Euler, Reader of Newton: Mechanics and Algebraic Analysis

Abstract

We follow two of the many paths leading from Newton’s to Euler’s scientific productions, and give an account of Euler’s role in the reception of some of Newton’s ideas, as regards two major topics: mechanics and algebraic analysis. Euler contributed to a re-appropriation of Newtonian science, though transforming it in many relevant aspects. We study this re-appropriation with respect to the mentioned topics and show that it is grounded on the development of Newton’s conceptions within a new conceptual frame also influenced by Descartes’s views sand Leibniz’s formalism.

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Maronne, S. & Panza, M. (2014). Euler, Reader of Newton: Mechanics and Algebraic Analysis. Advances in Historical Studies, 3, 12-21. doi: 10.4236/ahs.2014.31003.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Aiton, E. J. (1989). The contributions of Isaac Newton, Johann Bernoulli and Jakob Hermann to the inverse problem of central forces. In H.-J. Hess (Ed.), Der ausbau des calculus durch leibniz und die brüder Bernoulli, Studia Leibnitiana, Sonderhefte (pp. 48-58). Stuttgart: Steiner-Verlag.
[2] Backer, R. (Ed.) (2007). Euler reconsidered. Tercentenary essays. Heber City: Kendrick Press.
[3] Bartoloni-Meli, D. (1993). The emergence of reference frames and the transformation of mechanics in the Enlightenment. Historical Studies in the Physical Sciences, 23, 301-335.
[4] Blay, M. (1992). La naissance de la mécanique analytique. Paris: PUF.
[5] Bos, H. J. M. (2001). Redefining geometrical exactness. Descartes’ transformation of the early modern concept of construction. Sources and studies in the history of mathematics and physical sciences. New York: Springer.
[6] Bradley R., & Sandifer, E. (2007). Leonhard Euler. Life, work and legacy. Amsterdam: Elsevier.
[7] Calinger, R. (1976). Euler’s letters to a princess of Germany as an expression of his mature scientific outlook. Archive for History of Exact Sciences, 150, 211-233.
[8] Cassirer, E. (1907). Das erkenntnisproblem in der philosophie und wissenschaft der neueren zeit, vol. II. Berlin: Bruno Cassirer.
[9] Descartes, R. (1637). La géométrie. In Discours de la méthode pour bien conduire sa raison et chercher la vérité dans les sciences. Plus la dioptrique. Les météores & la géométrie qui sont des essais de cette méthode (pp. 297-413). Leyde: I. Maire.
[10] Euler, L. (1736). Mechanica, sive motus scientia analytice exposita. 2 vols. Petropoli: Ex Typographia Academiae Scientiarum. In (Euler, OO, Series II, 1-2).
[11] Euler, L. (1743). De causa gravitatis [publ. anonymously]. Miscellanea Berolinensia, 7, 360-370. In (Euler, OO, Series II, 31, 373-378).
[12] Euler, L. (1744). Methodus inveniendi lineas curvas maxime minimive proprietate gaudentes. Lausanæ et Genevæ: M. M. Bousquet et Soc. In (Euler, OO, Series I, 24).
[13] Euler, L. (1746). De la force de percussion et de sa véritable mesure. Mémoires de l’Académie des Sciences de Berlin, 1, 21-53. In (Euler, OO, Series II, 8, 27-53).
[14] Euler, L. (1748). Introductio in analysin infinitorum. Lausanæ: Apud Marcum-Mich ælem Bousquet & Socios. In (Euler, OO, Series I, 8-9).
[15] Euler, L. (1748). Recherches sur les plus grands et les plus petits qui se trouvent dans les actions des forces. Histoire de l’Académie Royale des Sciences et des Belles Lettres [de Berlin], 4, 149-188. In (Euler, OO, Series I, 5, 1-37).
[16] Euler, L. (1748). Réflexions sur quelques loix générales de la nature qui s’observent dans les effets des forces quelconques. Histoire de l’Académie Royale des Sciences et des Belles Lettres [de Berlin], 4, 183-218. In (Euler, OO, Series I, 5, 38-63).
[17] Euler, L. (1750). Recherche sur l’origine des forces. Mémoires de l’Académie des Sciences de Berlin, 6, 419-447. In (Euler, OO, Series II, 5, 109-131).
[18] Euler, L. (1750). Découverte d’un nouveau principe de mécanique. Mémoires de l’Académie des sciences de Berlin, 6, 185-217. In (Euler, OO, Series II, 5, 81-110).
