Archimedes’ writings: through Heiberg’s veil 193
proposition that also calls for a diagram. Codex A also marked this propo-
sition with the marginal numeral A. Heiberg prints the entire sequence i
246–260.24 preceding ‘proposition 1’ as a single paragraphed block of text,
that is the ‘introduction’, followed by the sequence of ‘propositions’ starting
at i 260.25. But clearly Archimedes’ intention was to create a smooth tran-
sition mediated by the passage i 258.19–260.24, which does not fall easily
under either ‘introduction’ or ‘propositions’.
Very similar transitions are seen in SC i , SC ii , QP and PE i , with Heiberg
making diff erent choices: in SC i and SC ii the transitional material is
incorporated into the ‘introduction’; in QP and PE i it is incorporated into
the ‘propositions’. Further, while the fi rst proposition of the Method has a
complex argument that calls for a diagram, Archimedes rounds it off with
a second-order comment that makes it appear rather like part of the ‘intro-
duction’ ( ii 438.16–21). Heiberg, very misleadingly, prints this comment as
if it formed part of proposition 2: clearly Archimedes’ point was to smooth,
once again, the transition from introduction to propositions. If we bear in
mind that the complex interplay of introduction and propositions is typical
of the Arenarius , and that FB ii , PE ii and DC do not possess an intro-
duction at all, we discover that Heiberg’s neat dichotomy of introduction
divided from text is found in SL alone!
Heiberg’s clear articulation of the text into ‘propositions’ falling into
paragraphs tends to obscure, once again, the variety of formats found in
the corpus. Quite oft en, the text relapses into briefer arguments set in a
general language that does not call for a diagram. Heiberg marks such
passages off and heads them as ‘corollaries’ or porisma , but this is done
against the manuscripts’ evidence where, instead, such passages form part
of the unbroken fl ow of the text. Th is happens twenty times in the corpus.
Heiberg systematically introduces the title porisma into the printed text,
noting in the apparatus that the manuscripts ‘omit’ this title! For instance
PE i : Heiberg prints πορισμα α in ii 130.22 and πορισμα β in ii 132.4,
with the following apparatus: 130.22 om. AB Πο D, 132.4 om. AB. Th at is:
one copy of A introduced, in the fi rst case, a marginal mark anticipating
Heiberg’s own intrusion. But the original text had no such headings. Th e
important consequence is that the original text allowed stretches of text,
inside the main fl ow of ‘propositions’, where no detailed, diagrammatic
argument was required – and without segregating such passages by a title
such as ‘corollary’.
Th e variety of the original is wider than that. Th us, for instance, some
propositions have a complex internal structure not neatly captured by the
simple division into general statement and particular proof (such as the