348 reviel netz
geometry would be that results should be transferable from one set of
numerical values to any other soluble set, on the analogue of the transfer-
ability of geometrical results from one diagram to another: this would be
the implication of picking a mode of presentation which is so suggestive of
that of elite geometry.
It is also likely that the very exposure to certain quasi-algebraic prac-
tices (basically those of additions or subtractions of terms until one gets
a simple equation of species) as well as the choice of simple parameters
would instil the skills required for the fi nding of solutions with diff erent
numerical values from those found by Diophantus himself, so that the text
of Diophantus, taken as a whole, does teach one how to fi nd solutions in
terms more general than those of the particular numerical terms chosen
for an individual Diophantine solution. 21 Having said that, however, the
fundamental point remains that Diophantus allows his generality, such as
it is, to emerge implicitly and from the totality of his practice. Th ere is no
eff ort made to make the generality of an individual claim explicit and visible
locally. He does not solve the problem of dividing a square number into two
square numbers in terms that are in and of themselves general – which he
could have done by pursuing such problems in general terms.
Why doesn’t he do that? Th ere are three ways of approaching this. First,
readers’ expectations on how generality is to be sustained would have been
informed with their experience in elite Greek geometry. Th ere, generality
is not so much explicitly asserted, as it is implicitly suggested. 22 It is true
that the nature of Greek geometrical practice – based on the survey of a
fi nite range of diagrammatic confi gurations – does not map precisely into
Diophantus’ practice. Greek geometry allows a rigorous, even if an implicit,
form of generality, which Diophantus’ technique does not support. Th is
mismatch, in fact, may serve as partial explanation for the emerging gap in
Diophantus’ generality.
Second, if indeed I am right and Diophantus’ goals were primarily
completion and homogeneity, and that the general statement may have
been introduced in the service of such goals, than our problem is to a large
extent diff used. Diophantus did not provide explicit grounds for his gen-
erality, but this is because he was not exactly looking for them. He did not
introduce general statements for the reason that he was looking for general
solutions. Rather, he introduced general statements because he perceived
such statements to be an obligatory feature of a systematic arrangement22 As argued in N1999: ch. 6 (a comparison also made by Th omaidis 2005 ).21 Th is, if I understand him correctly, is the claim of Th omaidis 2005.