118 bernard vitrac
which functions rather well in the case of dichotomy 1, also applies to
dichotomy 2. 128
(7) Moreover, the case of the stereometric books, on which Knorr founded
his argument, seems problematic to me. Th e Arabo-Latin translations
are particularly close to each other in these books. Knorr relied on
this point to deduce that the same thing would happen to their Arabic
models and thus also the versions of al-Hajjâj and Ishâq–Th âbit. 129 W h a t
I have called dichotomy 2 hardly occurs there at all. 130 However, there
are, in two manuscripts of this last version (Copenhagen, Mehrens 81;
Istanbul, Fâtih 3439), glosses indicating that Book x is the last which
Ishâq has translated and that what follows is ‘Hajjajian’. Th e author
of the gloss to the manuscript in Copenhagen specifi es exactly that it
‘comes from the second translation of al-Hajjâj’, i.e., the abridgement. 131
From this reference, Klamroth deduced that Ishâq had translated only
Books i – x and that Th âbit had taken xi – xiii from the translation of
al-Hajjâj. Th is thesis has been challenged by Engroff and I obviously
have no expertise on this point, but it seems to me that the stereomet-
ric books undeniably constitute a particular case. 132 Even then, at-Tûsî
had remarked that there is no structural divergence between what he
believed to be the two versions of the stereometric books. 133 I would
add that there is not, to my knowledge, any mention of the sort ‘Th âbit
says ...’ beyond Book x. 134
A fi nal element must be taken into account. In Proposition xiii .11
it is established that the side of a pentagon inscribed in a circle with
a rational diameter is irrational, of the ‘minor’ type. Th us, in Book
x , ‘ἄλογος’ is translated as ‘asamm’ (‘deaf ’) by al-Hajjâj and ‘ghayr
muntaq’ (‘un-expressible’) by Ishâq–Th âbit. Th e divergence appears,
for example, between Avicenna and the manuscript Petersburg 2145
on the one hand and the other Ishâq–Th âbit manuscripts on the other128 It seems to me that Brentjes equally admits the idea that the so-called al-Hajjâj version No. 2
represents an improved and abridged re-edition. See Brentjes 1996 : 221–2.
129 See Knorr 1996 : 259–60.
130 See Table 2 of the Appendix.
131 S e e E n g r o ff 1980 : 9.
132 S e e E n g r o ff 1980 : 9–10, 12–13. Let us add that at the end of Book xi in the manuscript Tehran
Malik 3586, a gloss indicates that Th âbit ibn Qurra had revised only Books i – x and that Books
xi , xii and xiii are Hajjajian! See Brentjes 2000 : 53.
133 See Rommevaux, Djebbar and Vitrac 2001 : 275, n. 184.
134 In the anonymous commentary cited above at n. 125 , the references relative to the divergences
between the versions of Ishâq–Th âbit and al-Hajjâj stop aft er the fi rst third of Book x. Th is
observation is well explained in the line of the gloss inserted in the manuscript Tehran Malik
3586 (cf. above, n. 132 ).