120 bernard vitrac
sort of post-factum explanations in Byzantine Greek manuscripts (cf.
above the example of xi .1) shows that the Greek text is itself enriched
through recourse to the relevant elements of the commentary, prob-
ably through the intermediacy of marginal annotations by simple
readers or by scholars.
(10) Th e intervention of the epitomes in the indirect tradition is quite prob-
able. Th ere are, however, diff erent ways of abridging a text like that of
the Elements. An editor could eliminate portions considered inauthen-
tic or some theorems dealing with a theme judged too particular.
Regroupings could be made. Abbreviated proofs could be substituted,
using in particular the previously discussed formulae for potential
and analogical proofs or by removing the uninstantiated general state-
ments, which are oft en less comprehensible than the example (set out
in ecthesis and diorism ) accompanied by a diagram and labelled with
letters. More radically, all the proofs could be removed, and only what
Bourbaki called a ‘fascicule de résultats’ might be retained, or some
number of books no longer considered indispensable might be cut
out. In this case, the very structure of the treatise and its plan, which
have oft en been criticized, would be changed. Such recensions are
not at all rare beginning from the sixteenth century, but in the major-
ity of ancient and medieval versions, even in a recension like that of
Campanus which introduces numerous local changes, the Euclidean
progression through thirteen books is maintained, even if at some
stage supplementary books ( xiv, xv, xvi , ...) were added.
Alternatively, the other operations of abbreviations listed above are
all mentioned in the medieval prefaces, such as those of al-Maghribî, 140
the recension now called pseudo-Tûsî 141 or the Leiden Codex, wherein
the authors described recensions or epitomes. Moreover, as we have
noted above, according to the preface of the Leiden Codex, al-Hajjâj,
in order to win the favour of the new Khalif al-Ma’mûn, improved his
fi rst translation ‘by rendering it more concise and shortening it. He
did not fi nd an addition without removing it, nor a lacuna without
fi lling it, nor a fault without repairing and correcting it, until he had
purged, improved, summarized and shortened it all.’ 142 I t i s p o s s i b l e
140 One can read a Latin translation in Heiberg 1884 : 16–17, with several errors of identifi cation
about the cited Arabic authors (and even about the author of the preface! See Rommevaux,
Djebbar and Vitrac 2001 : 230, 239). It allows us however to have some idea of the liberties
taken by the authors of recensions. Completed by Sabra 1969 : 14–5 who corrects the
identifi cations and Murdoch 1971 : 440 (col. b).
141 It is taken up again by Murdoch in the article cited in the preceding note.
142 Translation in Djebbar 1996 : 97.