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The calculus controversy (often referred to with the German term ''Prioritätsstreit'', meaning ‘priority dispute’) was an argument between 17th-century mathematicians Isaac Newton and Gottfried Leibniz (begun or fomented in part by their disciples and associates) over who had first invented the mathematical study of change, calculus. It is a question that had been the cause of a major intellectual controversy, one that began simmering in 1699 and broke out in full force in 1711. Newton claimed to have begun working on a form of the calculus (which he called "the method of fluxions and fluents") in 1666, at the age of 23, but did not publish it except as a minor annotation in the back of one of his publications decades later (a relevant Newton manuscript of October 1666 is now published among his mathematical papers〔D T Whiteside (ed.), ''The Mathematical Papers of Isaac Newton'' (Volume 1), (Cambridge University Press, 1967), part 7 "The October 1666 Tract on Fluxions", (at page 400, in 2008 reprint ).〕). Gottfried Leibniz began working on his variant of the calculus in 1674, and in 1684 published his first paper employing it. L'Hôpital published a text on Leibniz's calculus in 1696 (in which he recognized that Newton's ''Principia'' of 1687 was "nearly all about this calculus"〔Marquis de l'Hôpital's original words about the 'Principia': "lequel est presque tout de ce calcul": see the preface to his ''Analyse des Infiniment Petits'' (Paris, 1696). The ''Principia'' has been called "a book dense with the theory and application of the infinitesimal calculus" also in modern times: see Clifford Truesdell, ''Essays in the History of Mechanics'' (Berlin, 1968), at p.99; for a similar view of another modern scholar see also 〕). Meanwhile, Newton, though he explained his (geometrical) form of calculus in Section I of Book I of the ''Principia'' of 1687,〔Section I of Book I of the ''Principia'', explaining "the method of first and last ratios", a geometrical form of infinitesimal calculus, as recognized both in Newton's time and in modern times – see citations above by L'Hospital (1696), Truesdell (1968) and Whiteside (1970) – is available online in its English translation of 1729, (at page 41 ).〕 did not explain his eventual fluxional notation for the calculus in print until 1693 (in part) and 1704 (in full). ==Background== The last years of Leibniz's life, 1710–1716, were embittered by a long controversy with John Keill, Newton, and others, over whether Leibniz had discovered calculus independently of Newton, or whether he had merely invented another notation for ideas that were fundamentally Newton's. Newton manipulated the quarrel. The most remarkable aspect of this struggle was that no participant doubted for a moment that Newton had already developed his method of fluxions when Leibniz began working on the differential calculus. Yet there was seemingly no proof beyond Newton's word. He had published a calculation of a tangent with the note: "This is only a special case of a general method whereby I can calculate curves and determine maxima, minima, and centers of gravity." How this was done he explained to a pupil a full 20 years later, when Leibniz's articles were already well-read. Newton's manuscripts came to light only after his death. The infinitesimal calculus can be expressed either in the notation of fluxions or in that of differentials, or, as noted above, it was also expressed by Newton in geometrical form, as in the 'Principia' of 1687. Newton employed fluxions as early as 1666, but did not publish an account of his notation until 1693. The earliest use of differentials in Leibniz's notebooks may be traced to 1675. He employed this notation in a 1677 letter to Newton. The differential notation also appeared in Leibniz's memoir of 1684. The claim that Leibniz invented the calculus independently of Newton rests on the fact that Leibniz # Published a description of his method some years before Newton printed anything on fluxions; # Always alluded to the discovery as being his own invention. Moreover, this statement went unchallenged for some years; # Rightly enjoyed the strong presumption that he acted in good faith; # Demonstrated in his private papers his development of the ideas of calculus in a manner independent of the path taken by Newton. According to Leibniz's detractors, to rebut this case it is sufficient to show that he: * saw some of Newton's papers on the subject in or before 1675 or at least 1677 * obtained the fundamental ideas of the calculus from those papers. They see the fact that Leibniz's