The History of Mathematical Proof in Ancient Traditions

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of Koine anywhere in the manuscript tradition of ‘Doric treatises’ – a pres-
ence which is oft en considerable, even preponderant – is taken by Heiberg
to represent no more than the failure of scribes whose Doric may not have
not have been up to Archimedes’ text. I shall return to discuss all of this in
considering the global texture of Archimedes. What is clear, however, is
that Heiberg’s initial decision – whether or not to treat a treatise as ‘Doric’ –
had consequences at the local level. Understandably enough, Heiberg felt
less compelled to preserve the text of the ‘Koine treatises’, considering them
the product of some late re-edition, as opposed to Archimedes’ pristine
words preserved in the Doric. Th us the ‘Doric works’ come to serve as the
benchmark against which the verbal texture of Archimedes as a whole is
to be judged. Th is is comparable to the ‘Eutocius’ eff ect and indeed may
be related to it. (Was the transition to Koine related to the presence of
Eutocius’ commentaries?)

Palimpsest
Since the text of the Method is printed by Heiberg in its original Koine, we
would expect him to bracket its text more extensively. As I will point out in
the next section, the Method provides enough textual diffi culties to allow
for such editorial intervention. In fact, Heiberg leaves the text of the Method
almost as it is. Th e reason must be, I believe, what we may call a purely
sociological or even psychological factor. Th e text of the Method is recov-
ered from the Palimpsest, through Heiberg’s major palaeographic tour de
force. In sociological terms, Heiberg has already displayed his professional
skill by his very recovery of the text and is therefore less under pressure to
scrutinize it so as to display his professionalism. In psychological terms, I
suspect Heiberg must have become attached to the words he did manage to
read – it would be a pity to go through all the trouble just so as to discover
some late gloss! (A reader of the Palimpsest myself, I am all too familiar
with this urge.) For whatever reason, the fact is that the texts recovered
from the Palimpsest are among those Heiberg trusts the most. Since these
also happen to be among the more advanced works by Archimedes (in par-
ticular FB ii as well as the Method ) this has the tendency of confi rming the
role of the advanced works as paradigmatic.

Arenarius
Th e Arenarius is an outsider in the Archimedean corpus: written mostly in
discursive prose rather than in the style of proofs and diagrams, it presents
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