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Nicole's Contribution to the Foundations of the Calculus of Finite Differences

Published online by Cambridge University Press:  20 January 2009

Charles Tweedie
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While engaged in a study of the Methodus Differentialis of Jas. Stirling (1730) I have been struck by the fact that Nicole's Papers on the same subject, printed in the Memoires de l'Academie Royale des Sciences (Paris), appear to form a fitting prelude to the work published by Stirling. The dates of Nicole's Papers are 1717, 1723, 1724, 1727, and it is almost certain that Stirling was well acquainted with their contents, for he remarks on page 24 of the Methodus Differentialis:—“Hac de re primus quod sciarn egit D. Taylor in Methodo Incrementorum. Eadem etiam fusius et elegantissime traditur a D. Nicol in Actis Academiae Regiae Parisiensis.”

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 36 , February 1917 , pp. 22 - 39
Copyright
Copyright © Edinburgh Mathematical Society 1917

References

* Francois Nicole (1683–1758), described by Cantor as a pupil of Montmort, published at the age of nineteen “The Rectification of the Cissoid.” In addition to his memoirs on finite differences, he also wrote several memoirs on geometry and probability.

* Meth. Diff., p. 12.

* Really due to Newton, see § 14.

* “De descriptione Curvae Parabolici generis per data quotcunque punctaegerunt plures celebres Geometrae post Newtonum. Sed omnes eorum solutiones eaedem stunt cum hisce jam exhibitis ; quae quidem a Newtonianis vix discrepant, etc.”

* Pierrc Remond de Montmort, born at Paris in 1678, and left with a sufficient patrimony, devoted himself to the study of mathematics. In 1715, accompanied by the Abbé Conti, he visited London, and made the acquaintance of Newton and other scholars. During his stay in London he had more particularly the help of his compatriot Demoivre, who writes in his Miscellanea Analytica, p. 149:—“Habuit me comitem, interpretem, ductorem ; apud Newtonum aliosque doctos viros admissus est, urbaniter ab iis exceptus, tandemque Societati Regiae annumeratus.” His Essai d'Analyse sur les jeux de Hazard appeared in 1708 and in 1713. He died in 1719.