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.
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.
@article{RHM_2002__8_2_207_0,
author = {Loget, Fran\c{c}ois},
title = {Wallis entre {Hobbes} et {Newton.} {La} question de l'angle de contact chez les anglais},
journal = {Revue d'histoire des math\'ematiques},
pages = {207--262},
publisher = {Soci\'et\'e math\'ematique de France},
volume = {8},
number = {2},
year = {2002},
zbl = {1052.01003},
language = {fr},
url = {http://archive.numdam.org/item/RHM_2002__8_2_207_0/}
}
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 SP - 207 EP - 262 VL - 8 IS - 2 PB - Société mathématique de France UR - http://archive.numdam.org/item/RHM_2002__8_2_207_0/ LA - fr ID - RHM_2002__8_2_207_0 ER -
%0 Journal Article %A Loget, François %T Wallis entre Hobbes et Newton. La question de l'angle de contact chez les anglais %J Revue d'histoire des mathématiques %D 2002 %P 207-262 %V 8 %N 2 %I Société mathématique de France %U http://archive.numdam.org/item/RHM_2002__8_2_207_0/ %G fr %F RHM_2002__8_2_207_0
Loget, François. Wallis entre Hobbes et Newton. La question de l'angle de contact chez les anglais. Revue d'histoire des mathématiques, Tome 8 (2002) no. 2, pp. 207-262. http://archive.numdam.org/item/RHM_2002__8_2_207_0/
[1] [1656] Francisci Xavierii Aynscom, [...] Expositio ac deductio geometrica quadraturarum circuli R.R. Gregorii a S. Vincentio [...] cui præmittitur liber de natura et affectionibus rationum ac proportionum geometricarum, Anvers : J. Meursium, 1656.
[2] [1996] Squaring the Circle : Hobbes on Philosophy of Geometry, Journal of the History of Ideas, 57 (1996), p.19-38. | MR
[3] [1658] Euclides restitutus, sive prisca geometriæ Elementa, Brevius & facilius contexta, in quibus præcipue proportionum theoriæ, nova, firmiorique Methodo promuntur a Io : Alphonso Borellio in Messanensi pridem, nunc vero in Pisana Academia Matheseos Professore, Pise : F. Honophrius, 1658.
[4] [1979] Les mathématiques et la méthode mathématique chez Hobbes, Revue internationale de philosophie, 33 (1979), p.415-431. | MR
[5] [1574] Euclidis Elementorum libri XV. Accessit XVI solidorum Regularium comparatione. Omnes perspicuis demonstrationibus accuratisque scholiis illustrati, Rome : V. Accoltum, 1574.
[6] [1589] Euclidis Elementorum libri XV, accessit XVI de solidorum regularium cujuslibet intra quodlibet comparatione, omnes perspicuis demonstrationibus accuratisque scholiis illustrati, nunc iterum editi, ac multarum rerum accessione locupletati, Rome : apud Sanctium et Socios, 1589.
[7] EUCLIDE [1990-2001] Les Éléments-Introduction générale par M. Caveing-Traduction et commentaires par B.Vitrac, Paris : PUF, 1990-2001 (4 vol.).
[8] [1948] Sir Isaac Newton's Notebook, 1661-1665, Cambridge Historical Journal, 9-2 (1948), p.239-250.
[9] [Works] The English works of T. Hobbes of Malmesbury, now first collected and edited by Sir William Molesworth, bart., Londres : Longmans, Browns, Green and Longmans, 1839-1845 (11 vol.).
[10] [Opera] Thomæ Hobbes Malmesburiensis Opera philosophica quæ latine scripsit omnia in unum corpus nunc primum collecta studio et labore Gulielmi Molesworth, Londres : J. Bohn, 1839-1845 (7 vol.).
[11] [1655/2000]Elementorum philosophiæ sectio prima : de Corpore [...], Londres : A.Crooke, 1655 ; éd. citée : Elementa Philosophiæ I : De corpore, éd. Karl Schumann, Paris : Vrin, 2000.
[12] [1656] Elements of Philosophy, the first section, concerning body. Written in Latine [...] and now translated into English. To which are added Six Lessons to the Savilian professors of the Mathematicks of the Institution of Sir Henry Savile, in the University of Oxford, Londres : R. & W. Leybourn, for A.Crooke, 1656 ; [Hobbes, Works, VII, p.181-356].
