Th e Elements and uncertainties in Heiberg’s edition 89
of rather easily identifi able textual units, facilitates this work. In the same
way, the formulaic character of Greek geometrical language has been main-
tained in the translations and permits the identifi cation of local variants
which would probably be more diffi cult in a philosophical or medical text.
My sample size is suffi ciently large to propose a typology, although the
qualitative considerations are provisional and clearly depend on the given
range of the analysed corpus. 52 In the absence of critical editions of the
Arabic versions and in accounting for the multitude of recensions, epito-
mes and annotated versions inspired by Euclid’s work, we cannot pretend
to determine with any degree of certainty the extent of the corpus to be
taken into consideration. For the present purposes, I use the various com-
ponents of the direct tradition, the so-called Greco-Latin version 53 a n d
the available information concerning the Arabic translation attributed to
Ishâq ibn Hunayn and revised by Th âbit ibn Qurra, as well as the fragments
attributed to al-Hajjâj in the manuscripts of the Ishâq–Th âbit version, the
Arabo-Latin translations attributed respectively to Adelard of Bath and
Gerard of Cremona. Th is group corresponds to what the specialists of the
Arabic Euclid call the ‘primary transmission’, in order to distinguish it from
the secondary elaborations (recensions, epitomes, ...). 54
I currently work with a list of about 220 structural alterations of which
the principal genres and species appear in Figure 1.2. Th ey relate to well-
defi ned textual units: Defi nition, Postulate, Common Notion, Proposition,
Case, Lemma, Porism, even a collection of such units, particularly when
there is a change in the order of presentation. Th e debate which divided
Klamroth and Heiberg in the 1880s concerned a corpus of this genre, itself
strongly determined by the indications provided in the medieval recen-
sions such as those of Nasîr at-Din at-Tûsî and of the author known as
pseudo-Tûsî.^55
Th e ‘global/local’ distinction is necessary because of the question of the
proofs. It is easy to identify the phenomenon of double proofs. Generally
the second proofs are introduced by an indicator ‘ἄλλως’ (‘in another way’)
(^52) I add that the information which I have gleaned about the medieval Arabic (and Hebrew)
tradition is second-hand and depends on the accessibility of the publication or the goodwill
with which my friends and colleagues have responded to my requests. Particular thanks are
due to S. Brentjes, T. Lévy and A. Djebbar.
(^53) A very literal version, directly translated from Greek into Latin in southern Italy during the
thirteenth century, discovered and studied by J. Murdoch in 1966 and edited by H. L. L. Busard
in 1987.
(^54) See Brentjes 2001: 39–41 and De Young 2004: 313–19. Other information is likewise accessible,
thanks to the Greek or Arabic commentators, as well as through the scholia in Greek and
Arabic manuscripts.
(^55) See Rommevaux, Djebbar and Vitrac 2001: 235–8 and 284–5.