The History of Mathematical Proof in Ancient Traditions

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86 bernard vitrac


1855, published only extracts. Th enceforth, the text was edited and trans-
lated into multiple languages. 38
In the course of the two decades during which Heiberg worked on the
tradition of the text of Euclid, new information, accessible thanks to the
indirect tradition, 39 could have led him to alter certain editorial decisions
made in the years 1883–6 at the time when he argued with Klamroth.
Th ese alterations might have stemmed notably from taking into account
manuscript b (in the portion where it diverges) and the indirect medi-
eval tradition. Th e works which he published in the years 1888–1903 are
indispensable to those who use his critical edition. Regrettably, Heiberg
did not produce a second revised edition, as he did for Archimedes, aft er
the discovery of the so-called Archimedes Palimpsest. 40 Th is text gave
access to the previously unavailable Greek texts of On Floating Bodies and
Th e Method of Mechanical Th eorems. To his eyes, the necessity of a revised
edition was probably much smaller in the case of the Elements of Euclid,
but the resumption of such a work would perhaps have led him to revise his
position concerning the indirect medieval tradition.
We know this tradition somewhat better than Klamroth or Heiberg,
thanks to a more developed textual inventory. At least a score of manu-
scripts of the version called Ishâq–Th âbit have been identifi ed today, 41
whereas Klamroth knew only two! Multiple works on the methods and
contexts of medieval translations from Greek into Syriac or Arabic, or from
Arabic into Latin or Hebrew, either in general or more directed toward
mathematical texts, including the Elements , have been undertaken. Busard
has published seven Arabo-Latin versions from the twelft h and thirteenth
centuries 42 as well as a Greco-Latin version from the twelft h century dis-
covered by J. Murdoch. 43 We even have partial editions of the Books v and

(^38) See notably Th omson and Junge 1930. It might be argued that this partial knowledge led
Heiberg to some debatable conclusions concerning the collection of the ‘Vatican’ scholia (see
Vitrac 2003: 288–92) and the pre-Th eonine state of the text of Book x (see Euclid/Vitrac, 1998:
iii 381–99). Let us add that the integrity of the text attributed to Pappus and the uniqueness of
the author (pace Th omson and Junge 1930) are not at all certain (see Euclid/Vitrac, 1998:iii:
418–19).
(^39) It ought to include the new information contained by the scholia found in the margins of the
Greek manuscripts and we once again know about these sources thanks to the monumental
work of Heiberg. See EHS, v, 1–2 and Heiberg 1888, to which should be added Heiberg 1903.
(^40) Regrettably, in his ‘revision’ (EHS), Stamatis did not supplement ‘Heiberg with Heiberg’.
(^41) See Folkerts 1989 (with the corrections of Brentjes 2001: 52, n. 13). Some of these manuscripts
contain fragments attributed to the translation by al-Hajjâj.
(^42) Respectively Busard 1967–1972–1977 (HC), 1983 (Ad. I), 1984 (GC); Busard and Folkerts
1992 (RC); Busard 1996, 2001 (JT), 2005 (Campanus). Complete references are provided in the
bibliography.
(^43) Busard 1987.

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