Archimedes’ writings: through Heiberg’s veil 187
‘top fi ve Archimedean geometrical rolls’, ‘top four Archimedean physical
rolls’, perhaps representing a previous arrangement of rolls by baskets,
perhaps of some majuscule codices with only four to fi ve works each. 15 I n
each sequence, the internal order is roughly from the simpler to the more
complex.
It so happens that the works preserved via traditions other than codex
A tend to be less focused on pure geometry. Th ree of the works pre-
served via C – FB i , FB ii , Meth. – have a marked ‘physical’ character. Th e
Stomachion , also preserved via C, may be a unique study in geometrical
combinatorics. 16 And while the Book of Lemmas does touch on pure
geometry, the Cattle Problem is an arithmetical work. Th e fragments,
fi nally, refer to such diverse topics as astronomy, optics or the arithmetico-
geometrical study of semi-regular solids reported by Pappus.^17 I n s h o r t ,
the emphasis on pure geometry – very natural based on codex A alone – is
less faithful to the corpus as a whole as recognized today. Or indeed as
recognized by some other past traditions. For the order of codex C was
distinct:
PE i (?) 18 – PE ii – FB i – FB ii – Meth. – SL – SC i – SC ii – DC – Stom.
Th is has fi ve works referring to the physical world (PE i – ii , FB i – ii ,
Method ) followed by fi ve works of a non-physical character (SL, SC i – ii ,
DC, Stomachion ). Once again, the origin in some earlier arrangement
is likely, and the main classifi catory principle is the same – referring, or
failing to refer, to an outside physical reality. Th e striking diff erence is that
codex C chose to position the physical works prior to the non-physical
ones.
At issue is a fundamental question regarding Archimedes’ scientifi c
character. Was he primarily a pure geometer, who indulged in some
exercises of a more physical or non-geometrical character? Or was he
primarily an author of ‘mixed’ works, so that the more purely geometrical
works – such as Sphere and Cylinder – should be seen as no more than
one further option in the spectrum of possible Archimedean variations?
A very diff erent Archimedes would emerge if we were to order his works,
say, as follows:
15 Th ese two options, of course, do not rule each other out. See Blanchard 1989 for some
suggestive comparisons.
16 Netz et al. 2004.
17 Hultsch 1876 : 350–8.
18 Th e beginning of the Archimedes portion of the Palimpsest appears to be lost. Th e text begins
towards the end of PE ii. Th ere could be works prior to PE i , or the manuscript could start with
PE ii only. Either option, however, is less likely than that the manuscript started with PE i.