196 reviel netz
here we can test Heiberg’s judgement. Heiberg’s decisions elsewhere – that
this or that was by Archimedes himself, this or that was by an interpola-
tor – will probably never be verifi ed or refuted. But whenever we can now
read passages of the Palimpsest that were illegible to Heiberg, we thereby
test a conjecture. Th e issue of course is not to see how good Heiberg was
as a philologer. He was a superb one and, indeed, the new readings of the
Palimpsest oft en corroborate Heiberg’s guesses to the letter. I shall now con-
centrate, however, on three false guesses – which together form a systematic
whole, characteristic of Heiberg’s overall approach to the text of Archimedes.
Th is is also a good example of the enormous sway Heiberg’s edition had
over Archimedes’ destiny through the twentieth century. Heiberg’s edition
was careful and prudent: pointed brackets surrounding passages that he
fully guessed, dots to mark lacunae that he could not read at all (oft en
with remarks in the apparatus asserting the length of such lacunae), dots
underneath doubtful characters. It is true that today we fi nd that a number
of characters Heiberg printed with confi dence were wrong, but this is a
natural phenomenon in a palimpsest where the overlaying text occasion-
ally creates the illusion of false characters. All of this was accompanied by
a Latin translation – as was Heiberg’s practice elsewhere – where doubtful
passages were carefully marked by being printed in italics. In short, any
careful reader could tell which part of the text was Heiberg’s, and which
was Archimedes’. And yet, Heiberg’s infl uence was such that all later editors,
translators and readers operated, as it were, on the basis of Heiberg’s Latin
translation, largely speaking ignoring the diff erence between the Latin
printed in Roman characters (which Heiberg read confi dently) and the
Latin printed in italics (which Heiberg merely guessed or supplied). Here,
more than anywhere else, Heiberg’s text supplanted that of Archimedes.
Th is had real consequences, subtle but consistent – so as to change the
overall texture of the treatise.(1) Th e fi rst case is the most clear-cut. We now recognize Method propo-
sition 14 (to follow Heiberg’s misleading numerals) as one of the
most important proofs ever written by Archimedes, but this is on the
strength of a new reading, illegible to Heiberg. As read by Heiberg, this
proposition is a mere variation on themes developed elsewhere in the
Method , of little deep value.
Th e Method typically operates by the combination of two principles:
a method of indivisibles (conceiving an n +1-dimensional object as
constituted by a continuity of n -dimensional objects), and the appli-
cation of results from geometrical mechanics for the derivation of