Th e Elements and uncertainties in Heiberg’s edition 93
In comparing Heiberg’s text with the text of the Arabo-Latin translations
by Adelard of Bath and by Gerard of Cremona, I have noted (at least) three
textual dichotomies (in decreasing order of importance): 62
Dichotomy 1: Edition Heiberg (υ P ) versus medieval tradition
(existence of 18 Defi nitions, 12 Propositions, 19 Porisms, all the
additional material (!), numerous changes in order, the majority of
substitutions of proofs)
Dichotomy 2 (in Books i – x ): Adelardian tradition versus Gerard of
Cremona translation (al-Hajjâj / Ishâq–Th âbit?) 63
(existence of 16 Defi nitions, 10 Propositions, 2 Porisms, some
changes in order, double proofs in GC)
Dichotomy 3: P versus Th
(existence of 3 Propositions, 2 Porisms, 3 additions, 2 inversions of
Defi nitions, several modifi cations)
To return to certain elements from our fi rst part , the Heiberg edition
is founded on Dichotomy 3. Th e Danish editor refused to account for
Dichotomy 1 demonstrated by Klamroth. Knorr fi nally proposed an inter-
pretation somewhat similar to that of Heiberg. His interpretation was linear
and consisted of two terms (pre-Th eonine/Th eonine), simply replacing P
with the hypothetical Greek archetype which he believed possible to recon-
struct for the medieval tradition. Taking into account the information at
his disposal, Heiberg was not able to identify Dichotomy 2. Knorr appears
to have ignored it, which is at the very least surprising, as he declared
that the Arabo-Latin versions which he used (Adelard and Gerard) were
neither divergent, nor contaminated. Th is break in the indirect tradition
in Books i – x dashes hopes of reconstructing a common archetype for the
indirect medieval tradition. 64 As for the local variants, they number in
the hundreds, probably amounting to 1000–1500 and concerning about
80 per cent of the Propositions in the Greek text. It might be thought that
a single instance of an analogical proof or a simple stylistic intervention in
a Proposition is hardly signifi cant. If examples of this type are disregarded,
70 per cent of the Propositions from the Euclidean treatise nonetheless
(^62) For details, see the three tables given in the Appendix.
(^63) Accounting for the Arabo-Latin versions adds a supplementary diffi culty from my point
of view (to return to the Greek) since it is a doubly indirect tradition. But the structural
divergences which we observe between Adelard of Bath and Gerard of Cremona nearly
always fi nd an explanation in their Arabic precursors, in particular in the diff erences between
al-Hajjâj and Th âbit, as they are described – for right or wrong – by the copyists, commentators
and authors of the recension (for example at-Tûsî).
(^64) It is particularly clear in Book x; see Rommevaux, Djebbar and Vitrac 2001: 252–70.