The History of Mathematical Proof in Ancient Traditions

Th e Elements and uncertainties in Heiberg’s edition 103 One in Proposition iv .10 of the Adelardo-Hajjajian tradition, connect ...

104 bernard vitrac enrichment was not confi ned to the fi nal, more complicated portion of the text in question. It is even prob ...

Th e Elements and uncertainties in Heiberg’s edition 105 will the side measure the side; and, if the side does not measure the s ...

106 bernard vitrac arithmetical books, the Ishâq–Th âbit version (itself inspired by Heron) is the best evidence of this ‘better ...

Th e Elements and uncertainties in Heiberg’s edition 107 When the various versions are considered, 97 the inversions are not the ...

108 bernard vitrac two alternative proofs for Propositions x .105–106 are inserted at diff erent places in the manuscripts. 100 ...

Th e Elements and uncertainties in Heiberg’s edition 109 proportions. Deductively, the linear proofs may be characterized as min ...

110 bernard vitrac If the principle of improvement advanced by Knorr is applied, we are led to think that the linear proofs of t ...

Th e Elements and uncertainties in Heiberg’s edition 111 cases, by the fact that the aforementioned manuscripts have compiled th ...

112 bernard vitrac those who deliberately changed the text of the Elements – diff erent criteria could be used. From the logical ...

Th e Elements and uncertainties in Heiberg’s edition 113 the Persian commentator an-Nayrîzî, we know that the author of the fi r ...

114 bernard vitrac respect to No. 1 (direct tradition/indirect medieval tradition) or even to No. 2, within the Arabic and Arabo ...

Th e Elements and uncertainties in Heiberg’s edition 115 tradition has the benefi t of many more improvements, and the Greek tra ...

116 bernard vitrac (4) To explain this state of aff airs, I see at least two explanations, that perhaps work in tandem: Either ...

Th e Elements and uncertainties in Heiberg’s edition 117 least compared with each other in order to produce Th âbit’s revision o ...

118 bernard vitrac which functions rather well in the case of dichotomy 1, also applies to dichotomy 2. 128 (7) Moreover, the ca ...

Th e Elements and uncertainties in Heiberg’s edition 119 hand. 135 It is interesting to note that in Proposition (Heib.) xiii .1 ...

120 bernard vitrac sort of post-factum explanations in Byzantine Greek manuscripts (cf. above the example of xi .1) shows that t ...

Th e Elements and uncertainties in Heiberg’s edition 121 that this passage contains some rhetorical exaggerations or stock phras ...

122 bernard vitrac diagrams, saut du même au même , and even, as it seems to me, faults in reading the uncial script. Manuscript ...