Abstract
Usually, one speaks of mathematization of a natural or social science to mean that mathematics comes to be a tool of such a science: the language of mathematics is used to formulate its results, and/or some mathematical techniques is employed to obtain these results.
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References
J. L. Lagrange, Mechanique analitique, La veuve Desaint, Paris (1788); IInd ed., Mecanique analytique, Coureier, Paris, 2 vols. 1811–1815
C. Tlruesdell, Essays in the History of Mechanics, Springer-Verlag, Berlin, Heidelberg, New York (1968). p. 134. (“A Program toward Rediscovering the Rational Mechanics of the Age of Reason”, first publication in 1960, Archive for History of Exact Sciences, 1,1960-1962, 3-36).
C. Truesdell, A First Course in Rational Continuum Mechanics, vol. 1, p 9, Academic Press, New York, San Francisco, London (1977).
Ref 2, p. 335 (“Recent Advances in Rational Mechanics”, first published, in a different version in Science, 127,1958, pp. 729-739).
Ref 3, vol. I, p- 4. As Truesdell explicitly remarks the term “things” refers here to natural things (as animals, plants, seas, minerals, planets, etc.) and man's artifices.
Ref 2, p. 335 (“Recent Advances [...]”, op. cit.)
I. Newton, Philosophiae naturalis principia. mathematiaca [...], Jussu Soc. Regiae ac Typis J. Streatner, Londini (1687); Praefatio ad lectorem, first page [not numerated], 2nd. ed., without publisher, Catabrigaiæ 1713; 3th ed., apud G. and J. Innys, Londini, (1726).
Ref 2, p. 133-134 (“A Program [...]”, op. cit.)
Ref 7, Præfatio ad lectorem, first page [not numerated]
L. Euler, Mechanica, she motus scientia analytice expasita, ex typ. Acad. sci. imp., Petropoli, 2 vols. (1736).
Ref. 2 p. 106 (“A Program [...]”, op. cit.).
M. Blay, La naissance de la mechanique analytique. La science du mcuvement au tournat desXVIIème et XVIIIème sièle, PUF, Paris (1992).
Ref 12, p. 8.
Ref 12, pp. 153-221 and 277-321, where a complete bibliography of Varignon's papers on this subjects is given.
D. Bertoloni-Meli, Equivalence and Priority: Newton versus Leibniz, pp. 201–205Clarendon Press, Oxford (1993).
C. Fraser, “Classical mechanics”, in I. Grattan-Guinness (ed. by), Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, particularly pp. 973–975 Routledge, London and New York (1994), 2 vols. with continued pagination, pp. 971-986
Ref 16., p. 974.
L. Euler, “Decouverte d'un nouveau principe de mécanique”, Mem. Acad. Sci. Berlin, 6 (1750, publ. 1752), pp. 185–217. Note that in this paper, Euler presents the Nawton's law (in his new formulation) as a “new principle of mechanics” that he pretends to have discovered. Lots of papers have been written on the subject of Newton's second Law where distinct interpretation of it and of its role and meaning in the Principia are discussed. Among the more recent ones, cf. ref 19: Verlet where a large bibliography is given.
L. Verlet, “F=ma and the Newtonian Revolution: an Exit from Religion through Religion”, History of Science, 34 (1996), pp. 303–346.
Aristotle, Physics , in Aritoteles graece, ex recensione I. Bekkeri, editit Academia Regia Borusica, apud G. Reinerium, Berolini, 1831,2 vols., vol. I, pp. 184–267
M. Panza, “Dalla metafisica del moto alia scienza matematica della natura. Considerazioni critiche a proposito di alcuni problemi cinematici trecenteschi”, in L. Bianchi (ed. by), Filosofia e teologia nel trecento. Studi in ricordo di Eugenio Randi, édité par la Fédération Internationale des Instituts d'Etudes Médiévales, Louvain la Neuve (1994), pp. 413–478.
H. Carteron, La notion de force dans le systhéme d'Aristotle, p. 211 Vrin (Paris), (1923).
Ref 20,192b 21
Ref. 20,219b 2.
Ref20,250a4.
E. Giusti, “Galilei e le leggi del moto”, in G. Galilei, Discorsi e dimostrazioni matematiche intorno a due nuove scienze.,,, p. XIII ed. by E. Giusti, Einaudi, Torino (1990), pp. IX–LX
Ref. 26, p. XXIII.
M. Clagett, The Science of Mechanics in the Middle Ages, Univ. of Wisconsin Press, Madison, Wisconsin (1959).
Ref 28 pp. 238 e 241-42 [doc. 4.4. (“William Heytesbury, Rules for Solving Sophisms”), 14-17 e 89-97].