[13] [1657] ΣΤΙΓΜΑΙ Αγεωμετρίας, Αγποικίας, Αντίπολιτείας, Αματηϑείας, or Marks of the absurd geometry, rural language, scottish church politics and barbarisms of John Wallis, Professor of geometry and doctor of divinity, Londres, 1657.
[14] [1660] Examinatio et emendatio mathematicæ hodiernæ, qualis explicatur in libris Walisii, [...] distributa in sex dialogos, Londres : A. Crooke, 1660 ; [Hobbes, Opera, IV, p.1-232].
[15] [1666] De Principiis et Ratiocinatione Geometrarum ubi ostenditur incertitudinem falsitatemque non minorem inesse scripti eorum, quam scripti physicorum et ethicorum. Contra fastum professorum Geometriæ, s.l., 1666 ; [Hobbes, Opera, IV, p.385-465].
[16] [1671] Rosetum geometricum, sive Propositiones aliquot frustra antehac tentatæ, cum censura brevi doctrinæ Wallisianæ de motu [...], Londres : G. Crooke, 1671.
[17] [1672] Lux mathematica ; excussa collisionibus J. Walisii Theologiæ doctoris geometriæ in celeberrima academia oxoniensi professoris publici et T. Hobbesii malmesburiensis. Multis et fulgentibus aucta radiis authore R.R., Londres : G. Crook, 1672.
[18] [1674] Principia et problemata aliquot geometrica antehac desperata nunc breviter explicata et demonstrata, Londres : G. Crook, 1674 ; [Hobbes, Opera, V, p.151-214].
[19] [1973] Critique de De mundo de Thomas White, H.W. Jones (éd.), Paris : J. Vrin, 1973.
[20] [Œuvres]Œuvres complètes de Christiaan Huygens, Société hollandaise des sciences (éd.), La Haye : Martinus Hijhoff, 1888-1950 (22 vol.). | JFM
[21] [1993] Hobbes on Method of Modern Mathematics, Revue d'histoire des sciences, 46 (1993), p.153-193. | MR | Zbl
[22] [1998] Leibniz on the Foundations of the Calculus : The Question of the Reality of Infinitesimal Magnitudes, Perspectives on Science, 6 (1996), p.6-40. | MR
[23] [1999] Squaring the Circle - The War between Hobbes and Wallis, Chicago : University of Chicago Press, 1999. | MR | Zbl
[24] [1663] Cyclomathia, seu Multiplex circuli contemplatio, tribus libris comprehensa [...], Lyon : B. Coral, 1663.
[25] [2000] La querelle de l'angle de contact (1557-1685) - Constitution et autonomie de la communauté mathématique entre Renaissance et Âge baroque, thèse de doctorat, Paris : EHESS, 2000.
[26] [1984] La polemica fra J.Peletier e C.Clavio circa l'angolo di contatto, Atti del Convegno Internazionale “Storia degli studi sui fondamenti della Matematica e connessi sviluppi interdisciplinari”, Pisa-Tirrenia, 26-31 marzo 1984, Luciani, vol. I, p.226-256.
[27] [1988] John Wallis : lettura della polemica fra Peletier e Clavio circa l'angolo di contatto, dans M. Galluzzi (éd.), Atti del Convegno ‘Giornate di storia della matematica', Cetraro, 8-12 settembre 1988, p.318-365. | Zbl
[28] [1990] ‘... in Christophorum Clavium De Contactu Linearum Apologia' - Considerazioni attorno alla polemica fra Peletier e Clavio circa l'angolo di contatto (1579-1582), Archive for History of Exact Sciences, 41 (1990) p.115-137. | MR | Zbl
[29] [1992] Filologia, epistemologia e contenuti matematici in Henry de Monantheuil circa l'angolo di contatto, dans Conti (L.), éd., Momenti di cultura matematica fra '500 e '600. La matematizzazione dell'universo, Assisi : Porziuncola, 1992, p.105-130.
[30] [1997] Barrow, Wallis and the Remaking of 17th Century Indivisibles, Centaurus, 12 (1997), p.11-22. | MR | Zbl
[31] [Math. Papers] The Mathematical Papers, of Isaac Newton [...] Edited by D.T. Whiteside [...], Londres : Cambridge University Press, 1967-1981 (8 vol.). | MR | Zbl
[32] [1687] Philosophiæ naturalis principia mathematica, Londres : J. Streater, 1687.
