194 reviel netz
analysis-and-synthesis pairs typical of SC ii , as well as the extraordinar-
ily complex internal structures – punctuated by several diagrams – of FB
ii .8–10). Other propositions do not even display this simple division: for
instance, several key propositions of SC i , starting with 23, take the form
of a ‘thought experiment’ where a certain operation is carried out followed
by an observation. Such propositions do not call for a general statement.
Further, many of the propositions of QP do not have a general statement
and start instead directly with diagrammatic labels. Now, Heiberg does
report correctly the contents of such deviant propositions, but his overall
system of articulating the text by explicit numerals tends to force the read-
ings of all propositions into a single mould. More, indeed, can be said for
the case of QP. Th e manuscripts do mark numerals for the fi rst four propo-
sitions (the fi rst three of which, however, defy easy counting, as they form
the transitional material from introduction to propositions). Th en, from
proposition 5 onwards, no numerals are present. Heiberg dutifully notes
this fact but in a misleading fashion (analogous to his treatment of the title
‘corollary’): he goes on printing the numerals, noting in the critical appara-
tus to proposition 5 that from this point onwards the numerals are ‘omitted’
by the manuscripts.
Th is is not a unique case: the manuscripts for DC and Method never
contain numerals for proposition numbering; Heiberg introduces the num-
bering and then makes the apparatus report their ‘omission’.
A similar pattern can be seen inside the introductory material. Th ere,
Archimedes oft en includes material of substantive axiomatic import –
certain assumptions, or defi nitions, that he requires later on for his argu-
ment. Typically, Heiberg introduces titles to head such passages (that, in the
original, belong directly to the fl ow of the introduction), and then numbers
the individual claims made in such passages. Th us, Heiberg’s introduction
of SC i is divided (following Torelli) into three parts: a general discussion
proper ( i 2–4), αξιωματα or ‘defi nitions’, so headed and numbered 1–6 ( i
6), λαμβανομενα or ‘postulates’, so headed and numbered 1–5 ( i 8). Titles
and numbers are not in the original. Similar systematizations of the axio-
matic material take place in Method , SL (inside the later axiomatic passage,
ii 44.16–46.21) and PE i.
Heiberg’s position must have been that all such titles and numerals were
required and so would have been lost only through some textual corrup-
tion. Otherwise, he could at the very least have marked off such editions
by, say, pointed brackets, or, at the very least, commenting in the apparatus
add. for ‘I added’ instead of om. for ‘the manuscripts omitted...’ Th is posi-
tion blinded Heiberg to the serious textual question regarding the origins