The History of Mathematical Proof in Ancient Traditions

(Elle) #1

Th e Elements and uncertainties in Heiberg’s edition 73


‘authorized’ manners which played a decisive role in the transmission.
Th ese two circumstances produced the archetypal codex (or codices) of the
Roman era and the transliterated example or examples in minuscule begin-
ning in the ninth century. On the other hand, on these occasions there was
the risk and opportunity that the substance or presentation of these texts
would be radically modifi ed.
Th e oldest preserved complete examples of the Elements in thirteen
books were produced immediately aft er the transliteration into minuscule
which has just been called into question.
Th ey are:



  • one manuscript from the Vatican Library, Va t i c a n u s g r. 190, assigned to
    the years 830–50 according to palaeographic and codicological consid-
    erations;^12

  • one manuscript from the Bodleian Library at Oxford, D’Orville 301,
    which, other than its exceptional state of conservation, has the advan-
    tage of having been explicitly dated, since its copying, ordered from the
    cleric Stephanos by Arethas, who was then deacon, was completed in
    September 888.
    Two remarks are in order:


(1) Th ese pieces of evidence are from more than a thousand years aft er the
hypothetical original of Euclid.
(2) Th e case of the Elements is, however, one of the most favourable
(or,  perhaps, least unfavourable?) in the collection of profane Greek
texts.
Other than these two precious copies, about eighty manuscripts contain-
ing the text (either complete or in part) are known; of these roughly thirty
predate the fi ft eenth century. Likewise, a palimpsest, dated to the end of
the seventh or the beginning of the eighth century and written in uncial,
contains extracts from Books x and xiii. 13 It thus seems assured that the
study of the Elements had not completely ceased during the so-called Dark
Ages of Byzantine history (650–850). Also known are several papyrus frag-
ments, 14 the oldest of which are ascribed to the fi rst century and the most


(^12) Cf. Irigoin 2003: 215 (original publication, 1962). Cf. Follieri 1977, particularly 144; Mogenet
and Tihon 1985, 23–4 (Vatican fr. 190 = ms probably from the fi rst half of the ninth century)
and 80–1. At the time of Heiberg, this copy was assigned to the tenth century, and the
manuscript in the Bodleian was considered the oldest. One sometimes still fi nds this debatable
assertion.
(^13) See Heiberg 1885.
(^14) Cf. EHS: I: 187–9 and Fowler 1987: 204–14 and Plates 1–3.

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