78 bernard vitrac
for the establishment of his edition. A debate – but not to say a polemic 18 –
between the two scholars followed on the subject of the obligation of
recognizing the value of the indirect tradition from the medieval era.
At any rate, Heiberg knew that there had been at least two Arabic
translations, that of al-Hajjâj (produced before 805 and modifi ed by the
author for the Kalif al-Ma’mun between 813 and 833), then that of Ishâq ibn
Hunayn (†910–11) revised by Th âbit ibn Qurra (†901). Klamroth believed
himself to have the al-Hajjâj version for Books i – vi and xi – xiii and that
of Ishâq for Books i – x. Th e Hebrew and Arabo-Latin translations likewise
began to be studied. Heiberg also knew (especially) about several recensions
(falsely) attributed to Nâsir ad-Dîn at-Tûsî (1201–73) and that of Campanus
(†1296).^19
From the comparison of Greek manuscripts produced by Heiberg and
from the statement that Klamroth had furnished concerning the Arabic
Euclid emerges an assessment of the situation which I will describe roughly
in the following way:- For the ‘direct’ Greek tradition, it is necessary to distinguish two versions
of the text in the collection of the thirteen Books of the Elements , and
even three for xi .36– xii .17. A simple structural comparison of the
manuscripts is suffi cient to establish this point. Th e two divergent ver-
sions of the complete text 20 are represented on the one hand by the man-
uscript Va t i c a n u s g r. 190 ( P ) – the oldest complete manuscript – and, on
the other, by the strongly connected BFVpqS manuscripts,^21 as well as
the Bologna manuscript (denoted as b ) , 22 for the whole of the text, save
the section xi .36– xii .17. In these twenty-one Propositions, the Bologna
manuscript presents a structure completely diff erent from that of P and
BFVpqS , which on the whole are less divergent from each other than
they are with respect to b. - For the indirect tradition of the Arabic translations, the report of
Klamroth was that there was a considerable diff erence between the Greek
and Arabic traditions. Th is diff erence went beyond the scope of the
(^18) I allow myself to recall the fi rst part of Rommevaux, Djebbar and Vitrac 2001: 227–33 and
235–44, in which I analyse the arguments of the two parties.
(^19) For a synthesized presentation of the Arabic, Arabo-Latin and Arabo-Hebrew traditions as
they are known today, see Brentjes 2001a: 39–51 and De Young 2004: 313–23.
(^20) Th is is what I have termed ‘dichotomy 3’ (see Appendix, Table 3).
(^21) Codex Bodleianus, D’Orville, 301 (B), Codex Florentinus, Bibl. Laurentienne, xxviii, 3 (F),
Codex Vindobonensis, philos. Gr. 103 (V); Codex Parisinus gr. 2466 (p); Codex Parisinus gr.
2344 (q); Codex Scolariensis gr. 221, F, iii, 5 (S). Th e sigla used here are the same as those used
by Heiberg.
(^22) Codex Bononiensis, Bibl. communale, n°. 18–19.