Th e Elements and uncertainties in Heiberg’s edition 77
manuscripts elaborated in the Byzantine world. Consequently, important
decisions must be made about instances in which the medieval translations
show important textual divergences from the version of the same work pre-
served in Greek. As we will see, it is exactly this situation which occurs in
the case of the Elements of Euclid.
In the case of such divergences, at least two explanations may be
imagined:
(1) Th e medieval translators took great liberties with the text, and they did
not hesitate to adapt it to their own ends.
(2) Th eir versions were based on Greek models appreciably diff erent from
those which we know. Th us, we can imagine that these models were
(i) more authentic, or, (ii) on the contrary, more corrupt, than our
manuscripts.
In either case, it will be necessary to make an account of the history of the
text, to establish the innovative informality or rigorous fi delity of the trans-
lators, to account for the methods and the context of the transmission. It is
clear that, within the framework of hypotheses 1 or 2(ii), trans lations will
not be taken into account in the establishment of the text. But if we prove
that the translators scrupulously respected their models (non 1), which
were less corrupted (2(i)) – let us remain realistic, though – what then?
Th e textual inventory in the case of the Elements
In order to produce his critical edition (1883–8), Heiberg had (partially)
collated about twenty manuscripts. He continued this task for fi ft een years
aft er the publication of the aforementioned edition, extending the scope
to nearly thirty other manuscripts. He compared his edition with papyrus
fragments, as they were discovered. 16 In order to establish his text, he
used seven of the eight manuscripts from before the thirteenth century.
He systematically explored the indirect tradition of quotations by Greek
authors and the tradition of fragments of ancient Latin translation. As for
the medieval versions, they were not particularly well known. Heiberg used
several previous works and, as far as the phase of Arabic translations of the
ninth century was concerned, he accepted the description published by
M. Klamroth in 1881, 17 at which time he inventoried the materials useful
(^16) See Heiberg 1885 and Heiberg 1903.
(^17) At the time when he edited the chapter devoted to the medieval Arabic history of the text of
the Elements in Heiberg 1882, he seems not to know Klamroth 1881, which he later criticized
in his 1884 article.