The History of Mathematical Proof in Ancient Traditions

Lemmas

c^

VI.22/23;

X.9/10;

X.13/14;

X.16/17;

X.18/19; {

X.20/21};

X.21/22;

{X

.27/28};

X.28/29 {1}, {2}; {

X.29/30}; {

X.31/32}; {

X.32/33};

{X

.33/34}; {

X.34/35};

X.41/42;

X.53/54;

X.59/60;

XI

.23/24;

XII

.2/3;

XII

.4/5;

XIII

.2/3;

XIII

.13/14; Lemma aft

er

XIII

.18

Changes in order

In Df.

Df.

V.12–13; Df.

VI

.3–4; Df.

VII

.13–14; Df.

VII

.17–20; Df.

XI

.9–22

In Prop.

V.12–13;

VI

.9–13;

VI

.18–20;

VI.31–32;

VII

.21–22;

VII

.29–32;

X.10–11;

X.14–15;

X.25–26;

X.111–111Por.;

XI.33–34;

XII

.8–9;

XII

.11–12;

XIII

.4–5;

XIII

.8–12;

XIII

.14–15

Modifi

cations

Substitution of proof

III.14p, 31p, 37;

III

.33 (Construction);

X.105–107;

XI

.37

Df.

XI.1–2 (÷2)

III.1 Por.;

X.72 Por. (transformed into a Proposition)

Formulations ≠

III

.25;

V.23

VIII

.16–17 = Ad.15 = GC 16 = GC

VIII

.14 Por. + 15 Por.

Inversion

X.111, 111 Por. and transformation (in Prop.);

XI.31 (× 2);

XI

.34 (× 2)

Total

139

Notes:a^

In this table, the medieval tradition (as defi

ned above, p. 89) serves as a reference: (+), (–), (÷2), (× 2) signify presence, absence, fusion, subdivision

respectively in this tradition.

b^

On the meaning of

vulgo

, see n. 28.

c^

Th e case of the Lemmas is slightly diff

erent. Heiberg explicitly dismisses some ({}), keeps others, all the while maintaining that they are all certainly

interpolated (with the sole possible exception of x .28/29 {1}, {2}).