The History of Mathematical Proof in Ancient Traditions

D i c h o t o m y 1

(Heiberg’s edition

versus

medieval Arabic and Arabo-Latin tradition

a^ )

T y p e o f divergence

Textual elements

D e fi

nitions

Df. iii. additional (+); Df. iv.3–7 (−)

; Df. xi.5–7 (–); xi.15, 17 (–);

Df.

XI.23 (–); Df.

XI

.25–28 (–)

Propositions

III

.12 (–); {v

II.20

vulgo

b^ } (–); {vii.22

vulgo

} (–); Ishâq-Th

âbit

IX.30–31 (+);

X.7–8 (–);

X.9 (iii) (–);

X.13 (–); {

X.13

vulgo

} (–);

X.16 (–);

X.24 (–);

X.112–114 (–); {

X.117

vulgo

} (–); {

XI

.38

vulgo

} (–);

XII

.6 (–);

XII

.13 (–);

XII

.14 (–)

Porisms

{II

.4Por} (+); {

III.

31Por.},

IV

.5 Por. (–);

V.4 (or 7) Por. (–);

V.19 Por.,

VI.

20 Por.1 (–);

IX

.2 Por (+);

IX.5 Por (+);

IX.

11 Por. (–);

X.4 Por. (–);

X.6 Por. (–);

X.9 Por. (–);

X.23 Por. (–);

X.114 Por. (–);

XI.33 Por. (–);

XI

.35 Por. (–);

XII

.7 Por (–);

XII

.8 Por (–);

XIII

.16 Por. (–);

XIII

.17 Por. (–)

(+ / –)

Additional material Special Cases

{Pseudo-special case in

III

.11} (–); Special case in

III

.20, 24, 27 (–);

Special case in

III

.35, 36, 37 (+); Special case in

V.8 (–);

{Special case in

VI

.27} (–); {Special case in

XI.23} (–)

Additions

{Addition to

III

.16 Por.} (–); {Addition to

VI

.33} (–); Addition to

X.1 (–);

12 {Additions} {to

X.10, 18, to

X.23 Por., to

X.32/33; to

X.36, 37, 38, 39, 40, 41,

to Df.

X (series ii); to

X.85–90}; Addition (?) to

XIII

.18 (–)

Double Proofs

{III

.7p, 8p;

VI

.20p, 30;

VII

.31

aliter

} (–); {

X.1

aliter

} (+);

{XI

.22;

XII

.17p

aliter

} (–);

XIII

.1–3

aliter

(+); {

XIII

.5

aliter

} (–);

{XIII

.1–5

aliter

by analysis/synthesis} (–); {

XIII

.18p

aliter

} (–)