claim went unchallenged for some years as immaterial No attempt was made to rebut #4, which was not known at the time, but which provides the strongest of the evidence that Leibniz came to the calculus independently from Newton. This evidence, however, is still questionable based on the discovery, in the Inquest and after, that Leibniz both back-dated and changed fundamentals of his 'original' notes, not only in this intellectual conflict, but in several others (he also published 'anonymous' slanders of Newton regarding their controversy which he tried, initially, to claim he was not author of). Assuming good faith, however, Leibniz's notes as presented to the inquest came first to integration, which he saw as a generalization of the summation of infinite series, whereas Newton began from derivatives. However, to view the development of calculus as entirely independent between the work of Newton and Leibniz misses the point that both had some knowledge of the methods of the other (though Newton did develop most fundamentals before Leibniz started) and in fact worked together on a few aspects, in particular power series, as is shown in a letter to Henry Oldenburg dated October 24, 1676, where Newton remarks that Leibniz had developed a number of methods, one of which was new to him.〔The manuscript, written mostly in Latin, is numbered Add. 3977.4; it is contained in the library at the University of Cambridge. See (this page ) for more details.〕 Both Leibniz and Newton could see by this exchange of letters that the other was far along towards the calculus (Leibniz in particular mentions it) but only Leibniz was prodded thereby into publication. That Leibniz saw some of Newton's manuscripts had always been likely. In 1849, C. I. Gerhardt, while going through Leibniz's manuscripts, found extracts from Newton's ''De Analysi per Equationes Numero Terminorum Infinitas'' (published in 1704 as part of the ''De Quadratura Curvarum'' but also previously circulated among mathematicians starting with Newton giving a copy to Isaac Barrow in 1669 and Barrow sending it to John Collins〔D Gjertsen (1986), "The Newton handbook", (London (Routledge & Kegan Paul) 1986), at page 149.〕) in Leibniz's handwriting, the existence of which had been previously unsuspected, along with notes re-expressing the content of these extracts in Leibniz's differential notation. Hence when these extracts were made becomes all-important. It is known that a copy of Newton's manuscript had been sent to Tschirnhaus in May 1675, a time when he and Leibniz were collaborating; it is not impossible that these extracts were made then. It is also possible that they may have been made in 1676, when Leibniz discussed analysis by infinite series with Collins and Oldenburg. It is ''a priori'' probable that they would have then shown him the manuscript of Newton on that subject, a copy of which one or both of them surely possessed. On the other hand it may be supposed that Leibniz made the extracts from the printed copy in or after 1704. Shortly before his death, Leibniz admitted in a letter to ''Abbé'' Antonio Schinella Conti, that in 1676 Collins had shown him some of Newton's papers, but Leibniz also implied that they were of little or no value. Presumably he was referring to Newton's letters of 13 June and 24 October 1676, and to the letter of 10 December 1672, on the method of tangents, extracts from which accompanied the letter of 13 June. Whether Leibniz made use of the manuscript from which he had copied extracts, or whether he had previously invented the calculus, are questions on which no direct evidence is available at present. It is, however, worth noting that the unpublished Portsmouth Papers show that when Newton went carefully into the whole dispute in 1711, he picked out this manuscript as the one which had probably somehow fallen into Leibniz's hands. At that time there was no direct evidence that Leibniz had seen this manuscript before it was printed in 1704; hence Newton's conjecture was not published. But Gerhardt's discovery of a copy made by Leibniz tends to confirm its accuracy. Those who question Leibniz's good faith allege that to a man of his ability, the manuscript, especially if supplemented by the letter of 10 December 1672, sufficed to give him a clue as to the methods of the calculus. Since Newton's work at issue did employ the fluxional notation, anyone building on that work would have to invent a notation, but some deny this. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Leibniz–Newton calculus controversy」の詳細全文を読む スポンサード リンク
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