Archimedes’ writings: through Heiberg’s veil 203
accessible; Archimedes had to be diffi cult. While perfectly explicit and
consistent, the mathematical genius is also remote and diffi cult. Th is, of
course, is no more than guesswork, ascribing to Heiberg motives he may
never have formulated explicitly for himself. I shall not linger on such
possibilities. And, indeed, let us not forget: Heiberg could well be right.
Th ere are probably grounds for saying that Euclid was easier to read than
Archimedes, that on the whole Euclid took more pains to make his text
accessible.
Th e one point I would like to stress, fi nally – and the one which Heiberg
almost inevitably would tend to obscure – is the variety of Archimedes’
writings. Heiberg’s editorial policy is in itself consistent, and it can’t help
refl ecting a single image Heiberg entertained of the texture of Archimedes’
writings. But in truth, the major feature of the corpus is that so many
of its constituent works are unlike the others. Some are extant in Doric,
some in Koine. Is this an artefact of the transmission alone? Perhaps. But
the argument for that is yet to be made. Th e Arenarius stands apart: it is
written in discursive prose. Th e Cattle Problem stands apart – it is written
in poetic form. Th e Method stands apart – it deals with questions of pro-
cedure, putting side by side various approaches. Even Sphere and Cylinder
ii stands apart – it is the only work dedicated to problems alone. Many
works diverge from the imaginary norm of pure geometry. Some works
are heavily invested in numerical values – not only the Measurement
of the Circle , but also the Arenarius and (in part) Spiral Lines , Planes in
Equilibrium i and Quadrature of Parabola (as well as the no longer extant
treatise on semi- regular solids and, likely, the Stomachion ). Some works are
heavily invested in physical considerations, such as Planes in Equilibrium
i – ii , Floating Bodies i – ii and Quadrature of Parabola. Even a book with
the straightforward theme and methods of Sphere and Cylinder i becomes
marked by the very striking format of presentation, with the polygons rep-
resented by series of curved lines (surely one of the most striking features
to arrest the attention of the original treatise – if indeed this convention is
due to Archimedes himself ). Which work by Archimedes remains ‘typical’?
Perhaps Conoids and Spheroids ...
Inside many works, again, Archimedes plays throughout with variety:
with putting side by side the physical and the geometrical, twice, in
Quadrature of Parabola as well as Method ; with putting side by side the
numerical and the geometrical, in Spiral Lines, Planes in Equilibrium,
Quadrature of Parabola, Semi-Regular Solids and Stomachion.
And so, is it so unlikely, fi nally, that Archimedes should, on occasion,
be more explicit, on occasion, more opaque? If the answer is positive, then