The History of Mathematical Proof in Ancient Traditions

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3 Th e texture of Archimedes’ writings: through

Heiberg’s veil

Reviel Netz

Th e reading of Archimedes will always be inextricably intertwined with
the reading of Heiberg. Th e great Danish philologer, involved with so
many other projects in Greek science and elsewhere, 1 had Archimedes
become his life project: the subject of his original dissertation, Quaestiones
Archimedeae ( 1879 ), which formed the basis for his fi rst Teubner edition
of Archimedes’ Opera Omnia ( 1880 ) and then, following upon the discov-
ery of codices B and C, the second Teubner edition of the Opera Omnia
( 1910 –15). Th e second edition appears to have settled the main questions
of the relationship between the manuscripts, and has established the read-
ings with great authority and clarity (it is this second and defi nitive edition
which I study here). Th is is especially impressive, given how few technical
resources Heiberg had for the reading of codex C – the famous Palimpsest.
Even if today we can go further than Heiberg did, this is to a large extent
thanks to the framework produced by Heiberg himself: so that, even if his
edition is superseded, his legacy shall remain. Let this article not be read
as a criticism of Heiberg – the most acute reader Archimedes has ever had.
Th e historical signifi cance of Heiberg’s publication is due not only to his
scholarly stature, but also to his precise position in the modern reception of
Archimedes. Classical scholarship is a tightly defi ned network of texts and
readers, organized by a strict topology. Th e ‘standard edition’ has a special
position. Its very pagination comes to defi ne how quotations are to be made.
Indeed, even more can be said for Archimedes specifi cally. First, the rise of
modern editions inspired by German philological methods, in the late nine-
teenth century, coincided with an early phase of an interest in the history of
science. Th us Heath’s work of translating and popularizing Greek mathemat-
ics in the English-speaking world took place in the same decades that Heiberg
was producing his edition of Archimedes. Th e version of Archimedes still
in use by most English readers – Heath 1897 – depends, paradoxically, on
Heiberg’s fi rst (and defi cient) edition. Czwalina’s German translation ( 1922 –
5) was based on the second edition, as was Ver Eecke’s French translation
( 1921 ). Perhaps the most useful version among those widely available today,

1 For Heiberg’s somewhat incredible bibliography, see Spang-Hanssen 1929.