The function of diorism in ancient Greek analysis |
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Authors: | Ken Saito Nathan Sidoli |
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Institution: | 1. Department of Human Sciences, Osaka Prefecture University, Japan;2. School of International Liberal Studies, Waseda University, Japan |
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Abstract: | This paper is a contribution to our knowledge of Greek geometric analysis. In particular, we investigate the aspect of analysis know as diorism, which treats the conditions, arrangement, and totality of solutions to a given geometric problem, and we claim that diorism must be understood in a broader sense than historians of mathematics have generally admitted. In particular, we show that diorism was a type of mathematical investigation, not only of the limitation of a geometric solution, but also of the total number of solutions and of their arrangement. Because of the logical assumptions made in the analysis, the diorism was necessarily a separate investigation which could only be carried out after the analysis was complete. |
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Keywords: | 01A20 01A30 01A35 |
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