24 karine chemla
to draw attention to the fact that the diagrams inserted by Heiberg in his
edition of Euclid’s Elements , among others, are quite diff erent from those
actually and stably contained in the manuscripts. Th e sources indicate
that the diagrams were more oft en than not quite particular, represent-
ing the general case not by means of a generic fi gure, but rather by means
of a remarkable and singular confi guration. By contrast, Saito and Sidoli
show how Heiberg tacitly altered the diagrams, modernizing them and
thereby conspicuously making them look more faithful to the situation
under study and more generic than they actually were. Th ese operations
inserted diagrams in the nineteenth-century edition of the Elements which
displayed an artifi cial continuity between past practices and mathemati-
cal practices at the time, not only with respect to their appearance, but
also with respect to their way of expressing the general. Furthermore, the
Greek diagrams were thereby shown as being demonstrably more diff erent
from the diagrams having specifi c dimensions contained in the Sanskrit or
Chinese sources than the manuscripts actually indicated. Such issues may
look minor, but they are not. In fact, Saito ( 2006 ) discusses a case in which
the option chosen by the philologist in the restoration of the fi gure has
had a crucial impact on the restored text. His conclusion is that, on both
counts, Heiberg’s choice seems to admit the results of a later intervention
as genuine. 37 It is important to notice that, in modernizing the diagrams in
this way, Heiberg removed any hint of the actors’ ways of drawing and using
fi gures, thereby impeding through his edition any study of the ancient prac-
tices with geometrical fi gures.
Saito’s and Sidoli’s critical analysis of the fi gures that Heiberg included in
his editions such as the Elements is in full agreement with what Reviel Netz
shows in the following chapter about Heiberg’s edition of Archimedes’ writ-
ings. In this chapter, Netz analyses more generally by which kinds of opera-
tion Heiberg’s philological interventions left a lingering imprint on Greek
mathematical texts of antiquity as we read them today. However, concen-
trating on the Danish philologist’s critical edition of Archimedes’ writings,
particularly the second edition published between 1910 and 1915, Netz
demonstrates further the specifi cs of Heiberg’s editorial operations with
respect to the Syracusan’s Opera Omnia. Netz’s analysis distinguishes three
types of intervention that, in his words ‘produce[d] an Archimedes who
was textually explicit, consistent, rigorous and yet opaque’. In particular,
Netz’s overall broader argument reveals how Heiberg shaped Archimedes’37 Saito 2006 : 97–144 compares Heiberg’s diagrams in Book i of the Elements with those of the
Greek manuscripts which formed the basis of his critical edition.