26 karine chemla
him to derive with respect to the text of proofs: Heiberg’s bracketing occurs
mainly in the texts for proofs, at precisely those points which suggest that
Heiberg felt that overly simple arguments in the course of a proof could not
be due to Archimedes. Th e more elementary the treatises, the more brack-
eting Heiberg carried out. In conclusion, Heiberg imposed on the text of
the proof his expectation regarding Archimedes’ way of proof.
Lastly, Netz brings to light the subtle ways at the global level of the corpus
of texts in which Heiberg established Archimedes as a mathematician who
adopted a uniform style and wrote down his treatises according to the same
systematic pattern. By contrast, Netz suggests that Archimedes’ writings
manifested variety in several ways and at diff erent levels. What matters
most for us, again, is how the philologist’s operations have a bearing on
our perception of proofs and the sequence of them in ‘axiomatic–deductive
organizations’. And, here, the description of the editorial situation that Netz
off ers us is quite striking. He reveals how Heiberg forced divisions between
propositions, types of propositions and components of propositions onto
texts that did not lend themselves equally well to the operations and thus
artifi cially created the sense of a standardized mathematical text, in con-
formity to modern expectations. In addition, Netz reveals Heiberg himself
decided to give some propositions the status of postulate and others that of
defi nition, with the manuscripts containing nothing of the sort. In that way,
beyond the Archimedean corpus, the whole corpus of Greek geometrical
texts acquired more coherence than what the written evidence records.
Together, these three chapters bring to light various respects by which
the critical editions tacitly convey nineteenth-century or early-twentieth-
century representations in place of Greek mathematical proofs to inat-
tentive readers. Still more will be developed on this point in relation to
Diophantus below. Th ese conclusions provide impetus for developing
further research on these topics, in order to understand how representa-
tions of ancient mathematics were formed in the nineteenth century and
how they adhered to other representations and uses of Greek antiquity.
Another chapter of the book inquires further in this direction of research. It
complements our critical analysis of the historical formation of our under-
standing of Greek ideas of proof and shows how fruitful further research of
that kind could be for sharpening our critical awareness.
In this chapter, Orna Harari draws on the hindsight of history and ques-
tions the conviction widely shared today that Aristotle’s theory of dem-
onstration in the Posterior Analytics can be interpreted in reference to its
presumptive illustration, that is, Euclid’s Elements. In fact, she establishes
that this use of these two pieces of evidence in relation to each other became