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John Keill

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Kiell was in the thick of it, as bright as any of the Harvard Dons.

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Community entry: John Keill

(Born: 1 Dec 1671 in Edinburgh, Scotland Died: 31 Aug 1721) in Oxford, England John Keill attended an Edinburgh school, then studied at Edinburgh University under David Gregory obtaining his degree in 1692. Keill went to Oxford with David Gregory in 1691 and studied at Balliol College, obtaining an Oxford degree in 1694. At Oxford Keill lectured on Newton's work and was soon appointed as a lecturer in experimental philosophy. He was appointed deputy to the professor of natural philosophy in 1699, a post he held until 1709. Keill was elected a Fellow of the Royal Society in 1700 and Savilian Professor of Astronomy at Oxford in 1712. Keill acted as a propagator of Newton's philosophy and argued against Whiston and others. He claimed that Leibniz had plagiarised Newton's invention of the calculus and he served as Newton's avowed Champion Keill wrote in Introductio ad veram (published in Leiden in 1725) The only true Philosophers are those who would account for all Effects and Phenomena by the known established Laws of Motion and Mechanics.

His smaller work is often referred to as authority by geologists and natural philosophers; it contains many experimental calculations, among which is that estimate of the depth of the sea, on which Breislak [1] in later times founded his celebrated calculation, that there never could have been a sufficient quantity of water in and about our globe to have kept the matter of it at any time in solution. It was considered by many, that Keill had used the venerable doctor Burnet, much his elder in years, a scholar, and a man esteemed for his private virtues, with too much asperity and unbecoming sarcasm. It appears that the respective theorists answered the attack, although in what manner we have been unable to discover. In 1700, Dr Thomas Millington, Sedelian professor of natural philosophy in Oxford, on his appointment as physician in ordinary to the king, substituted Keill as his assistant, to read his public lectures; and the term for enjoying the Scottish exhibition at Baliol college then expiring, he accepted an invitation from Dr Aldrich, dean of Christ’s church, to reside there. As his master Gregory was the first who introduced the Newtonian philosophy to the universities, Keill himself possesses the reputation of having been the first to demonstrate its principles on experiment; a task he is said to have performed through machinery of his own invention, but of what description, or to what extent he proceeded in his proofs, we are not informed.

The Priority Dispute: Newton's Analysis 1711

“ ... A full history of the priority dispute between Isaac Newton and Gottfried Wilhelm von Leibniz over the invention of the calculus is not possible here, but the role of the Analysis in the affair demands a short account. ... Many European mathematicians that Leibniz was the sole inventor of the calculus, because Newton had not actually published any of his mathematical work of the previous 20 years. Although Leibniz had always acknowledged Newton's work in private correspondence, the grounds for a public battle were now set. ... The next major event in the dispute was publication of an article by John Keill in the Philosophical Transactions of the Royal Society for 1708 who more or less directly accused Leibniz of having plagiarized the calculus from Newton, changing only the name (from fluxions) and method of notation. This edition of the Philosophical Transactions was not published until 1710 and Leibniz does not appear to have seen it until March of the following year. When he did read it, Leibniz wrote to the Secretary of the Royal Society demanding an apology. ... Meanwhile, London mathematics teacher William Jones conceived the idea of publishing a volume of Newton's mathematical works. Going through the papers of the now late John Collins he found Collins' copy of "De analysi." Realizing that this copy represented independent proof of Newton's priority in the invention of the calculus, Jones included it in the Analysis book of 1711 along with extracts from correspondence relating to the original exchanges between Newton and Leibniz that had taken place more than 30 years earlier. Accordingly, Jones's volume now became an important part of the priority dispute. That is to say, this report focused heavily on Collins' copy of "De anylysi" and his correspondence with Leibniz — all in support of Keill's original charge of plagiarism. ...”

The famous dispute as to the priority of Newton and Leibnitz in the invention of the calculus began in 1699 through the publication by Nicolas Fatio de Duillier of a contract in which he stated that Newton was not only the certified first, but by many years the first inventor, and insinuated that Leibnitz had stolen it. Leibnitz in his reply (Ada Eruditorum, 1700) cited Newtons letters and the testimony which Newton had rendered to him in the Principia as proofs of his independent authorship of the method. Leibnitz was especially hurt at what he understood to be an endorsement of Duilliers attack by the Royal Society, but it was explained to him that the apparent approval was an accident. The dispute was ended for a time. On the publication of Newtons tract De quadralura curvarum, an anonymous review of it, written, as has since been proved, by Leibnitz, appeared in the Ada Eruditorum, 1705.

The anonymous reviewer said: Instead of the Leibnitzian differences Newton uses and always has used fiuxions. . . just as Honor Fabri in his Synopsis Geometrica substituted steps of movements for the method of Cavalieri. This passage, when it became known in England, was understood not merely as belittling Newton by comparing him with the obscure Fabri, but also as implying that he had stolen his calculus of fluxions from Leibnitz. Great indignation was aroused; and John Keill took occasion, in a memoir on central forces which was printed in the Philosophical Transactions for 1708, to affirm that Newton was without doubt the first inventor of the calculus, and that Leibnitz had merely changed the name and mode of notation. The memoir was published in 1710.

Leibnitz wrote in 1711 to the secretary of the Royal Society (Hans Sloane) requiring Keill to retract his accusation. Leibnitzs letter was read at a meeting of the Royal Society, of which Newton was then president, and Newton made to the society a statement of the course of his invention of the fluxional calculus with the dates of particular discoveries. Keill was requested by the society to draw up an account of the matter under dispute and set it in a just light. In his report Keill referred to Newtons letters of 1676, and said that Newton had there given so many indications of his method that it could have been understood by a person of ordinary intelligence. Leibnitz wrote to Sloane asking the society to stop these unjust attacks of Keill, asserting that in the review in the Ada Eruditorum no one had been injured but each had received his due, submitting the matter to the equity of the Royal Society, and stating that he was persuaded that Newton himself would do him justice. A committee was appointed by the society to examine the documents and furnish a report. Their report, presented in April 1712, concluded as follows:

The differential method is one and the same with the method of fluxions, excepting the name and mode of notation; Mr Leibnitz calling those quantities differences which Mr Newton calls moments orfiuxions, and marking them with the letter d, a mark not used by Mr Newton. And therefore we take the proper question to be, not who invented this or that method, but who was the first inventor of the method; and we believe that those who have reputed Mr Leibnitz the first inventor, knew little or nothing of his correspondence with Mr Collins and Mr Oldenburg long before; nor of Mr Newtons having that method above fifteen years before Mr. Leibnitz began to publish it in the Ada Eruditorum of Leipzig. For which reasons we reckon Mr Newton the first inventor, and are of opinion that Mr Keill, in asserting the same, has been no ways injurious to Mr Leibnitz.

The report with the letters and other documents was printed (1712) under the title Commercium Epistolicum D. Johannis Collins et aliorum de analysi promota, jussu Societatis Regiae in lucem edilum, not at first for publication. An account of the contents of the Commercium Epistolicum was printed in the Philosophical Transactions for 1715. A second edition of the Commercium Epistolicum was published in 1722. The dispute was continued for many years after the death of Leibnitz in 1716.

To translate the words of Moritz Cantor, it redounded to the discredit of all concerned.