36 karine chemla
Aware that the symbols of Diophantus must be distinguished from those
of Vieta, Netz fi rst studies the specifi c historical context in which they were
designed and describes them in detail, on which basis he examines how
the editors of the nineteenth century transcribed them in their critical edi-
tions and translations. His conclusions are twofold. On the one hand, Netz
shows that the symbols are located at the level of noun-phrases, but are not
used for either the relations or the structural terms specifi c to a problem.
Moreover, he establishes their nature of being ‘allographs’ of the words
they stand for, that is, they write these words in another way. On the other
hand, Netz reveals that the use of these symbols is nowhere as systematic
in the manuscripts as Paul Tannery presented them in his 1893–5 edition. 42
Tannery designed the proofs, rather than the statement of problems, as
the locus for the use of symbols, a fact which does not correspond to what
is found in the manuscripts. Moreover, Tannery introduced a distinction
between some terms which he systematically rendered as symbols and
other terms which he always wrote down in full, thereby establishing two
diff erent kinds of terms, in contrast to the manuscripts which use abbrevia-
tions for both kinds in comparable ways. We meet again with the necessity
of a critical awareness regarding the critical editions carried out in the
nineteenth century.
Th is preliminary analysis provides a sound basis on which Netz can
address the main question raised by his chapter: what is the correlation
between Diophantus’ use of such symbols and the specifi c kind of proof he
systematically presented? In Netz’s view, Diophantus undertook to gather
problems he had received and complete their collection in a systematic way.
Moreover, his ambition was to present them for a literate, elite readership.
In relation to this goal, Diophantus opted for a solution of each problem
in the form of ‘analysis’. Hence Netz also addresses a part of the history of
proof that falls outside the scope of Euclid’s Elements. Th is holds true not
only because these proofs proceed through analysis. In addition, the point
in Diophantus’ Arithmetics is not to establish the truth of a statement, but
rather to fulfi l a task correctly. In a context in which the procedure of the
solution provided for problems was also a topic for debate, Netz argues,
writing down the reasoning which establishes how the task was correctly
fulfi lled contributed to showing the suitability of the mode of solution
adopted. In other words, for Netz, the proof here intended to highlight
the natural and rational character of the method chosen to solve a given42 Compare T1893/5. Th e 1974 reprint of the book is freely available on Gallica:
http://gallica.bnf.fr/.