M. Clagett, Nicolas Oresme and the Medieval Geometry of Qualities and Motion. A Treatise on on Uniformity and Difformity of Intensities Known as Tractatus de configurationibus qualitatum et motum (Edited with an Introduction, English Transaltion and Commentary by M. Clagett), The Univ. of Wisconsin Press, Madison, Milwaukee, London (1968).
Ref 21 for discussion of Heytesbury's proof.
G. Galilei, Dialogo [...] sopra i dm Massimi Sitemi del Monado [...], G. B. Landini, Fiorenza (1632) [in G. Galilei, Le Opere, Ed. Nat., a cura di A. Favaro, Barbera, Firenze 20 voll., 2th Giornata (Ed. Nat., pp. 254-256) 1890-1909, vol. VII]
G. Galilei, Discorsi e dimstrazioni matematiche intorno a due nuove scienze..., Appresso gli Esevirii, Leida, 3th Giornata (Ed. Nat, pp. 208–209). (1638) [in G. Galilei, Le Opere, cit., vol. VIII].
E. Giusti, Euclides] reformatus. La teoria delle proporzioni nella scuola galileiana, Bollati Boringhieri, Torino (1993).
E. Giusti, “Aspetti matematici della cinematica galileiana”, Bollettino di storia delle scienze matematiche, 1, p. XXIII (1981), 2, pp. 3–42.
Ref 26 pp. XIII-XLVII.
Ref 26, pp. XXIX-XXX
Ref 35,pl9.
R. Descartes, La Géométrie, in R. Descartes, Discours de la Methode [... ]. pp. 297–298 Plus la Dioptrique. Les Météores. Et la Géométrie qui sont des essaies de cette Méthode, I. Maire, Leyde (1637), pp. 295-413
N. H. Bos and K. Reich, “Der Doppelte Auftakt zur frühneuzeitlichen Algebra: Viète und Descartes”, in E. Scholz (ed. by), Geschichte der Algebra, Wissenschaftverlag, Mannheim, Wien, Zurich (1990), pp. 183–234
V. Jullien, Descartes. La Géométrie de 1637), pp. 75–76, PUF, Paris (1996).
Ref 34 p. 169.
M. Panza, “Quelques distinctions a l'usage de l'historiographie des mathematiques”, in J.-M. Salanskis, F. Rastier, R. Seeps (ed.), Herméneutique: textes, sciences, P.U.F., Paris (1997), pp. 357–383.
J. W. Herivel, The Background of Newton's Principia. A Study od Newton's Dynamical Researches in the Years 1664-1684, Clarendon Press, Oxford (1965).
D. T. Whiteside, “Newtonian Dynamics”, History of Sciences, 5 (1966).
D. T. Whiteside, “The Mathematical Principles underling Newton's Principia Mathematica”, Journal for the History of Astronomy, 1 (1970), pp. 116–138.
I. B. Cohen, Introduction to Newton's Principia, Harvard Univ. Press, Cambridge, Mass., (1971).
F. De Gandt, “Le style mathématique des Principia de Newton”, Revue d'Histoire des Sciences, 39 (1987).
F. De Gandt, Force and Geometry in Newtons's Principia, Princeton Univ. Press, Princeton, (1995).
Les Principia de Newton. Question et commentaires, special issue of the Revue d'histoire des sciences (RVS), 40, 3/4 (1987).
G. Barthélémy, Newton Mécanicien du cosmos, Vrin, Paris (1992).
M. Panza, “Eliminare il tempo: Newton, Lagrange e il problema inverso del moto resistente”, in M. Galuzzi (ed. by), Giornate di storia della matematica (proceedings of the meeting held in Cetraro, September, 8th-12th 1988), Editel, Commenda di Rende, Cosenza (1991), pp. 487-537 (see a discussion of an example of Newton treatment of motion of an isolated body, by comparing it to Lagrange's solution to the same problem
J. Dhombres, “Un style axiomatique dans l'écriture de la physique mathématique au 18éme siéle. Daniel Bernoulli et la composition des forces”, Sciences et Techniques en Perspective, 11 (1986- 1987), pp. 1–38.
J. Dhombres and P. Radelet De Grave, “Contingence et necessité en mecanique. Etude de deux textes inedits de Jean d'Alembert”, Physis, 28 (1991), pp.35–114.
P. Radelet De Grave, “Daniel Bernoulli et le parallélogramme des forces”, Sciences et Techniques en Perspective, 11 (1987), pp. 1–20.
