The History of Mathematical Proof in Ancient Traditions

(Elle) #1

122 bernard vitrac


diagrams, saut du même au même , and even, as it seems to me, faults
in reading the uncial script. Manuscript b could thus be the result of
a new transliteration, being more faulty since it was further removed
from the ninth century, and produced (for reasons which elude us) at
the same time as the copy, in the eleventh century, of the Bologna man-
uscript from a model which was either truly ancient (the hypothesis
of Knorr) or proceeding from another archetype, such as an abridged
version of the ‘Aigeias’ type. Here, I call upon the possibility of an
ancient model, whereas Heiberg imagined a Byzantine recension.

Whatever the case may have been, I do not believe that this really changes
the attitude that the editor of the Greek text may have adopted toward it. Th e
appeal to b xi .36– xii .17 may prove useful for removing some cases of textual
divergences between P and Th , in the aforementioned portion. However,
adopting these readings would probably create a philological monster which
never existed. Perhaps it can yet be used to improve the edition of a similar
Arabic version. Knorr wanted to adopt the text of b , rather than what he
called ‘the wrong text’ of Heiberg, because he hoped that a comparison of
the primary Arabic translations would permit the reconstitution of a Greek
archetype of comparable antiquity for the remainder of the treatise. Th is
reconstitution is impossible, at least for the present state of our knowledge.
Th erefore, the conception of a new critical edition of the Greek text
seems useless to me for the moment. Th e critical editions of the various
identifi ed Arabic, Arabo-Latin and Arabo-Hebrew versions would be pref-
erable. It would be necessary to produce an ‘instruction manual’ for the
reader to navigate these versions according to the problem, the time period,
the language of culture, even the Euclid available to (another) interested
author. Such a manual would be especially necessary in the cases of double
proofs or substitutions of proofs, cases which the indirect tradition has
considerably enriched.
Th is necessity has long been perceived by the historians of the medieval
and modern periods. Undoubtedly, the Hellenist would also admit the same
necessity. Th e movement to ‘return’ to the original which inspired the work
of the philologists of the nineteenth century seems to need a break. A less
partial knowledge of the indirect tradition provides us not only with much
richer information at a local level, but also with more uncertainty about its
ancient components. Th us stripped of our (false) certainties, we may feel a
little frustrated, but the hope remains that new discoveries of ancient papyri,
manuscripts of medieval translations of Euclid or of its commentators
will allow us to move forward.
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