200 reviel netz
over in Heiberg’s reconstruction though, once again, let this not be
construed as a criticism of Heiberg: for, once again, there was no way
for him to guess how diff erent Archimedes’ construction here was from
that of Heiberg’s models in CS.
(3) A fi nal example is from proposition 6. Here Archimedes determines
the centre of gravity of a hemisphere – as it appears from the beginning
of the proposition, the relatively legible verso side of fo. 163. Heiberg
thus knew what this proposition was about. Th e text then moves on to
the recto side of fo. 163, which was barely legible to Heiberg, fo. 170 –
mostly illegible in 1906 and one of the three leaves to have disappeared
since – and the recto of 157, completely unread by Heiberg. As men-
tioned, we have meanwhile lost fo. 170 but, at the same time, through
modern technologies, we have recovered practically the entire text of
fos. 163 (recto) and 157 (recto) As a result, we now know that Heiberg’s
reconstruction of the parts he could not read was wrong.
Heiberg’s modus operandi here was straightforward. While propos-
ition 6 was mostly illegible, proposition 9 was mostly easy to read,
especially in the well preserved (then) fos. 166–7 and 48–41. Th is
proposition 9 dealt with fi nding the centre of gravity of any segment of
the sphere, i.e. proposition 6 can be seen as a special case of proposi-
tion 9. What Heiberg did, then, was to reconstruct proposition 6 on
the basis of proposition 9. In proposition 9, Archimedes constructs
an auxiliary cylinder MN, whose various centres of gravity balance
with certain cones related to the segments of the sphere. Th is cylinder
is then imported by Heiberg into proposition 6 itself. But there is no
need of such an auxiliary construction in proposition 6. Indeed, the
fi nding of the centre of gravity of a hemisphere is much simpler than
that of fi nding the centre of gravity of a general segment (which is not
all that surprising as this happens oft en: a special case may have prop-
erties that make it easier to accomplish). Th e position of the centre of
gravity along the axis is found, in an elegant manner, by considering
just the cone which is already contained by the hemisphere. Heiberg’s
reconstruction of proposition 6 made it appear as if it were a precise
copy of proposition 9, merely plugging in the special properties of the
hemisphere. But it appears that Archimedes took two diff erent routes,
a more direct and elegant one for fi nding the centre of gravity of the
hemisphere, and an indirect one for fi nding the centre of gravity of a
general segment.
Once again, we can hardly blame Heiberg. He played it safe,
reconstructing a passage diffi cult to read on the basis of a closely