The History of Mathematical Proof in Ancient Traditions

D i c h o t o m y 2

(Adelardian traditions

versus

Ishâq–Th

âbit tradition received by Gerard of Cremona)

a

Type of divergence

Textual elements

In Books

i^

to

x

In Books

xi

to

xiii

(+ / –)

Defi nitions

Df.

III.6, 9; Df.

IV

.2; Df. V.10, 11, 18 (–) in Ad.

Df. IsT

V.17

bis additional; Df.

V.17

ter

(–) in Ad.

Df. IsT

VI

.2, 4

aliter

, VI

.6 additional (+) in (GC)

Df.

VI.3, 4, {5}; Df.

VII

.3–5 (–) in Ad.

Df. IsT

VII

.9

bis additional in GC

Substitution of Df. IsTh

VII

.15–16 additional in Ad.

Df.

XI.9 (–) in GC

Df.

XI.22 (–) in Ad.

2 Df.

XI.

aliter

in GC

Common notion

{CN4/5} (–) in Ad.

Propositions

I.45;

III

.37;

VI.12;

VIII

.11–12(a) (–) in Ad.

IsTh

VIII

.24–25 additional (+) in GC

X.27–28; 32 (–) in Ad.

Porisms

VI

.20Por. (n°2) in GC

Additional Porisms to

VIII

.14–15 (+) in GC

Additional material Additions

I.35

p^ aliter

= addition to

I.35 in GC

Additions to Df.

V.5, 7, 9–10 in GC

Addition at

X.54 in GC

Double proofs in GC

I.44

p^ aliter

; II

.4

aliter

; III

.9, 10, 25, 31

p , 33

aliter

;

III

.35, 36

aliter

; IV

.5, 8, 15

aliter

; V

.5

aliter

;

V.18

aliter

; VI

.9, 22, 31

aliter

; VIII

.22–23

aliter

;

X.6, 30, 33, 68–70, 91, 111, 115

aliter

; XI

.30

aliter

L e m m a s

X.32/33 (+) in GC GC

X.40/41 (Cf. Heiberg 41/42)