202 reviel netz
claim imaginable, and then fi nally develops in full a sequence of mere
arithmetical equivalences. Th is proposition 14 forms a microcosm of
the Method as a whole: its fundamental principle of composition is
sharp diff erence. Heiberg could hardly have guessed this, staring as he
did at the nearly illegible pages of the Palimpsest. Perhaps he should
have been more forthcoming in revealing his ignorance. Perhaps it
would have been best to avoid all those passages translated in Latin
printed in italics, so as to broadcast in all clarity the lacunose nature of
Heiberg’s own reading. But then again, the temptation to reproduce, in
full, the mathematical contents of the Method was irresistible and the
remarkable fact, aft er all, is that Heiberg came so close to achieving this
reproduction. Where he erred, that was in the spirit of the text more
than in its mathematical contents. And so he did reconstruct, mostly,
the mathematical contents of the Method – transforming along the way
the texture of Archimedes’ writings.Th e texture of Archimedes’ writings: summary
We have seen several ways in which Heiberg manipulated the evidence of
the manuscripts, transforming it to produce his text of Archimedes and,
through that transformation, projecting his image of Archimedes. Th e
manuscripts’ diagrams were ignored, producing an image of Archimedes
whose arguments were textually explicit. Th e bracketing of suspected inter-
polations produced an image of Archimedes whose arguments were less
immediately accessible. As for Heiberg’s overall conventions of presentation,
these would serve to make the argument appear more consistent than it
really was – visible most clearly in Heiberg’s reconstruction of the Method.
Th ere, obviously, Archimedes used a wide variety of approaches – which
Heiberg tended to narrow down. Th is drive towards consistency marked
Heiberg’s project as a whole.
All in all, then, Heiberg’s interventions make Archimedes to be textually
explicit, non-accessible and consistent. Now, it is not as if Heiberg, through-
out, adopted this editorial policy. Th e practices adopted for the edition
of Archimedes display Heiberg’s assumptions concerning Archimedes
himself. Th us, Vitrac shows, in his analysis of Heiberg’s edition of Euclid,
that, with the latter, Heiberg’s policies were quite diff erent, emphasizing
transparency – nearly the opposite of those of Archimedes.
Very likely, this editorial policy reveals, therefore, a certain image of
mathematical genius. Heiberg could well make his Euclid transparent and