The History of Mathematical Proof in Ancient Traditions

Mathematical proof: a research programme 23 Th is also holds true for most of the material added (propositions, lemmas, porisms) ...

24 karine chemla to draw attention to the fact that the diagrams inserted by Heiberg in his edition of Euclid’s Elements , among ...

Mathematical proof: a research programme 25 proofs according to his vision. In conclusion, we understand better how we were mist ...

26 karine chemla him to derive with respect to the text of proofs: Heiberg’s bracketing occurs mainly in the texts for proofs, a ...

Mathematical proof: a research programme 27 commonplace only in modern times. Th is brings us back to the issue of the part play ...

28 karine chemla historiographic ideas were formed, the values which past historians had deemed central, the agendas they adopte ...

Mathematical proof: a research programme 29 Archimedes’ view, this type of argument could not be conclusive and had to be follow ...

30 karine chemla order to conclusively resolve debates as a social phenomenon. Th e new and important research programme which h ...

Mathematical proof: a research programme 31 truth of a proposition that such techniques could be grasped. Th e hypothe- sis acco ...

32 karine chemla for an end, but their texts were also read as conveying other meanings. Th e ‘techniques’ read in the proofs do ...

Mathematical proof: a research programme 33 Th e lines of inquiry just outlined illustrate some of the issues that more generall ...

34 karine chemla fi rst terms of the sequences. However, this is how Nicomachus argues in favour of the general statement, where ...

Mathematical proof: a research programme 35 betray an ambition to reach a high level of generality. Mueller’s contrastive analys ...

36 karine chemla Aware that the symbols of Diophantus must be distinguished from those of Vieta, Netz fi rst studies the specifi ...

Mathematical proof: a research programme 37 problem. To this end, Diophantus shaped, primarily thanks to his symbols, a kind of ...

38 karine chemla From another viewpoint, Diophantus’ text can be contrasted with other types of problem texts, which also attest ...

Mathematical proof: a research programme 39 development of this inquiry provides means for interpreting these texts more accurat ...

40 karine chemla out correctly the task for which it is given, that is, that the algorithm yields the desired result. In this fr ...

Mathematical proof: a research programme 41 view, the proofs he reads in the formulation of the procedure intend to guarantee an ...

42 karine chemla paradigms that they were, they also provided a semantic fi eld for interpret- ing the operations of the algorit ...