• Journal for History of Mathematics
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• v.32 no.1
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• pp.27-44
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• 2019

This study analyses and discusses on the characteristic and the origin of the exhaustion method caused by the controversy over whether that method succeeded to the Antiphone's complete exhaustion idea and whether that method is similar to the method of limits. First, this study analyses 'principle of exhaustion method' which play an important role in that method in order to grasp the local characteristic of it. And this study speculates the origin of the exhaustion method by considering the time and situation of appearance and looking through the local characteristic of it. Also, this study takes a view of the overall characteristic of the exhaustion method by inquiring into the process of actual application of 'principle of exhaustion method' in a proof. As these results, this study reveals that the exhaustion method uprose not as a succession of Antiphone's idea but as a reaction to its idea, and that the exhaustion method has the recognized character of 'finitude' as distinct from the method of limits.