Th e Elements and uncertainties in Heiberg’s edition 79
unavoidable variations between manuscripts. Klamroth further declared
that the Arabic tradition was characterized by a particular ‘thinness’ and
several structural alterations in presentation (specifi cally, in modifi cation
of order, division or regrouping). 23Th e history of the text of the Elements in antiquity
Let us consider now the history of the text of the Elements. Starting with
these inventories, let us examine the interpretation of the diff erent pieces of
evidence which our two scholars proposed. Th e interpretation of Klamroth
is simple: the ‘thinness’ of the Arabic (and Arabo-Latin) tradition is an
indication of its greater purity. Th e textual destiny of the Elements has been
the amplifi cation of its contents, particularly for pedagogical reasons. Th e
medieval evidence about the translators’ methods and the context in which
they worked shows that the medieval translators had a real concern about
the completeness of translated texts. Th e gaps (with respect to the Greek
text) cannot be ascribed to negligence on the part of these translators.
Th e additions are interpolations in the Greek tradition. Consequently, for
Klamroth, it is necessary to take the indirect tradition into account, not
only for the history of the text, but also in the establishment of the text. 24
Th e history of the text proposed by Heiberg is completely diff erent. Th is
history is clearly dependent on the way in which the transmission of the
Elements was conceptualized by Hellenists since the Renaissance, particu-
larly since the Latin translation produced by Zamberti, taken directly from
the Greek and published at Venice in 1505. 25 Th e presentation of this last
work raised two essential questions:
(1) For Zamberti, the ‘return’ to the Greek text was a remedy for the
abuses to which the text had been subjected in medieval editions. Th e
focus of his concern was the then highly renowned Latin recension of
Campanus. Th is edition had just been printed at Venice in 1482 and
was itself composed from an Arabo-Latin translation. A debate arose
about the (linguistic and mathematical) competence of the translators
and the quality of the models which would establish for quite some
time the idea that the indirect medieval tradition could be discarded.
(2) Zamberti presented his Elements as if the defi nitions and the state-
ments of the propositions were due to Euclid, while the proofs were
(^23) He thus identifi ed a well-established line of demarcation between the direct tradition and the
indirect tradition. I have named this distinction ‘dichotomy 1’ (see Appendix, Table 1).
(^24) Generally, this position has been taken up by Knorr in his powerful 1996 study.
(^25) See Weissenborn 1882.