Th e Elements and uncertainties in Heiberg’s edition 117
least compared with each other in order to produce Th âbit’s revision of
Ishâq’s translation. Th ere is no reason for astonishment: these scholars
were not working to provide guidance to modern philologists who
want to establish the history of the text of the Elements. Th ey sought to
procure a complete and stimulating mathematical text. Knowing the
hazards of manuscript transmission, they compared diff erent copies,
and I believe that Th âbit ibn Qurra used other Arabic translations,
probably that of al-Hajjâj, and even some Greek commentaries, in
particular that of Heron of Alexandria, which has some consequences
for the structure of the revised text. At some points, it is more sophis-
ticated than the Greek text of Heiberg. 124 In the Arabo-Latin domain,
the Gerard of Cremona version also proceeds by juxtaposition of dif-
ferent texts, some of which Th âbit had already combined, but also the
alternate proofs that the tradition attributes to al-Hajjâj and which
oft en appears in the Latin of Adelard of Bath.
(6) Th e case of the translation (or translations) of al-Hajjâj is much more
diffi cult to judge because we know it only very incompletely and
indirectly through several citations by copyists of manuscripts of the
Ishâq–Th âbit versions and through the evidence of Tûsî and pseudo-
Tûsî. 125 Virtually all the characteristics that distinguish it – primarily
its thinness and the structure of several families of proofs – appear
in the Arabo-Latin version of Adelard of Bath. 126 Its antiquity and its
thinness make it tempting to ascribe to it a privileged role. Nonetheless,
the evidence from the preface of the Leiden Codex introducing the
commentary of an-Nayrîzî is troubling. 127 Th e principle of amplifi ca-
tion, to which Klamroth (and Knorr) subscribe concerning the textual
development, suppose that no deliberately abridged version has played
a role in the transmission of the text. It is to precisely this phenomenon
of abbreviation that the preface to the second translation (or revision)
of al-Hajjâj makes reference. Th us, I am not sure that this principle,
124 Th is is particularly clear in Books viii – ix , fi rst of all for the alternative proofs proposed
for viii .22–23, then the insertion of the converses to Prop. (Heib.) viii .24–25 and the
simplifi cation of the proof of ix .2, fi nally the addition of the Propositions (Ishâq–Th âbit)
ix .30–31 to simplify the proofs of ix .32–33 (= Heib. ix .30–31), without forgetting the addition
of Porisms (cf. n. 121 ).
125 S e e E n g r o ff 1980 : 20–39. Recently Gregg de Young has discovered an anonymous commentary
relatively rich in references to divergences between the versions of Ishâq–Th âbit and al-Hajjâj.
See de Young, 2002 /2003.
126 Twenty structural divergences are supposed to characterize the version of al-Hajjâj. Of these,
sixteen appear in Adelard. Th e other four from Book ix and the fi rst part of Book x – the lost
portion in Adelard’s translation – appear in the related Latin versions by Herman of Carinthia
and Robert of Chester.
127 See the text and French translation in Djebbar 1996 : 97, 113, partially cited below as n. 142.