192 reviel netz
following them, serving in this way to articulate the writing in a highly
marked form. Following that, Heiberg writes out his text in accordance
with the clear paragraph arrangement dictated by modern conventions,
with the general statement always occupying a separate paragraph. Th e
Byzantine manuscripts followed a somewhat diff erent layout. Numerals
for propositions – where present – are marginal notes that do not break
the sequence of the writing (this articulation is provided, however, by the
diagrams, as a rule positioned at the end of their respective propositions).
Division into paragraphs is less common in Byzantine manuscripts (where
it is performed by spacing inside the line of writing, where the break
is to take place, together with an optional bigger initial in the following
line, positioned outside the main column of writing). Typically, general
statements do not form in this sense a paragraph apart, such division into
paragraphs being reserved for more major divisions in the text – typically
for the very beginning of a proposition or, occasionally, in such major tran-
sitions as the passage from the ‘greater’ to the ‘smaller’ cases in the Method
of Exhaustion (so, for instance, codex C in SL 25, i 96.30). It is likely that
Archimedes’ original papyrus’ rolls were, if anything, less articulated than
that. 26 Not that this impugns Heiberg’s use of paragraphs: modern editions
universally ignore such questions of layout, imposing modern conven-
tions, and even though the layout of the manuscripts, as of Archimedes
himself, did not possess Heiberg’s visible articulation, it is fair to say that
the two divisions – of introduction from main propositions, and of general
statements from proofs – are genuinely part of Archimedes’ style.
However, because Heiberg is committed to a visible layout, he is also
forced to set clear-cut divisions where the original may be less clearly
defi ned.
First, even though the Archimedean text does operate between the
polarities of discursive prose and mathematical proposition, it is not as if
the transition between the two is typically handled as a break in the text.
Rather, Archimedes negotiates the transition in varied ways that make it
much smoother. To take a few examples: following the main introduc-
tory sequence in CS ( i 246–258.18), Archimedes moves on to a passage
( i 258.19–260.24) where several simple claims are either asserted without
argument, or are accompanied by a minimal argument without diagram-
matic labels (e.g. Archimedes explains that when a plane cuts both sides
of a cone, it produces either a circle or an ellipse). Only following that,
at i 260.25, Archimedes moves on to a longer and more complicated26 On early papyrus practices of articulation of text, see Johnson 2000.