114 bernard vitrac
respect to No. 1 (direct tradition/indirect medieval tradition) or even
to No. 2, within the Arabic and Arabo-Latin translations. 115- It convinces us that some part of what exists in Greek, and preserved
by Heiberg in his edition, is very probably inauthentic. - It gives a possible interpretation to some ‘isolated’ variants in Greek
by integrating them into a broader picture which makes sense. For
example, it makes sense of families of alternative proofs created by
the same editorial principles. 116
(2) However, because of the number of variants, the homogeneity of the
entire indirect tradition, which Klamroth believed existed, no longer
exists in Books i – x. I have called this dichotomy 2, within the Arabic,
Arabo-Latin and, it seems, the Hebraic traditions. For certain portions,
notably Books iii , viii and x , it seems that (at least) two rather struc-
turally diff erent editions existed and they contaminated each other sig-
nifi cantly. Consequently, it will be impossible to reconstitute a unique
Greek prototype for this portion of the whole of the medieval tradition
as Knorr had wanted.^117
If the study of the material contents, order, presentation, and proofs
of the preserved versions of the thirteen books is resumed, it is not to
be expected to fi nd that among the preserved versions, one of them,
for instance Adelard I or Ishâq–Th âbit, may be declared closer to the
original in all its dimensions than all the other versions. Th e ‘local’
criteria used by Klamroth, Heiberg and Knorr, either focusing on the
material contents (according to the principle of expansion) or on the
improvement of the form, do not converge upon a global criterion
which applies to the entirety of the collection of the thirteen books.
Th e result is thus that the indirect tradition appears more authentic in
regard to the material contents but not for the order of presentation.
For the problems of order and of presentation, conversely, the indirect
115 See Tables 1–3 of the Appendix.
116 We have seen an example of this with the superfi cial proofs of x .105–106. Another family
of double proofs may be reconstituted for Propositions vi. 20p, 22, 31, x .9, xi .37. See Vitrac
2004 : 18–20.
117 It should be emphasized that Knorr had not considered the problem at its full scale: - He considered at most a group of 21 Propositions and proceeded by induction.
- He did not take into account more than one single criterion of structural divergence – that
of material contents – with one exception: the proof of xii .17, poorly handled in the indirect
tradition and interpreted not as an accident of transmission but in terms of development. - He took into account neither changes in order nor the rich collection of double proofs.
- He did not ask himself the question of whether the two Arabo-Latin translations that he
used, Adelard and Gerard, were representative of the whole of the indirect tradition. Whether
these translations are representative is not at all certain in the stereometric books (cf. below,
pp. 118–19).