In 1692 Newton's friends in Holland informed Wallis that Newton's ‘notions [of fluxions] pass there with great applause by the name of “Leibnitz Calculus Differentialis.”’ Wallis was then publishing his works, and stopped the printing of the preface to the first volume to claim for Newton the invention of fluxions in the two letters sent by Newton to Leibnitz through Oldenburg 13 June and 24 Oct. 1676, ‘ubi methodum hanc Leibnitio exponit tum ante decem annos nedum plures ab ipso excogitatam.’ Newton wrote two letters to Wallis in 1692, giving an account of the method, and they appeared in the second volume of Wallis's ‘Works’ (1695).
The volumes were reviewed in the ‘Acta Lipsica’ for June 1696 (Leibnitz's periodical), and the reviewer found no fault with Wallis for thus claiming the invention for Newton ten years before, but expressed the view that it ought to have been stated, although he admitted that Wallis might possibly be unaware of the fact, that at the date of Newton's letter of 1676 Leibnitz had already constructed his calculus. Leibnitz's letter to Oldenburg, containing a description of his method, was written in 1677.
The matter rested thus till 1699, when Fatio de Duillier referred in a tract on the solid of least resistance to the history of the calculus. He stated that he held Newton to have been the first inventor by several years, ‘and with regard to what Mr. Leibnitz, the second inventor of this calculus, may have borrowed from Newton, I refer to the judgment of those persons who have seen the letters and manuscripts relating to this business.’ Leibnitz replied in the ‘Acta Lipsica’ in May 1700. He asserted that Newton had in his scholium in the ‘Principia’ acknowledged his claim to be an original inventor, and, without disputing or acknowledging Newton's claims of priority, asserted his own right to the discovery of the differential calculus. Duillier sent a reply to the ‘Acta Lipsica,’ but it was not printed.
Newton published his treatise on ‘Quadratures’ in 1704, as an appendix to the ‘Optics.’ In the introduction he repeated the statement already made by Wallis, that he had invented the method in 1665–6. Wallis was now dead (he died in 1703). A review of Newton's work, proved by Gerhardt to have been written by Leibnitz, and admitted by Leibnitz to be his in a letter to Conti, 9 April 1716, appeared in the ‘Acta Lipsica’ for January 1705. In this review (Raphson, History of Fluxions, pp. 103–4), the author wrote, after describing the differential calculus, ‘cujus elementa ab inventore D. Godofredo Gullielmo Leibnitio in his actis sunt tradita.’ ‘Pro differentiis igitur Leibnitianis D. Newtonus adhibet semperque adhibuit fluxiones, iisque tum in suis Principiis Naturæ Mathematicis tum in aliis postea editis eleganter est usus; quemadmodum ut Honorarius Fabrius in sua Synopsi Geometrica motuum progressus Cavallerianæ methodo substituit.’ Newton's friends took this as a charge of plagiarism of a particularly gross character. Newton had copied Leibnitz, so it was suggested, changing his notation, just as Fabri had changed the method of Cavalieri. Newton's own view of it (Brewster, Life of Newton, vol. ii. chap. xv.) was: ‘All this is as much as to say that I did not invent the method of fluxions … but that after Mr. Leibnitz, in his letter of 21 June 1677, had sent me his differential method I began to use, and have ever since used, the method of fluxions.’ Dr. Keill, Savilian professor, replied in a letter to Halley (Phil. Trans. 1708), in which he states that Newton was ‘sine omni dubio’ the first inventor: ‘eadem tamen Arithmetica postea mutatis nomine et notatione modo a Domino Leibnitio in Actis Eruditorum edita est.’ Newton was at first offended at this attack on Leibnitz, but, on reading Leibnitz's review, supported Keill's action. Leibnitz complained of the charge to the Royal Society, and requested them to desire Keill to disown the injurious sense his words would bear. In his letter to Sloane, the secretary, 4 March 1711, he writes: ‘Certe ego nec nomen Calculi Fluxionum fando audivi nec characteres quos adhibuit Ds Newtonus his oculis vidi antequam in Wallisianis operibus prodiêre’ (Royal Society Letter-Book, xiv. 273; Rix, Report on Newton-Leibnitz MSS. p. 18). Keill drew up a letter, read to the society on 24 May 1711, and ordered to be sent to Leibnitz, in which he explained that the real meaning of the passage was that ‘Newton was the first inventor of fluxions, or of the differential calculus, and that he had given in the two letters of 1676 to Oldenburg, transmitted to Leibnitz, “indicia perspicacissimi ingenii viro satis obvia unde Leibnitius principia illius calculi hausit aut haurire potuit”’ (Comm. Epist. p. 110). Leibnitz again appealed to the Royal Society, who appointed a committee to search old letters and papers, and report on the question. In his second appeal (ib. p. 118) Leibnitz accepted the view of the ‘Acta Lipsica’ as his own, stating that no injustice had been done to any party; ‘in illis enim circa hanc rem quicquam cuiquam detractum non reperio, set potius passim suum cuique tributum’ are his words. The committee
