Wallis between Hobbes and Newton. The question of the horn angle in England

François Loget

Revue d'histoire des mathématiques (2002)

  • Volume: 8, Issue: 2, page 207-262
  • ISSN: 1262-022X

Abstract

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This paper treats an aspect of the dispute during the second half of the 17th century between Thomas Hobbes and John Wallis concerning the horn angle. Wallis published two treatises on this subject, one in 1656, the other in 1685. During this time, his views on the question of the horn angle changed perceptibly, as he confronted Hobbes on various mathematical topics, including the horn angle. Here, I analyze the positions of both protagonists via the texts they wrote throughout their polemic. I also explore two texts written by Newton during the same period, in which he treats the question of the horn angle and presents the solution he would soon publish in the Philosophiae naturalis principia mathematica. I argue that Wallis was led to change his interpretation of the horn angle both in reaction to the solution originally proposed by Hobbes and to accommodate changing views on mathematical objects resulting from the development of infinitesimal mathematics.

How to cite

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Loget, François. "Wallis entre Hobbes et Newton. La question de l’angle de contact chez les anglais." Revue d'histoire des mathématiques 8.2 (2002): 207-262. <http://eudml.org/doc/252090>.

@article{Loget2002,
abstract = {Cet article traite d’un aspect de la controverse qui a opposé Hobbes et Wallis dans la deuxième moitié du xviie siècle, celui portant sur l’angle de contact. Wallis a publié deux traités sur l’angle de contact, l’un en 1656, l’autre en 1685. Entre ces deux dates sa position sur la question de l’angle de contact a sensiblement évolué. Durant la même période, il s’est opposé à Hobbes sur divers sujets de mathématiques, dont l’angle de contact. J’étudie les positions des deux protagonistes à travers les différents textes qu’ils ont consacrés à cette question, y compris dans leurs publications polémiques. J’étudie enfin deux textes écrits durant la même période dans lesquels Newton aborde la question de l’angle de contact et élabore la solution qu’il publiera dans les Philosophiæ naturalis principia mathematica. Je défends l’hypothèse que Wallis a été poussé à changer sa manière de considérer l’angle de contact d’une part pour réagir à la solution originale proposée par Hobbes et d’autre part pour prendre en compte l’évolution de la conception des objets mathématiques issue du développement des mathématiques infinitésimales.},
author = {Loget, François},
journal = {Revue d'histoire des mathématiques},
keywords = {Hobbes; Wallis; Newton; géométrie; angle de contact; Wallis, Newton; angle of contact, angle of contingency, horn angle; non-Archimedean systems},
language = {fre},
number = {2},
pages = {207-262},
publisher = {Société mathématique de France},
title = {Wallis entre Hobbes et Newton. La question de l’angle de contact chez les anglais},
url = {http://eudml.org/doc/252090},
volume = {8},
year = {2002},
}

TY - JOUR
AU - Loget, François
TI - Wallis entre Hobbes et Newton. La question de l’angle de contact chez les anglais
JO - Revue d'histoire des mathématiques
PY - 2002
PB - Société mathématique de France
VL - 8
IS - 2
SP - 207
EP - 262
AB - Cet article traite d’un aspect de la controverse qui a opposé Hobbes et Wallis dans la deuxième moitié du xviie siècle, celui portant sur l’angle de contact. Wallis a publié deux traités sur l’angle de contact, l’un en 1656, l’autre en 1685. Entre ces deux dates sa position sur la question de l’angle de contact a sensiblement évolué. Durant la même période, il s’est opposé à Hobbes sur divers sujets de mathématiques, dont l’angle de contact. J’étudie les positions des deux protagonistes à travers les différents textes qu’ils ont consacrés à cette question, y compris dans leurs publications polémiques. J’étudie enfin deux textes écrits durant la même période dans lesquels Newton aborde la question de l’angle de contact et élabore la solution qu’il publiera dans les Philosophiæ naturalis principia mathematica. Je défends l’hypothèse que Wallis a été poussé à changer sa manière de considérer l’angle de contact d’une part pour réagir à la solution originale proposée par Hobbes et d’autre part pour prendre en compte l’évolution de la conception des objets mathématiques issue du développement des mathématiques infinitésimales.
LA - fre
KW - Hobbes; Wallis; Newton; géométrie; angle de contact; Wallis, Newton; angle of contact, angle of contingency, horn angle; non-Archimedean systems
UR - http://eudml.org/doc/252090
ER -

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