336 reviel netz
‘number’. It is only the second number – the one counted as ‘1’ - which
serves as an unknown in this problem. Only this, then, by Diophantus’
explicit defi nition, counts as a ς; appropriately, then, Tannery prints the
fi rst ‘number’ as a fully spelled-out word and the second as a symbol. But
as the reader may guess by now, there are many cases in the manuscripts
where ‘number’ of the fi rst type is abbreviated, as well, using Diophantus’
symbol ς. 8 Th us the symbol is understood, at least by Diophantus’ scribes,
to range not across a semantic range (the unknown number), but across a
phonological or orthographic range (the representation of the sound, or
trace, ‘arithm-’). It would indeed be surprising if it were otherwise, given
that scribal symbolism, as a system, was understood in such phonological
or orthographic terms.
Th e text in example (1) above followed closely (with some variation of
orthography) Tannery’s edition. It is clearly punctuated and spaced (as it
is not in the manuscripts, not even the Renaissance ones). It has accents
and aspiration marks (like the Renaissance manuscripts, but most probably
unlike Diophantus’ text in late antiquity). It also sharply demarcates the
two kinds of writing: explicit and markedly Diophantine symbols, which,
in the proof itself, Tannery systematically presents in abbreviated form, on
the one hand; and standard scribal abbreviations, which Tannery systemati-
cally resolves (as, indeed, philologers invariably do).
As Tannery himself recognized, his systematization of the symbolism
was not based on manuscript evidence. I shall not say anything more on
the unmarked symbolism, such as the case markings, whose usage indeed
diff ers (as one expects) from one manuscript to another. Th ey should
be mentioned, so that we keep in mind the full context of Diophantus’
symbols. But even more important is that Diophantus’ own marked
symbolism is not systematically used in the manuscripts. Th e symbols
described above are oft en interchanged with fully written words. Th is is
as much as can be expected. Both Δ υ and Δυναμις stand for exactly the
same thing – the sound pattern or trace /dunamis/ – and so there is no
essential reason to use one and not the other. Th us a free interchangeability
is predicted.
Notice fi rst the form of example (1) in all the Paris manuscripts,
comparing the (translated) form of Tannery’s text to that of the manuscripts:(^8) Th is was pointed out already by Nesselmann 1842 : 300–1. Indeed, my impression is that
awareness of such quirks of Diophantus’ text was more widespread prior to Tannery: following
the acceptance of his edition, knowledge of the manuscripts (as well as of the early printed
editions – whose practices, I note in passing, are comparable to those of the manuscripts)
became less common among scholars of Diophantus’ mathematics.