Th e Elements and uncertainties in Heiberg’s edition 105
will the side measure the side; and, if the side does not measure the side,
neither will the square measure the square.’ If the indirect tradition is con-
sulted, an interesting division is observed:
- In the translation of Ishâq–Th âbit the contrapositives do not exist,
but each of the Propositions viii .14–15 is followed by a Porism which
expresses the same thing. 90 - In the translation of al-Hajjâj^91 and in the Adelardian tradition 92 is found
a single Proposition combining the equivalent of Heib. viii .16–17. Th e
assertion about cube numbers is simply left as a potential proof. - Gerard of Cremona transmits the two version successively. 93
I think there is hardly any doubt in this case. Th e Propositions viii .16–17
of the Greek manuscripts are inauthentic and all the versions, including
those of the indirect tradition, contain augmentations or additions which
proceed along diff erent modalities and which are probably of Greek origin.
Logical concerns have certainly played a role in the transmission of the text. 94
Th e change in the order of vi .9–13
Th e examples that we have examined until now are rather simple in the
sense that their motivations appear rather clearly to be the improvement of
a defective proof (cf. xi .1), or fi lling a gap or explaining a deductive connec-
tion (supplementary material and Propositions). In a signifi cant number
of cases we have seen the advantages of taking into account the Arabic and
Arabo-Latin indirect tradition. However, it ought not to be believed that
this simplicity is always the case or that the indirect tradition systematically
presents us with the state of the text least removed from the original. As we
have already seen regarding the supplementary Propositions, the altera-
tion of Books x – xiii is especially clear in the Greek, although among the
91 Th is we know thanks to Nâsir ad-Dîn at-Tûsî. See Lévy 1997 : 233.
92 See Busard 1983 (Prop. viii. 15 Ad. I ): 239.359–240.371.
93 See Busard 1984 , respectively, 201.11–16 (= viii. 14 Por. GC ), 202. 11–16 (= viii .15 Por GC )
and 202.19–40 (= viii .16 GC ).
94 One might add here the supplementary Porism to Prop. ix .5 found in the Ishâq–Th âbit and
Gerard of Cremona translations. ix .4 establishes that a cube, multiplied by a cube, yields a
cube, and ix .5 states that if a cube, multiplied by a number, yields a cube, the multiplier was a
cube. Th e Porism to ix .5 affi rms that a cube, multiplied by a non-cube, yields a non-cube and
that if a cube, multiplied by a number, yields a non-cube, the multiplier was a non-cube. In a
subfamily of Ishâq–Th âbit manuscripts, this Porism has been moved aft er ix .4. In Gerard of
Cremona, there is a Porism aft er ix .4 and one aft er ix .5! See De Young 1981 : 201, n. 7 , 202–3,
480–1 and Busard 1984 213.29–31 and 213.51–6.
90 See De Young 1981 : 151, 154–5, 431, 435.