We don't know much about Theodorus, either, but we do know a bit more than
we do about Theaetetus, and what little we do know doesn't match him up
very well with material in Elements Book X. (But to argue that properly
might take a bit of time and paper. Can anyone give any good references?)
Then, what is _The Theaetetus_ about? It may not really be about
mathematics - it could well be about 'epistemological problems', as you
say - but if that is the case, then it is strange that it contains this
chronologically first, extended, detailed, and correct (except perhaps for
...), discussion of incommensurability.
When you say 'induction', do you mean our way of constructing inductive
proofs? I do think that the Greeks could and may have produced such kinds
of arguments, but not one around this passage in The Theaetetus. What would
they have been proving here? You need some simpler and clearer case than
that to get things across, say something like the result on
side-and-diameter numbers, that
D^2 - 2 S^2 = 2 s^2 - d^2 = 1 .
Finally, why is Root 17 notorious? Is there any other reason outside this
dialogue and perhaps those who comment on it?
I've been putting this reply together rather quickly, and there may be
obvious mistakes and omissions in it!
Best wishes
David Fowler