to advance from here? With regard to the edition of a minimally
coherent Greek text, I am not sure. However, other sources clarifying the
history of the text are provided to us, thanks to the indirect tradition and,
in this arena, our situation is a little more favourable than the time-frame of
the Klamroth–Heiberg debate.


New contributions to the textual inventory


With regard to the indirect tradition of the quotations by Greek authors, we
have two more valuable sources:



  • Th e Persian commentator an-Nayrîzî has transmitted to us a certain
    number of testimonies about the commentaries of Heron and Simplicius,
    whose original Greek texts are now lost. Some of them provide interesting
    information about the history of the text. 37 Heiberg had taken note of this
    evidence. He had even taken part in the edition of Codex Leidensis 399
    through which the commentary was fi rst known, although this edition
    was produced aft er Heiberg’s edition of the Elements. He gives an analysis
    of these new materials, among other things, in an important 1903 article.

  • In the same vein, he had nothing except a very fragmentary knowledge
    about the commentary on Book x , attributed to Pappus and preserved
    in an Arabic translation by al-Dimashqî, from which Woepcke, around


(^36) In this regard, the indirect medieval tradition, so rich in new textual variants, teaches us
nothing about the history of the text during antiquity, particularly about the existence or not
of several editions of the Elements.
(^37) In the case of Heron, see Brentjes 1997–8: 71–7; in this article Brentjes suggests that other
Arabic authors knew about the commentary by Heron independently of an-Nayrîzî, in
particular Ibn al-Haytham. In Brentjes 2000: 44–7, she shows that it is probably true for
al-Karâbîsî, also. Heron proposed a number of textual emendations, among other things. See
Vitrac 2004: 30–4.

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