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| Type of paper : | Article dans une revue internationale ou nationale avec comité de lecture répertoriée par l'AERES ou dans les bases de données internationales (ISI Web of Knowledge, Pub Med...) (ACL) |
|---|---|
| Authors : | Panza, Marco |
| Full title : | Rethinking geometrical exactness |
| Part number : | 38 |
| Year : | 2111 |
| Periodical : | Historia Mathematica |
| Page numbering : | 42-95 |
| Keywords : | Euclid's plane geometry ; Early modern geometry ; Descartes's geometry |
| 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. |
| URL : | http://halshs.archives-ouvertes.fr/halshs-00540004/fr/ |
| Data recorded on : | Friday, 26th November 2010 à 23:12:08 |
| Data updated on : | Thursday, 22th November 2012 à 18:26:53 |
Panza, Marco. – Rethinking geometrical exactness, Historia Mathematica [Online], vol. 38, 2111, p. 42-95. – Available online : <http://halshs.archives-ouvertes.fr/halshs-00540004/fr/>. – A crucial concern of early modern geometry was fixing appropriate norms for deciding whether some objects, procedures, or arguments should or should… (
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