Archimedes’ writings: through Heiberg’s veil 183
Heiberg, for reasons that will be made clear immediately). Why should the
text be fuller here than in the preceding proposition? Consistency, there-
fore, requires an excision.
I now move to the third reason for Heiberg’s bracketing. To understand
it, let us note the following: the received text for Archimedes’ proposi-
tions 3 and 4 seems to open a strange gap between propositions 3 and 4.
Why would Archimedes off er no more than a brief ‘this is possible’ claim
in proposition 3, expanding it in proposition 4? If anything, the opposite
- going from a more spelled-out expression to a briefer one – would be
more natural. On the other hand, the entire picture makes perfect sense if
we pursue the following hypothesis. Now, the text of Eutocius contains a
commentary to proposition 3, starting with the following words: ‘And let
[the construction be made]. For this is possible, with KL being produced
etc .’ ( iii 18.24–5). Let us assume that Archimedes’ text had none of the
backwards-looking argument, and that some late reader has taken Eutocius’
commentary, fi rst inserting the words ‘for this is possible’ from Eutocius’
commentary into the text of proposition 3, then using Eutocius as a kind
of crib from which to insert a very brief backwards-looking argument into
proposition 4 (for which there is no commentary by Eutocius).
We see how the various factors – the presence of Eutocius’ commentary,
the elementary nature of the claims made, the use of a backwards-looking
argument, textual inconsistency – all come together to inform Heiberg’s
considerations.
Was Heiberg right? I tend to believe he was, at least in part. Th is, for the
following reason. Either we take the words ‘for this is possible’ in proposition
3 to represent Eutocius’ original words, inserted into the text of Archimedes;
or we take them as Archimedes’ original words, quoted by Eutocius as part
of his commentary. Now, the word order of those words is dunaton gar touto.
Th is word order is natural as an anticipation of the genitive absolute used
by Eutocius in his commentary; inside Archimedes’ full phrase, the word
order expected would more likely be touto gar dunaton. Th e excision in
proposition 3 therefore seems likely. And if so, it becomes somewhat more
likely that the words in proposition 4, too, are due to some late reader. But
then again, perhaps Archimedes’ text was strangely inconsistent, off ering no
argument in proposition 3 but some minimal argument in proposition 4?
Obviously, such questions can be answered only based on some overarching
argument concerning Archimedes’ style, an argument which would have to
be derived – circularly – from the established text of Archimedes.
In some cases, and in particular in the longer passages, Heiberg’s exci-
sions seem very reasonable. One of the clearest cases is SC i .13 ( i 56.10–24).