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Three classes of curves in Descartes'Geometry
SHI Xianghui *
Key Laboratory of Mathematics and Complex Systems, Ministry of Education, China, School of Mathematical Sciences, Beijing Normal University, Beijing 100875
*Correspondence author
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Funding: RFDP （No.No.273901）, the SRF for ROCS (SEM) （No.No. 105213006）, NSFC （No.No.11171031）
Opened online:22 May 2012
Accepted by: none
Citation: SHI Xianghui.Three classes of curves in Descartes'Geometry[OL]. [22 May 2012] http://en.paper.edu.cn/en_releasepaper/content/4478590
 
 
Descartes' three volume Geometry discuss three classes of curves: (1) curves generated by regulated continuous motions, (2) curves generated by (uniform) pointwise construction, and (3) curves given by an algebraic equation. It's widely hold that Descartes considers the three classes essentially the same class of curves. But one can barely find an argument for this in the literature. In this paper an argument for the view is presented. The discussion is carried out from both technical and philosophical points of view. The situation here is quite similar to that of Church's Thesis in recursion theory regarding computable functions.
Keywords:geometry; algebraic equation; representation of curves; regulated continuous motion; pointwise construction
 
 
 

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