The History of Mathematical Proof in Ancient Traditions

Th e Elements and uncertainties in Heiberg’s edition 75

(see Figure 1.1). Generally, it is used to decide between variant manuscripts
or as confi rmation in the testing of conjectures about the state of the text
before the production of the oldest preserved manuscripts.
In brief, the work of the editor comprises two dimensions: (1) the estab-
lishment of the text, and (2) the reconstruction of what philologists call
the ‘textual history’, that is to follow the avatars of the manuscripts, but
also the commentaries and translations through which we have access to
the text, to review the evidence about the use of the work in education, in
controversies, or its presence in libraries. Although the one dimension is
certainly articulated with respect to the other, it is nonetheless convenient
to distinguish between them.
For the reconstruction of the textual history, all information ought to be
taken into account. Because the collected sources will probably be contra-
dictory (variants among manuscripts, incompatible quotations, etc.), it is
necessary to classify the information and search for plausible explanations
(accidents in copying, editorial action by a re-editor, infl uence of a com-
mentary through marginal notations, decisions of the translator, infl uence
of pedagogical, philosophical or mathematical context) in order to provide
an account of the development of the manuscript. Since the history of the
text serves to justify the choices made in its establishment (see the fl ow-
chart, in Figure 1.1 above), it must be understood how the two aspects of
the philological work are articulated.

Figure 1.1 Textual history: the philological approach.

Work of the Editor of the Greek Text

Direct Tradition

Quotes by

Greek Authors

(Non-Mathematical

Authors, Comment-

ators on Euclid.

Other Geometers)

Greek

Manuscripts,

Papyri

Indirect Tradition

Establishment of Text Reconstruction of the History of the Text

Citations by

Authors in a

Language other

than Greek

?

Translations

Ancient

Latin,

Syriac (?)

Arabic,

Persian,

Latin,

Hebrew,

Syriac,

Armenian

Medieval

Textual Inventory