76 bernard vitrac
In the case of the Elements , the group of sources which constitutes the indi-
rect tradition is rich. First of all, in the case of citations by ancient authors,
the Elements received commentaries on several occasions (namely, by Heron
of Alexandria, Pappus of Alexandria, Proclus of Lycia, Simplicius (?)). 15 Th e
Elements were also used abundantly by the authors of late antiquity. Some
extracts of several of these commentaries are found in the thousands of
marginal annotations contained in the manuscripts of the text. Moreover,
tracing the indirect tradition of the translations, quotations and commen-
taries in languages other than Greek is practically unmanageable, even
when the task is limited to ancient and medieval periods. Consequently, it is
impossible to imagine an exhaustive textual history undertaken by a single
individual.
Th e fi rst task for whoever wants to edit the text will be to limit the
pertinent information, in a way that is not only selective enough to be
operational, but also wide-ranging enough that no essential elements are
left behind. In the matter of editing a Greek text, in Greek, it is reasonable
that the philologists privilege the direct tradition of manuscripts and papyri
for the establishment of the text. Th ey also emphasize the obvious limits of
the diff erent elements of the indirect tradition. Whether the quotations are
in Greek or not, philologists note that the citations were sometimes made
from memory. As for the translations, they introduce into the process of
transmission not only the passage from one language to another in which
the linguistic structures may be somewhat diff erent, but also the prelimi-
nary operation of the comprehension of the text, which is not necessarily
implied for a professional copy. Indeed, there is even something about
which to be happy when the Greek text no longer exists. Hellenists are
generally grateful to the Latin, Syriac, Arabic, Persian, Armenian and
Hebrew translators for having preserved whole fi elds of ancient literature.
In the case of mathematics, the medieval Arabic translations have had great
importance for our knowledge of Apollonius, Diocles, Heron, Menelaus,
Ptolemy and Diophantus, to mention only the best-known cases. Th ese
examples suggest not only that the savants of the Arab world had assidu-
ously sought out Greek manuscripts – indeed, they have borne frequent
witness to this subject – but also that they had some skill in fi nding them
in formerly Hellenized areas. Th e decline of Greek as a scientifi c language
and the ascendancy of Syriac and then Arabic made translation necessary.
Th e possibility is thus foreseen that, in so doing, these translations
had preserved an earlier state of the text than that transmitted by the(^15) Th e fi rst and last are accessible indirectly, thanks to the Persian commentator an-Nayrîzî.
Heron is also cited several times by Proclus.