[19] Euler, L. (1751). Harmonie entre les principes generaux de repos et de mouvement de M. de Maupertuis. Histoire de l’Académie Royale des Sciences et des Belles Lettres [de Berlin], 7, 169-198. In (Euler, OO, Series I, 5, 152-172).
[20] Euler, L. (1751). Essay d’une démonstration métaphysique du principe générale de l’équilibre. Histoire de l’Académie Royale des Sciences et des Belles Lettres [de Berlin], 7, 246-254. In (Euler, OO, Series II, 5, 250-256).
[21] Euler, L. (1751). Sur le principe de la moindre action. Histoire de l’Académie Royale des Sciences et des Belles Lettres [de Berlin], 7, 199-218. In (Euler, OO, Series I, 5, 179-193).
[22] Euler, L. (1755). Institutiones calculi differentialis cum eius usu in analysi finitorum ac doctrina serierum. Impensis Academia Imperialis Scientiarum Petropolitan?. Berolini: ex officina Mich?lis, Reprint (1787), Ticini: typographeo P. Galeatii [we refer to this reprint]. Also in (Euler, OO, Series I, 10).
[23] Euler, L. (1765). Theoria motus corporum solidorum seu rigidorum [...]. Rostochii et Gryphiswaldi?: litteris et impensis A. F. R?se. In (Euler, OO, Series II, 3).
[24] Euler, L. (1768). Institutionum Calculi Integralis, 3 vols. Petropoli: Impensis Academia Imperialis Scientiarum. In (Euler, OO, Series 1, 11-13).
[25] Euler, L. (1768-1772). Lettres à une princesse d’Allemagne sur divers sujets de physique & de philosophie (3 vols.). Saint-Petersbourg: Imprimerie de l’Académie Impériale des Sciences. In (Euler, OO, Series III, 11-12).
[26] Euler, L (LPAH). Letters of Euler on different subjects in natural philosophy. Adressed to a German Princess (2 vols.). Translation of (Euler, 1768-1772) by H. Hunter. 3rd Edition. Edinburgh: Printed for W. and C. Tait [...].
[27] Euler, L. (IAIB). Introduction to analysis of the infinite. New York, Berlin: Springer Verlag. English Translation of (Euler, 1748) by J. D. Blanton, 2 vols.
[28] Euler, L. (ICDB). Foundations of differential calculus. New York, Berlin: Springer Verlag. English translation of (Euler, 1755, Vol. I) by J. D. Blanton.
[29] Euler, L. (OO). Leonhardi Euleri Opera Omnia (76 vols). Leipzig, Berlin, Basel: Societas Scientiarum Naturalium Helvetic?.
[30] Euler, L. The Euler archive. The works of Leonhard Euler online. http://math.darmouth.edu/euler
[31] Ferraro, G. (2004). Differentials and differential coefficients in the eulerian foundations of the calculus. Historia Mathematica, 31, 34-61.
[32] Fraser, C. G. (1983). J. L. Lagrange’s eraly contributions to the principles and methods of mechanics. Archive for History of Exact Sciences, 28, 197-241.
[33] Fraser, C. G. (1985). D’Alembert principle: The original formulation and application in Jean d’Alembert’s Traité de Dynamique (1743). Centaurus, 28, 31-61 and 145-159.
[34] Fraser, C. G. (1989). The calculus as algebraic analysis: Some observations on mathematical analysis in the 18th century. Archive for History of Exact Sciences, 390, 317-335.
[35] Fraser, C. G. (1994). The origins of Euler’s variational calculus. Archive for History of Exact Sciences, 470, 103-141.
[36] Fraser, C. G. (2003). The calculus of variations: A historical survey. In H. N. Jahnke (Ed.), A history of analysis (pp. 355-384). New York: American Mathematical Society and London Mathematical Society.
[37] Galuzzi, M. (1990). I marginalia di Newton alla seconda edizione latina della Geometria di Descartes e i problemi ad essi collegati. In G. Belgioioso (Ed.), Descartes, Il metodo e i saggi. Atti del Convegno per il 350e anniversario della pubblicazione del Discours de la Méthode e degli Essais (2 vols) (pp. 387-417). Firenze: Armando Paoletti.
[38] Gaukroger, S. (1982). The metaphysics of impenetrability: Euler’s conception of force. The British Journal for the History of Science, 15, 132-154.
