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Joël
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I recommend the reading of a wonderful 15-page text of Imre Lakatos, "Another case study of the method of proofs and refutations", which discuss precisely what Cauchy knew and didn't know and did and didn't do about this. It is published as an appendix in "Proofs and Refutations".

Google Book page of "Proofs and Refutations":

Joël
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