Archimedes’ writings: through Heiberg’s veil 165
we have some evidence from all three traditions). 2 Th e agreement between A
and C is striking. We can also see that Moerbeke’s Latin translation involved
a considerable transformation of the diagrams he had available to him from
codex A. Th is may serve to explain why, when we don’t have the separate evi-
dence of A and just compare codices B and C, the two appear diff erent: this
is likely to be the infl uence of Moerbeke’s transformation. In short, the evi-
dence suggests that the various early Byzantine manuscripts were probably
identical in their diagrams. Th is is certainly the case for the two independent
early Byzantine manuscripts A and C, for the works SC i , SC ii , SL and DC –
representing the bulk of Archimedes’ extant work in pure geometry.
In all likelihood, such resemblance stems from a close dependence on a
Late Ancient archetype. Whether or not this archetype can be pushed back
to the original publication by Archimedes – whatever that could mean – is
an open question. To the extent that the manuscript evidence displays strik-
ing, original practices, a kind of lectio diffi cilior makes it more likely that it
is an original practice. Th e argument could never be very strong and it is
probably for this cogent reason that Heiberg avoided off ering an edition
of the manuscripts’ diagrams. However, even if the following need not
represent the original form of Archimedes’ works, it certainly represents
one important way in which Archimedes was read for at least some part of
antiquity. In understanding Archimedes’ modern reception, it is helpful to
compare this with the ancient reception to which the manuscripts testify.
In what follows, then, I compare Heiberg’s diagrams with the Late Ancient
archetype reconstructed for the two books on Sphere and Cylinder (con-
centrating on these two books for the reason that I have already completed
their edition). I arrange my comments as three comparisons – three ways in
which Heiberg transformed the original found in the manuscripts.
Heiberg goes metrical
I put side by side the two diagrams for SC i .16 (see Figure 3.1 ). Th e diff er-
ences as regards the triangle – in fact, a ‘fl at’ view of a cone – are immaterial.
Neither do I emphasize at the moment the diff erences in overall layout (it is
clear that Heiberg saves more on space, aiming at a more economic produc-
tion; this may have been imposed by the press). Th e major diff erence has to
do with the nature of the circles Λ, Θ and K. Heiberg has them concentric,
(^2) Here and in what follows I use a system of abbreviation of the titles of works by Archimedes, as
follows: SC ( Sphere and Cylinder ), DC ( Measurement of the Circle ), CS ( Conoids and Spheroids ),
SL ( Spiral Lines ), PE ( Planes in Equilibrium ), Aren. ( Arenarius ), QP ( Quadrature of Parabola ),
FB ( Floating Bodies ), Meth. ( Method ), Stom. ( Stomachion ), Bov. ( Cattle Problem ).