[39] Guicciardini, N. (1995). Johann Bernoulli, John Keill and the inverse problem of central forces. Annals of Science, 52, 537-575.
[40] Guicciardini, N. (1996). An episode in the history of dynamics: Jakob Hermann’s proof (1716-1717) of Proposition 1, Book 1, of Newton’s Principia. Historia Mathematica, 23, 167-181.
[41] Guicciardini, N. (1999). Reading the Principia: The debate on Newton’s mathematical methods for natural philosophy from 1687 to 1736. Cambridge: Cambridge University Press.
[42] Guicciardini, N. (2004a). Dot-age: Newton’s mathematical legacy in the eighteenth century. Early Science and Medicine, 9, 218-256.
[43] Guicciardini, N. (2004b). Geometry and mechanics in the preface to Newton’s Principia: A criticism of Descartes’ Géométrie. Graduate Faculty Philosophy Journal, 25, 119-159.
[44] Hermann, J. (1716). Phoronomia, sive de viribus et motibus corporum solidorum et fluidorum libri duo. Amstelædami: Apud R. & G. Wet-stenios H. FF.
[45] Lagrange, J. L. (1761). Applications de la méthode exposée dans le mémoire précédent à la solution de différents problèmes de dynamique. Mélanges de Philosophie et de Mathématiques de la Société Royale de Turin, 2, 196-298.
[46] Maclaurin, C. (1742). A treatise of fluxions: In two books. Edinburgh: T.W. and T. Ruddimans.
[47] Maglo, K. (2003). The reception of Newton’s Gravitational Theory by Huygens, Varignon, and Maupertuis: How normal science may be revolutionary. Perspectives on Science, 11, 135-169.
[48] Maltese, G. (2000). On the relativity of motion in Leonhard Euler’s science. Archive for History of Exact Sciences, 54, 319-348.
[49] Maupertuis, P. L. M. (1740). Loi du repos des corps. Histoire de l'Académie Royale des Sciences [de Paris], Mémoires de Mathématiques et Physique, 170-176. In (Euler, OO, Ser. II, 5, 268-273).
[50] Maupertuis, P. L. M. (1744). Accord de différentes loix de la nature qui avoient jusqu’ici paru incompatibles. Histoire de l’Académie Royale des Sciences de Paris, 417-426. In (Euler, OO, Ser. II, 5, 274-281).
[51] Maupertuis, P. L. M. (1746). Les Loix du mouvement et du repos déduites d’un principe métaphysique. Histoire de l’Académie Royale des Sciences et des Belles Lettres de Berlin, 267-294. In (Euler, OO, Ser. II, 5, 282-302).
[52] Maupertuis, P. L. M. (1750). Essay de Cosmologie. s. n., s. l.
[53] Maupertuis, P. L. M. (1756). Examen philosophique de la preuve de l’existence de dieu employée dans l'essai de cosmologie. Histoire de l’Académie Royale des Sciences et des Belles Lettres [de Berlin], 12, 389-424.
[54] Mazzone, S., & Roero, C. S. (1997). Jacob Hermann and the diffusion of the Leibnizian Calculus in Italy. Biblioteca di “Nuncius”: Studi e testi, 26. Firenze: Olchski.
[55] Newton, I. (1670-1671). De methodis serierum et fluxionum. In (Newton, MWP, vol. 3, chapter 1, pp. 32-254).
[56] Newton, I. (1687). Philosophi æ naturalis Principia Mathematica. Londini: Iussu Societatis regiae ac Typis Josephi Streater. [2nd ed. (1713), Cantabrigiæ; 3rd ed. (1726), Londinis: apud G. & J. Innys].
[57] Newton, I. (1704a). Opticks or a treatise of the reflexions, refractions, inflexions and colours of light. Also two treatises of the species and magnitude of curvilinear figures. London: Printed for S. Smith and B. Walford.
[58] Newton, I. (1704b). Enumeratio linearum tertii ordinis. In (Newton, 1704a, 138-162 of the second numbering).
[59] Newton, I. (1704c). Tractatus de quadratura curvarum. In (Newton, 1704a, 163-211 of the second numbering).
[60] Newton, I. (1756). Four letters from Sir Isaac Newton to doctor Bentley containing some arguments in proof of a deity. London: Printed for R. and J. Dodsley.
