The History of Mathematical Proof in Ancient Traditions

Changes in order

In Df. In Prop.

Df.

VII

.21–23

VI

.23–26;

VII

.7–13;

VIII

.19–20;

IX

.11–12;

IX.14–19–20;

IX.25–26–27;

X.10–12–14–15

Modifi

cations

Substitutions of proof

Substitution of proof in

V.6, 18;

VI

.20,

VIII

.22–23 in GC

Substitution of Proof at

X.68–70 in Ad.

Formulations ≠

Variations of formulation in Df.

III

.11

Replacement of Df.

V.4 in Ad. (continuous proportion)

Ad., Post.6 = GC CN 10 = grec CN 9 I.15 Por.;

IV

.15 Por.

Statements ≠ for

II.1–9

‘Triangle’ variation for

II.14 in Ad.

Variation in lettering for

VII

(simple in Ad. / double in GC) Ad.

VIII

.15 = GC

VIII

.16 (= Heib.

VIII

.16–17)

= GC

VIII

.14 Por. +

VIII

.15 Por.

Fusion of

X.29–30 into a single Proposition

and removal (in the Adelardian tradition) Subdivision of

X.31–32 into four Propositions in GC

or into three in the Adelardian tradition

Total

83

3

Note:a^

Adelardian tradition: Ad. + RC (Busard and Folkerts, 1992 ) + JT (Busard 2001 ). From a structural point of view, the versio

ns of Hermann of Carinthia

(Busard 1967 –1972–1977) and Campanus (Busard 2005 ) belong to the tradition. It is necessary to take these versions into con

sideration because Ad. is

mutilated (through the loss of Book ix and the fi

rst third of Book x ). Th

e specialists ascribe the structural particul

arities of the Adelardian tradition to its

dependence on a model something like al-Hajjâj. Th

e version of Gerard of Cremona juxtaposes two textual families (without mixing them too much). Th

e

fi rst is similar to the Adelardian tradition, the other approaches the Ishâq–Th

âbit version.