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The pulsation between the articulated and projective, optical, algebraic conceptions of the Cartesian ovals. (La pulsation entre les conceptions optiques, algébriques, articulées, et projectives, des ovales cartésiennes.) (French) Zbl 0997.01004
Tournès, Dominique (ed.), L’océan Indien au carrefour des mathématiques arabes, chinoises, européennes et indiennes. Actes du colloque, Saint-Denis, La Réunion, 3-7 novembre 1997. Saint-Denis: Publication de L’I.U.F.M. de la Réunion. 359-394 (1998).
In this long and well documented paper the authors go along the history of Descartes’ Ovals with the aim to show Descartes’ conception of the nature of curval lines as geometrical and mechanical is not an inconsistency or an oscillation of the French mathematician, but concerns something of quite coherent and important that is similar to some distinctions made by later mathematicians. The authors, in fact, believe Descartes’ ideas can be better understood on the light of a theorem of Kempe (1875), where is proved that algebraical curves are exactly those which can be locally drawn by an “articulated mechanism”. The paper presents the contribution to Ovals by Descartes, Newton, Tschirnhaus, Leibniz, Quételet, Chasles, Cayley and Kempe.
For the entire collection see [Zbl 0977.00019].
01A45 History of mathematics in the 17th century
51-03 History of geometry