P. Radelet De Grave, “Les forces et leur loi de composition chez Newton”, Revue Philomphique de Louvain, 86 (1988), p. 505–522,
P. Radelet De Grave, La composition des mouvements, des vitesses et des forces“, in H.-J, Hesse uni F. Nagel (hrsg. von), Der Ambau des Calculus durch Leibniz und die Brüder Bernoulli [...], Studio Leibmtiana, Sonderheft 17 (1989), pp. 25–47.
G. W. Leibniz, “Nova methodus pro maximis et minimis [...]”, Acta Eruditorum (1684), pp. 467–473.
Ref 12 part. l, ch. 3, pp. 63-109, where the necessary bibliographical references are given.
Ref 12, p. 109.
Ref 12 part. II, ch. 1, pp- 113-152, where the necessary bibliographical references are given.
Ref 12 p. 129.
Ref 12, pp. 150 and 152.
Ref 12, part II, ch. 2, pp. 153-221, where the necessary bibliographical references are given.
Ref 12, p. 161.
Ref 15, pp. 208-215, where a bibliography is given for the famous controversy on the inverse problem of central forces.
I. Newton, Philosophiæ naturalis principia mathematiaca, perpetuis Commentariis illustata, communi studio PP. T. Le Seur & F. Jacquier, Barrillot & Filli, 3 toms in 4 vols., 1739-1742 (G).
P. Varignon, “Du mouvement en general partout sorte de courbes, et des forces centrales, tant centrifuge que centripétes, necessaires aux corp qui les décrivent”, Hist. Acad. Roy. Sci. [de Paris], Mem. Math. Phy., (1700, publ. 1703; pres. 31/3/1700), pp. 83–101.
Refl2, pp. 193-213.
Ref 68, p. 85.
Ref 12, pp 197-198.
P. Varignon, “Des mouvements faits das des milieux qui leur resistent en raison quelconque”, Hist. Acad. Roy. Sci. [de Paris], Mem. Math. Phy. (1707, publ. 1708; pres. 13-17/8/1707), pp. 382–476.
Ref 12, pp. 280-299.
Jean Bernoulli, Discours sur les loix de la communication du mouvement [...], C. Jombert, Paris (1727).
M. Otte and M. Panza (ed, by) Analysis and Synthesis in Mathemetics. History and Philsophy, Boston Studies in the Philosophy of Science, 196, Kluwer, Dordrech, Boston, London, (1997).
Ref. 75, M. Panza, “Classical sources for the concepts of analysis and synthesis”, pp. 365-414.
M. Panza, La forma della quantita. Analisi algebrica e analisi superiore: il problema dell'unità della matemetica nel secolo dell'Illuminismo, Cashiers d'Histoire et de Philosophie des Sciences, 38 and 39, Ch. II.2. (1992).
J. B. 1. R. d' Alembert, “Eléments des sciences” (1st part), in Encyclopédie, ou dictionnaire raisonné des sciences, des arts et de métiers, Briasson, David 1'ainé, le Breton, Durand, Paris, 1751-1780, 35 vols., vol. V, 1755, pp. 491a–497a.
M. Panza, “De la nature épargante aux forces généreuses : le principe de moindre action entre mathématiques et métaphysique. Maupertuis et Euler, 1740, 1751”, Revue d'histoire des Sciences, 48 (1996), pp. 435–520.
M. Panza, “Die Entstehung der analytischen Medianik im 18. Jahrhundert”, in H. N. Jahnke (Hrsg.), Geschichte der Analysis, Spektrum Akad. Verl., Heidelberg, Berlin (1999), pp. 171–190.
I. Kant, Kritik der reinen Vernunft, Hartknoch, Riga, 1787; ibid., vol. III, 1911, pp. 1–552 (B).
I. Kant, Kritik der reinen Vernunft, Hartknoch, Riga, 1781; the pages 1 -405 are in Kant's gesammelte Schriften (herausg. von de Königlich Preukischen Akademie der Wissenschaften; after: Deutsche Academie der Wissenschaften zu Berlin; after: Academie der Wissenschaften der D.D.R.), G. Reimer and (from 1922) W. De. Gruyter, Berlin (1900-...), vol. IV, 1911, pp. 1-252 (A).
M. Panza, “De la nature épargante aux forces géneréuses : le principe de moindre action entre mathématiques et métaphysique. Maupertuis et Euler, 1740, 1751”, Revue d'histoire des Sciences, 48 (1996), pp. 435–520.
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Panza, M. (2002). Mathematisation of the Science of Motion and the Birth of Analytical Mechanics: A Historiographical Note. In: Cerrai, P., Freguglia, P., Pellegrini, C. (eds) The Application of Mathematics to the Sciences of Nature. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0591-4_19
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