22 karine chemla
edition of Archimedes’ writings.^36 What can we learn about the issue of
proof by examining the philologist’s impact on our present-day vision of
Euclid and Archimedes?
Th e three chapters of this book that are devoted to the analysis of the
nineteenth-century editions of Greek geometrical texts from antiquity –
the fi rst one dealing with the Elements , the second one with the general
issue of the critical edition of diagrams and the third one with Archimedes’
texts – represent three critical approaches to Heiberg’s philological choices
and their impact on the editing of the proofs. Th eir argumentation benefi ts
from the wealth of twentieth-century publications on the Arabic and Latin
translations and editions of the Greek geometrical texts. Let us outline
here briefl y the distinct textual problems on which these chapters focus.
Each chapter represents one way in which our understanding of the proofs
preserved in the geometrical writings of ancient Greece is aff ected by their
representation developed in the editions commonly employed.
In his contribution to the volume, Bernard Vitrac examines diff erent
types of divergences between proofs, to which the various manuscripts that
bear witness to Euclid’s Elements testify. More specifi cally, Vitrac focuses on
a corpus of diff erences that were caused by deliberate intervention. Since
these transformations were most certainly carried out by an author in the
past who wanted to manipulate the logical or mathematical nature of the
text, they indicate clearly the points at which we are in danger of attributing
to Euclid reworking of the Elements undertaken aft er him.
Th ree types of divergences are examined. Th e fi rst one, about which
the debate described above broke out, relates to the terseness of the text
of proofs: some proofs are found to be more complete from a logical point
of view in some manuscripts than in others. Vitrac brings to light that the
interpretation made by the two opponents in the debate relied on divergent
views of the possible evolution of such a book as the Elements. Klamroth’s
thesis presupposed that the evolution of the text could only be a progressive
expansion, motivated by the desire to make the deductive system more and
more complete from a logical or a mathematical point of view. In contrast,
Heiberg suggested that the Arabic and Latin versions were based on an
epitome of the Euclidean text, on which account he could marginalize their
use in restoring the Elements. Vitrac provides an analysis of the various
logical gaps and concludes that the later additions to the Greek text that
the indirect tradition allows us to perceive in the Greek manuscripts are
linked to a logical concern regarding the mathematical content of the text.36 Chemla 1999.