[61] Newton, I. (MWP). The mathematical papers of Isaac Newton (8 vol.). Edited by D.T. Whiteside. Cambridge: Cambridge University Press.
[62] Newton, I. (PMCW). The Principia. Mathematical Principles of Natural Philosophy. A New Translation by I. Bernard Cohen and Anne Whitman, assisted by Julia Budenz, preceded by a Guide to Newton’s Principia by I. Bernard Cohen. Berkeley, Los Angeles, London: University of California Press.
[63] Panza, M. (1992). La forma della quantità. Analisi algebrica e analisi superiore: Il problema dell'unità della matematica nel secondo dell’illuminismo (2 vols.). Number 38-39 in Cahiers d’histoire et de philosophie des sciences. Nouvelle série. Paris: Société française d’histoire des sciences.
[64] Panza, M. (1995). De la nature épargnante aux forces généreuses. Le principe de moindre action entre mathématique et métaphysique: Maupertuis et Euler (1740-1751). Revue d’Histoire des Sciences, 48, 435-520.
[65] Panza, M. (2002). Mathematisation of the science of motion and the birth of analytical mechanics: A historiographical note. In P. Cerrai, P. Freguglia, & C. Pellegrini (Eds.), The Application of Mathematics to the Sciences of Nature. Critical moments and Aspects (pp. 253-271). New York: Kluwer/Plenum publishers.
[66] Panza, M. (2003). The origins of analytic mechanics in the 18th century. In H. N. Jahnke (Ed.), A History of Analysis (pp. 137-153). New York: American Mathematical Society and London Mathematical Society.
[67] Panza, M. (2005). Newton et les origines de l’analyse: 1664-1666. Paris: Librairie Albert Blanchard.
[68] Panza, M. (2007a). What is new and what is old in Viète’s analysis restituita and algebra nova, and where do they come from? Some reflections on the relations between algebra and analysis before Viète. Revue d’Histoire des mathématiques, 13, 85-153.
[69] Panza, M. (2007b). Euler’s Introductio in analysin infinitorum and the program of algebraic analysis: quantities, functions and numerical partitions. In R. Backer (Ed.), Euler reconsidered. Tercentenary essays (pp. 119-166). Heber City: Kendrick Press.
[70] Panza, M. (2012). From velocities to fluxions. In A. Janiak, & E. Schliesser (Eds.), Interpreting Newton: Critical essays (pp. 219-254). Cambridge: Cambridge University Press.
[71] Pappus (CMH). Pappi Alexandrini Collectionis [...]. Edited with Latin translation and commentary by F. Hultsch. 3 vols. Berolini: Weidmann.
[72] Pulte, H. (1989). Das prinzip der kleinsten wirkung und die kraftkon-zeptionen der rationalen mechanik. Volume 19 of Studia Leibnitiana. Stuttgart: F. Steiner Verlag.
[73] Rashed, R. (2005). Les premières classifications des courbes. Physis, 42, 1-64.
[74] Romero, A. (2007). La Mécanique d’Euler: Prolégomènes à la pensée physique des milieux continus [...]. Ph.D. Thesis, Paris: Université Paris Diderot—Paris 7.
[75] Schroeder, P. (2007). La loi de la gravitation universelle. Newton, Euler et Laplace. Paris: Springer.
[76] Szabó, I. (1987). Geschichte der mechanischen prinzipien. Basel, Boston, Stutgart: Birkhäuser.
[77] Truesdell, C. A. (1960). The rational mechanics of flexible or elastic bodies, 1638-1788. Bale: Birkhäuser. In (Euler, OO, Ser. II, 11, 2).
[78] Truesdell, C. A. (1968). Essays in the history of mechanics. Berlin: Springer.
[79] Truesdell, C. A. (1970). Reactions of late baroque mechanics to success, conjecture, error, and failure in Newton’s Principia. In Robert Palter, (Ed.), The annus mirabilis of sir Isaac Newton 1666-1966 (pp. 192-232). Cambridge, Mass.: MIT Press.
[80] Varignon, P. (1725). Nouvelle mécanique ou statique. 2 vols. Paris: C. Jombert.
[81] Viète, F. (1591). In artem analiticem isagoge. Turonis: J. Mettayer.
[82] Wilson, C. (1992). Euler on action at a distance and fundamental equations in continuum mechanics. In P. M. Harman, & A. E. Shapiro, (Eds.), The investigation of difficult things (pp. 399-420). Cambridge: Cambridge University Press.

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