Rethinking geometrical exactness

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• 作者：Marco Panza
• 关键词：Euclid&#x2019 ; s plane geometry ; Early modern geometry ; Descartes&#x2019 ; s geometry
• 刊名：Historia Mathematica
• 出版年：2011
• 出版时间：February 2011
• 年：2011
• 卷：38
• 期：1
• 页码：42-95
• 全文大小：1077 K

文摘

A crucial concern of early modern geometry was fixing appropriate norms for deciding whether some objects, procedures, or arguments should or should not be allowed into it. According to Bos, this is the exactness concern. I argue that Descartes’s way of responding to this concern was to suggest an appropriate conservative extension of Euclid’s plane geometry (EPG). In Section 2, I outline the exactness concern as, I think, it appeared to Descartes. In Section 3, I account for Descartes’s views on exactness and for his attitude towards the most common sorts of constructions in classical geometry. I also explain in which sense his geometry can be conceived as a conservative extension of EPG. I conclude by briefly discussing some structural similarities and differences between Descartes’s geometry and EPG.