Archimedes’ writings: through Heiberg’s veil 181
many verbal and stylistic variations on the norm elsewhere. 12 Th e same
goes for Heiberg’s interventions in this text. In ii .236.24, Heiberg brackets
the particle men which is unanswered by the obligatory de ; in ii .258.11 he
brackets the particle eti which seems to be a mere scribal error anticipating
the following preposition epi. Th e case of 222.31, with the words tou kulin-
drou bracketed, is more complex. Th e text as it stands in the manuscript
does not make any sense, as Greek grammar or as mathematics. Heiberg
not only brackets tou kulindrou but also adds in a particle oun and changes
the gender of a relative pronoun. In short, Heiberg’s interventions are philo-
logical rather than mathematical in character; that they are so few is a mark
of Heiberg’s tact as an editor. Of course, Heiberg’s apparatus records many
more variations that Heiberg introduced into the main text and indeed all
three brackets could equally have been relegated to the apparatus alone.
Needless to say, the Arenarius does not thereby obtain a canonical position
for Heiberg’s reading of Archimedes: here, the lack of intervention signals,
paradoxically, a marginal status. What the Arenarius reminds us is that
Heiberg’s exclusions are so closely focused on the proofs-and-diagrams
style. Indeed, there are, I believe, no words bracketed inside the introductions
to Archimedes’ works.
To sum up: Heiberg intervened in Archimedes’ text mostly to exclude
words and passages that, in his view, do not square with what should have
been Archimedes’ style of proof, as judged mostly by the advanced works
extant in Doric.
Heiberg’s practice of excision: close-up on Sphere and Cylinder
Th e mathematics of Archimedes, especially in the more advanced works,
is very diffi cult. Generally speaking, Heiberg’s brackets tend to keep it that
way. Many of the excluded passages take the form of brief explanations
to relatively simple arguments. Th e excluded passages make the text of
Archimedes locally transparent , and this is what Heiberg avoids – in this
way also introducing a certain consistency which is absent from the manu-
scripts’ evidence.
Consider SC i .4. Archimedes constructs a triangle ΘKΛ, with KΘ given
and the angle at Θ right. It is also required that KΛ be equal to a certain line
H. At this point the text comments ( i 16.25): ‘For this is possible, since H is
greater than ΘK.’ Th is comment is bracketed by Heiberg. Th ere seem to be
three reasons for Heiberg’s bracketing.
12 N1999: 199.