[33] [Correspondence] The Correspondence of Henry Oldenburg - Edited and Translated by A. Rupert Hall & Marie Boas Hall, Madison and Milwaukee : University of Wisconsin Press, 1965-1986. | Zbl
[34] [1557] Jacobi Peletarii Cenomani In Euclidis Elementa Geometrica Demonstrationum Libri sex. Ad Carolum Lotharingum, Principem, Cardinalemque amplissimum, Lyon : J. Tornèse et G. Gaza, 1557.
[35] [1563] Jacobi Peletarii Cenomani Commentarii tres : I. de dimensione circuli ; II. de contactu linearum et de duabus lineis in eodem plano neque parallelis neque concurrentibus ; III. de constitutione horoscopi, Bâle : J. Oporinum, 1563.
[36] [1579] Jacobi Peletarii Cenomani In Christophorum Clavium, de Contactu linearum apologia. Ejusdem Demonstrationes tres : I. de Anguli rectilinei et curvilinei aequalitate ; II. de Lineae rectae in treis parteis continue proportionales sectione ; III. de Areae trianguli ex numeris aestimatione, Paris : H. de Marnef et G. Cavellat, 1579.
[37] [1581] Jacobi Peletarii medici et mathematici, De Contactu Linearum. Commentarius, Paris : R. Coulombel, 1581.
[38] [1993] Infinity and Creation : The Origin of the Controversy between T. Hobbes and the Savilian Professors Seth Ward and John Wallis, British Journal for the History of Science, 26 (1993), p.271-279. | MR | Zbl
[39] [1841] Miscellaneous Works and Correspondence of the Rev. James Bradley, Oxford : Clarendon Press, 1841 (2 vol.).
[40] [1980] Hobbes : The Art of the Geometricians, Journal of the History of Philosophy, 16 (1980), p.33-45.
[41] [1981] Hobbes : Geometrical objects, Philosophy of Science, 48 (1981), p.573-590. | MR
[42] [1621] Prælectiones tresdecim in principium Elementorum Euclidis Oxoniæ habitæ, Oxford : J. Lichfield, 1621.
[43] [1654] Elementa geometriæ planæ ac solidæ : Quibus accedunt selecta ex Archimedæ theoremata, Anvers : J. Meursium, 1654.
[44] [1655] J.W. [...] Elenchus geometriæ Hobbianæ ; sive, geometricorum quæ in ipsius elementis philosophiæ, a Thoma Hobbes [...] proferuntur refutatio, Oxford, 1655.
[45] [1656a] Due correction for Mr Hobbes. Or schoole discipline, for not saying his lessons right. In answer to his Six lessons, directed to the professors of mathematicks. By the professor of Geometry, Oxford : L. Lichfield for T. Robinson, 1656.
[46] [1656b] J.W. [...] Operum mathematicorum pars altera : qua continentur De angulo contactus & semicirculi disquisitio geometrica. De sectionibus conicis tractatus. Arithmetica infinitorum [...] Ecclipseos solaris observatio, Oxford : L. Lichfield, 1656.
[47] [1657] Hobbiani Puncti Dispunctio, or, the undoing of Mr Hobs's points, in answer to M. Hobs's Stigmai, id est Stigmata Hobbii, Oxford, 1656.
[48] [1662] Hobbius Heauton-timorumenos. Or a consideration of Mr. Hobbes his dialogues. In an epistolary discourse adressed to the Hon. R. Boyle, Oxford, 1662.
[49] [1685] A Treatise of Algebra [...] with some Additional Treatises. Of the Angle of Contact, with other things appertaining to the composition of Motion, with the results thereof, Londres : J. Playford, R. Davis, 1685.
[50] [1693-1699] Opera mathematica, Oxford : The Sheldonian Theater, 1693-1699 (3vol.).
[51] [1654] Vindiciæ Academiarum. Containing some briefe animadversions upon Mr Websters book, stiled, The Examination of Academies. Together with an appendix concerning what M. Hobbs and M. Dell have published on this argument, Oxford : L. Lichfield for T. Robinson, 1654.
[52] [1656] In T. Hobbii philosophiam exercitatio epistolica [...] Cui subjicitur appendicula ad calumnias ab eodem Hobbio [...] in authorem congestas responsoria, Oxford, 1656.
[53] [1980] Never at Rest-A Biography of Isaac Newton, Cambridge, New York : Cambridge University Press, 1980. | MR | Zbl
[54] [1642] De mundo dialogi tres, quibus materia, forma, caussae, et tandem definitio, rationibus pure e natura depromptis aperiuntur, concluduntur, Paris : Moreau, 1642.
