Archimedes’ writings: through Heiberg’s veil 173
indeed ‘correct’; the manuscripts’ smaller A is in a sense ‘false’. 8 Th e manu-
scripts agree with Heiberg, however, in the arrangement of the line seg-
ments, all in keeping with the practice described above (pp. 167–8).
Qualitatively, Heiberg represents the propositions’ requirement – of a
4 n -sided regular polygon circumscribed and inscribed about a circle – by
two octagons. Th e manuscripts, instead, have a system made of two nested
sequences of curved lines, 12 outside and 12 inside. Th e visual eff ect could
not have been more diff erent and here we see the manuscripts’ diagrams
becoming markedly non-iconic. A sequence of 12 curved lines, each nearly
a semicircle, does not make the visual impression of a polygon.
Th e manuscripts, in this case, have a very good reason to choose their
non-iconic system of representation. As we can see from Heiberg’s diagram,
it is diffi cult to make the visual resolution between such a polygon and a
ΘΓB Z
AE HΛAEΘHBΔΓZHeiberg Archimedes (reconstruction)Figure 3.5 Heiberg’s diagram for Sphere and Cylinder i.33 and the reconstruction of
Archimedes’ diagram.
(^8) Incidentally, note that I did not count such false planar inequalities in my treatment of
the non-metrical character of the manuscripts’ diagrams. My survey focused on the (very
common) case where homogeneous objects are put side by side – typically unmarked circles
or lines. I did not look into the case of heterogeneous objects, such as the simple circle A
alongside the more complex main circle in i .33.