346 reviel netz
components into some kind of coherent unity then would lead to a certain
transformation.
Th e way this applies to Diophantus is obvious. He brings together pre-
viously available problems. He arranges them in a relatively clear order,
ranging from the simple to the complex. He classifi es, creating clear units
of text, for instance the Greek Book vi , all dedicated to right-angled
triangle problems. In the introduction he discusses his way of writing
down the problems, and introduces a special manner of writing for the
purpose.
Th e structuring involves large-scale and small-scale transformations. Th e
large-scale transformation is a product of the arrangement of the disparate
problems in a rational structure. Th e problems oft en become combinatorial
variations on each other, e.g. ii .11–13:- To add the same number to two given numbers, and to make each a square.
- To take away the same number from two given numbers, and to make each of
the remainders a square. - To take away from the same number two given numbers, and to make each of
the remainders a square.
In such cases, it seems clear that Diophantus had used the rational structure
as a guide, actively searching for more problems, bringing completion to
his much more fragmentary sources. Th e huge structure – thirteen books,
of which, in some form or another, ten survive, with perhaps four hundred
problems solved – was built on the basis of such rational, combinatorial
completion.
Th e small-scale transformation involves each and every problem, which
is presented, always, in the form above. It is immediately obvious that, in
this respect, Diophantus consciously strove to imitate elite literate Greek
mathematics though (as suggested by the examples above) this in itself
would not determine the form of his text. Quite simply, there was more
than a single way of producing numerical problems in elite literate Greek
date was defended by Knorr 1993 ). I shall assume such a late date, while realizing of course
the hypothetical nature of the argument: the dating of Diophantus is the fi rst brick
of speculation in the following, speculative edifi ce. I would like to question, though, the very
habit of treating the post quem and the ante quem as defi ning a homogeneous chronological
segment. One’s attitude ought to be much more probabilistic – and should appreciate the fact
that not all centuries are alike. Here are two probabilistic claims:
(1) the fi rst century bce , and the fi rst century ce , both saw less in activity in the exact
sciences; the second century ce , as well as the fi rst half of the fourth century ce , saw more.
(2) Th e e silentio is more and more powerful, the further back in time we go. I think it is
therefore correct to say that Diophantus most likely was active either in the second century
ce or the fi rst half of the fourth century ce.