A Tentative Interpretation of the Epistemological Significance of the Encrypted Message Sent by Newton to Leibniz in October 1676

Jean G. Dhombres

Centre Alexandre Koyré-Ecole des Hautes Etudes en Sciences Sociales, Paris, France.

DOI: 10.4236/ahs.2014.31004                

Abstract

In Principia mathematica philosophi? naturalis (1687), with regard to binomial formula and so general Calculus, Newton claimed that Leibniz proposed a similar procedure. As usual within Newtonian style, no explanation was provided on that, and nowadays it could only be decoded by Newton himself. In fact to the point, not even he gave up any mention of Leibniz in 1726 on the occasion of the third edition of the Principia. In this research, I analyse this controversy comparing the encrypted passages, and I will show that at least two ideas were proposed: vice versa and the algebraic handing of series.

Keywords

Leibniz; Newton; Calculus Principia; Binomial Series; Controversy; Vice Versa

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Dhombres, J. (2014). Could or should Gregory of Saint-Vincent have had to use indivisibles to present his own quadrature of the hyperbola that led to the logarithm and to the exponential? To appear in a book by Birkhaüser Verlag, directed by Vincent Jullien, and entitled: Indivisibles.
[2]	Dhombres, J. (2014). Les savoirs mathématiques et leurs pratiques culturelles. Paris: Hermann.
[3]	Guicciardini, N. (1998). Did Newton use his calculus in the principia? Centaurus, 40, 303-344. http://dx.doi.org/10.1111/j.1600-0498.1998.tb00536.x
[4]	Harper, W. L. (2011). Isaac Newton’s scientific method. Oxford: Oxford University Press.
[5]	Huygens, C. (1668). Sur la quadrature arithmétique de l’hyperbole par Mercator et sur la méthode qui en résulte pour calculer les logarithms, d’après les registres de l’académie pour le 17 octobre 1668. Oeuvres de Huygens, 20, 261.
[6]	Koyré, A. (1968). Etudes newtoniennes. Paris: Gallimard.
[7]	Leibniz, G. W. (1686). De geometria recondita et analysi indivisibilium atque infinitorum. Acta Eruditorum. In Math. Schriften, V, 228.
[8]	Mercator, N. (1668). Logarithmotechnia: Sive methodus construendi Logarithmos, nova, accurate, & facilis, scripto antehàc communicata, Anno Sc. 1667. Londres: Wilhelm Godbid.
[9]	Newton, I. (1999). The principia: Mathematical principles of natural philosophy by Isaac Newton (translated by I. Bernard Cohen, Anne Whitman). Berkeley: University of California Press.
[10]	Panza, M. (2005). Newton et l’origine de l’Analyse, 1664-1666. Paris: Blanchard.
[11]	Pensivy, M. (1987). Jalons historiques pour une épistémologie de la série infinie du bin?me. Cahiers d’Histoire et de Philosophie des sciences.
[12]	Rupert Hall, A. (1980). Philosophers at war. The quarrel between Newton and Leibniz. Cambridge: Cambridge University Press. http://dx.doi.org/10.1017/CBO9780511524066
[13]	Turnbull, H. W. (1960). The correspondance of Isaac Newton, Vol. II, 1676-1687. Cambridge: At the University Press.
[14]	Whiteside, D. T. (1960). Patterns of mathematical thought in the later sevententh century. Archive for History of Exact Sciences, 1, 179- 388. http://dx.doi.org/10.1007/BF00327940
[15]	Whiteside, D. T. (1961). Newton’s discovery of the general binomial theorem. Mathematical Gazette, 45, 175-180. http://dx.doi.org/10.2307/3612767
[16]	Whiteside, D. T. (1967-1974). The mathematical papers of Isaac Newton. Cambridge: Cambridge University Press.