Document Type
Article
Publication Date
11-18-2010
Abstract
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.
Recommended Citation
Panza, Marco. “Rethinking Geometrical Exactness”, Historia Mathematica, 38, 1, 2011, pp. 42-95. https://doi.org/10.1016/j.hm.2010.09.001
Peer Reviewed
1
Copyright
Elsevier
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
Included in
Algebraic Geometry Commons, Geometry and Topology Commons, Logic and Foundations Commons, Logic and Foundations of Mathematics Commons, Other Mathematics Commons
Comments
NOTICE: this is the author’s version of a work that was accepted for publication in Historia Mathematica. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Historia Mathematica, volume 38, issue 1, in 2011. https://doi.org/10.1016/j.hm.2010.09.001
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