The History of Mathematical Proof in Ancient Traditions

(Elle) #1

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Th e fi rst operation, apparently begun in Rome at the beginning of our
era, is nothing more than the adoption of the book with pages, written on
both sides and with contents defi nitely more important than the volumen.
Th is shift allows the composition of textual collections and the develop-
ment of marginal commentaries which previously appeared in a separate
scroll. Writings that were not converted into this format had a relatively
small chance of being transmitted down to us. Th e texts known only
through papyrus scrolls are small in number and frequently nothing more
than fragments. In other words, in the case of the Elements , the creation
of (at least one) archetypal codex must be postulated. We know nothing
of when this fabrication occurred or who (whether a mathematician or an
institution similar to a library with a centre for copying) undertook this
labour. However, the adoption of the codex was a rather slow operation
which spanned from the fi rst through to the fourth centuries of our era,
and beyond. Th e fact that this adoption was applied in wholesale to the
texts from previous eras probably ought to be attributed to the revival of the
study of classical texts under the Antonines (second century). 10
Th e other operation, the Byzantine transliteration, was more limited
than the change from scrolls to codices. It was done in the Byzantine empire
from the end of the eighth century. Th e Byzantine transliteration consisted
of using a form of cursive minuscule for the edition of texts in place of the
majuscule writing termed uncial. Previously, cursive minuscule had been
limited to the draft ing of administrative documents, but uncial had proven
too large and thus ‘costly’ for use with parchment. Here, too, the success
and systematization of the process were certainly linked with a renewed
interest in ancient texts during the course of the ‘Byzantine Renaissance’,
which began in the 850s and was associated with individuals like Leo the
Wise (or the Philosopher), the patriarch Photius and Arethas of Cesarea.
Such transliteration was a rather delicate technical operation composed of
two phases – the fi rst (and the largest) of which fell in the ninth and tenth
centuries, the second in the years 1150–1300. 11 Here, again, translation
acted as a fi lter. Non-transliterated texts progressively ceased to be read.
Save for some fortunate circumstances, they disappeared.
For the ancient writings which survived these two transformations, we
may, if we are reasonably optimistic, emphasize on the one hand the fact
that on occasions in these two situations, the editors intervened in impor-
tant ways, and the specimens were produced according to particularly

(^10) On the change from scroll to codex, see the accessible summary by Reynolds and Wilson 1988:
23–6. Cf. also Blanchard 1989.
(^11) Cf. Irigoin 2003: 6–7.

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