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The last years of Leibniz's life, 1709–1716, 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 barren struggle was that no participant doubted for a moment that Newton had already developed his method of [[Newton's notationfluxions]] 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 wellread. Newton's manuscripts came to light only after his death. 
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The last years of Leibniz's life, 1709–1716, 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 barren struggle was that no participant doubted for a moment that Newton had already developed his method of [[Newton's notationfluxions]] when Leibniz began working on the differential calculus. Eric is cool. 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 wellread. 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 [[differential (infinitesimal)differential]]s, 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 infinitesimal calculus can be expressed either in the notation of fluxions or in that of [[differential (infinitesimal)differential]]s, 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. 
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