Your points are well taken. All that I would add
is that 200 BC Greeks did NOT offer direct proofs in
their axiomatic geometry. Note that Archimedes
and his 'The Method' stated indirect proofs as the
final standard, as Dijkesterhuis details on about
page 129, in his book Archimedes.
That is, moderns like Hardy have based their
views of Greek proofs from idealized positions,
almost Whiggish, ones that were not based on rigorous
historical studies. Hopefully last week's Christie's
auction and sale of a $2,000,000 document will tend to
clear the modern air in the near future on the real
history of Archimedes' The Method.
Until then, again, thank you for a most interesting
and pertinent post.
Regards,
Milo Gardner
Sacramento, Calif.