Malebranche et l’intuitionnisme mathématique
As early as the first publications of his differential and integral calculus, Leibniz stated that the essential principle for studying a curve was to consider it as an “infinitangular polygon” or a “polygon of infinitely many sides.” This supposition is not entirely original in the history of mathem...
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2025
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| Διαθέσιμο Online: | Accès Université d'Orléans et IFPM Accès Université d'Orléans et IFPM |
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cairn-RHS_782_0403RHSRevue d'histoire des sciences https://shs.cairn.info/revue-revue-dhistoire-des-sciences-2025-2-page-403?lang=fr https://doi.org/10.3917/rhs.782.0403 Malebranche et l’intuitionnisme mathématique Schwartz, Claire2025 fre Revue d'histoire des sciences | 78 | 2 | 2025-11-13 | p. 403-436 | 0151-4105 RHS_78274 As early as the first publications of his differential and integral calculus, Leibniz stated that the essential principle for studying a curve was to consider it as an “infinitangular polygon” or a “polygon of infinitely many sides.” This supposition is not entirely original in the history of mathematical practice, but Leibniz claims that, in the context of his invention, it is the one that ultimately leads to a general concept of a curve. This contribution is presented in the context of the reception of Leibniz’s calculus by a circle of mathematicians around the philosopher Nicolas Malebranche at the turn of the 17th century. These mathematicians had already undertaken a renewal of their skills, and so they did not appropriate Leibniz’s invention in virgin territory. Based on manuscripts, we examine the epistemological variations undergone by the concept of the infinitangular polygon through the new practice of writing represented by the Leibnizian calculus, as well as the forms of intertextuality employed by the actors.Dès les premières publications de son calcul différentiel et intégral, Leibniz explique que le principe essentiel pour étudier une courbe est de la considérer comme un «polygone infinitangulaire» ou un «polygone d’une infinité de côtés». Cette supposition n’est pas nouvelle dans l’histoire de la pratique mathématique mais Leibniz soutient que, dans le contexte de son invention, elle est celle qui conduit à un concept général de courbe. Cette contribution se place dans le contexte de la réception du calcul infinitésimal de Leibniz chez un cercle de mathématiciens réunis autour du philosophe Nicolas Malebranche au tournant du xviie siècle. Ces mathématiciens ont déjà entrepris un renouveau de leurs connaissances et ce n’est donc pas en terres vierges qu’ils s’approprient de l’invention leibnizienne. Manuscrits à l’appui, nous examinons les variations épistémologiques que subit le concept de polygone infinitangulaire à travers la nouvelle pratique d’écriture que représente le calcul leibnizien mais en tenant compte des formes d’intertextualité mises en œuvre par les acteurs.Cairn free access |
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Français |
| format |
Article ou chapitre numérique |
| building |
0/Bibliothèque numérique/ 1/Bibliothèque numérique/Cairn/ |
| description |
As early as the first publications of his differential and integral calculus, Leibniz stated that the essential principle for studying a curve was to consider it as an “infinitangular polygon” or a “polygon of infinitely many sides.” This supposition is not entirely original in the history of mathematical practice, but Leibniz claims that, in the context of his invention, it is the one that ultimately leads to a general concept of a curve. This contribution is presented in the context of the reception of Leibniz’s calculus by a circle of mathematicians around the philosopher Nicolas Malebranche at the turn of the 17th century. These mathematicians had already undertaken a renewal of their skills, and so they did not appropriate Leibniz’s invention in virgin territory. Based on manuscripts, we examine the epistemological variations undergone by the concept of the infinitangular polygon through the new practice of writing represented by the Leibnizian calculus, as well as the forms of intertextuality employed by the actors. |
| author |
Schwartz, Claire |
| spellingShingle |
Schwartz, Claire Malebranche et l’intuitionnisme mathématique |
| author_facet |
Schwartz, Claire |
| author_sort |
Schwartz, Claire |
| title |
Malebranche et l’intuitionnisme mathématique |
| title_short |
Malebranche et l’intuitionnisme mathématique |
| title_full |
Malebranche et l’intuitionnisme mathématique |
| title_fullStr |
Malebranche et l’intuitionnisme mathématique |
| title_full_unstemmed |
Malebranche et l’intuitionnisme mathématique |
| title_sort |
malebranche et l’intuitionnisme mathématique |
| publishDate |
2025 |
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| url |
https://ezproxy.univ-orleans.fr/login?url=https://shs.cairn.info/revue-revue-dhistoire-des-sciences-2025-2-page-403?lang=fr https://ezproxy.univ-orleans.fr/login?url=https://doi.org/10.3917/rhs.782.0403 |
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