The History of Mathematical Proof in Ancient Traditions

Th e Elements and uncertainties in Heiberg’s edition 83 as in the previously mentioned example of ix .19. 31 Contrary to Peyrard ...

84 bernard vitrac thoroughly called into question by W. Knorr in his article of 1996. In particular, our late colleague there af ...

Th e Elements and uncertainties in Heiberg’s edition 85 Th e second scenario which might account for the limited but real varia- ...

86 bernard vitrac 1855, published only extracts. Th enceforth, the text was edited and trans- lated into multiple languages. 38 ...

Th e Elements and uncertainties in Heiberg’s edition 87 vii – ix from the so-called Ishâq–Th âbit version. 44 A second manuscrip ...

88 bernard vitrac translations. Th is hypothetical archetype represented the state of the text prior to the re-edition of Th eon ...

Th e Elements and uncertainties in Heiberg’s edition 89 of rather easily identifi able textual units, facilitates this work. In ...

90 bernard vitrac or ‘ἤ καὶ οὕτως... ’ (‘Or, also thus ...’). 56 In the same way, in the Arabo- Latin translation of Gerard of C ...

Th e Elements and uncertainties in Heiberg’s edition 91 the category of global diff erences – that is, substitution of proof – b ...

92 bernard vitrac potential proofs (PP) introduced by the formulae: ‘So also for the same reasons ...’ (= ‘διὰ τὰ αὐτὰ δὴ καὶ .. ...

Th e Elements and uncertainties in Heiberg’s edition 93 In comparing Heiberg’s text with the text of the Arabo-Latin translation ...

94 bernard vitrac remain, the diff erence being especially apparent in the arithmetical Books vii – viii , as a matter of fact m ...

Th e Elements and uncertainties in Heiberg’s edition 95 (b) Th en the two textual families distinguished by Heiberg diverge: P ( ...

96 bernard vitrac Let us now consult the indirect medieval tradition, for example the Arabo-Latin translation by Gerard of Cremo ...

Th e Elements and uncertainties in Heiberg’s edition 97 It is possible to imagine (at least) two scenarios: either these post- f ...

98 bernard vitrac Sidon. Th e Euclidean proof of i .1 presupposes that there is not a common segment for two distinct straight l ...

Th e Elements and uncertainties in Heiberg’s edition 99 in the discussion of problematic places, variant readings of the indirec ...

100 bernard vitrac Questions of authenticity and the logical architecture of the Elements If the diff erent versions are conside ...

Th e Elements and uncertainties in Heiberg’s edition 101 a property likewise shown for the parallelepipeds ( xi .34) and pyramid ...

102 bernard vitrac from their absence, as Heiberg has done, that there is a deductive ‘lacuna’ in the proof of xii .15. However, ...