Newton laid the foundations for differential and integral calculus, several years before its independent discovery by Leibniz.
Meanwhile, Newton, though he explained his (geometrical) form of calculus in Section I of Book I of the Principia of 1687, did not explain his eventual fluxional notation for the calculus in print until 1693 (in part) and 1704 (in full). The prevailing opinion in the 18th century was against Leibniz (in Britain, not in the German-speaking world). Today the consensus is that Leibniz and Newton independently invented and described the calculus in Europe in the 17th century. A Brief History of Calculus. Calculus was created by Isaac Newton, a British scientist, as well as Gottfried Leibniz, a self-taught German mathematician, in the 17th century. It has been long disputed who should take credit for inventing calculus first, but both independently made discoveries that led to what we know now as calculus.  Isaac Newton did not invent the newton meter. It was invented by  others, and it was   the bane of his existence. He spent many fruitless hours, while on  break from his … weightier   and more forceful work, trying to get rid of it. Isaac Newton published a partial account of his theory of calculus in 1693 and a full account in 1704. According to his friends he had worked it out years before. The late date of publishing led to controversy at the time. Leibniz, a German mathematician published his method for calculus in 1684 before Newton Isaac Newton did not invent the newton meter. It was invented by  others, and it was   the bane of his existence. He spent many fruitless hours, while on  break from his … weightier   and more forceful work, trying to get rid of it. Newton did not invent the telescope. The first practical telescope was made by Hans Lippeshey and Zacharias Janssen in 1608 in the Netherlands. Galileo made significant improv … ements the following year. 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 prevailing opinion in the 18th century was against Leibniz (in Britain, not in the German-speaking world). Today the consensus is that Leibniz and Newton independently invented and described the calculus in Europe in the 17th century. Isaac Newton: the first physicist. Isaac Newton is popularly remembered as the man who saw an apple fall from a tree, and was inspired to invent the theory of gravity. If you have grappled with elementary physics then you know that he invented calculus and the three laws of motion upon which all of mechanics is based.  Leibniz probably believed that Newton was ignorant of this and expected Newton to dissociate Ibid., Page 105; G.V.Coyne, Newton’s controversy with Leibniz over the invention of the calculus, Page 111, In Newton AndThe New Direction In ScienceIbid. In this paper, Keill claims for Newton thepriority of the ﬁrst invention of the calculus, turning to Wallis’s publications of Newton’s letters for proof.Further, he asserts that the Leibniz’s publications were essentially the same as Newton’s work “havingchanged the name and symbolism”. But Leibniz did not see it until the autumn of 1714. The prevailing opinion in the 18th century was against Leibniz (in Britain, not in the German-speaking world). Today the consensus is that Leibniz and Newton independently invented and described the calculus in Europe in the 17th century. In Mathematics. Newton laid the foundations for differential and integral calculus, several years before its independent discovery by Leibniz. The 'method of fluxions', as he termed it, was based on his crucial insight that the integration of a function is merely the inverse procedure to differentiating it. 
https://en.wikipedia.org/wiki/Leibniz%E2%80%93Newton_calculus_controversy https://www.wyzant.com/resources/lessons/math/calculus/introduction/history_of_calculus http://www.answers.com/Q/When_did_Isaac_Newton_invent_calculus http://www.answers.com/Q/Why_did_isaac_newton_invent_calculus https://en.wikipedia.org/wiki/Leibniz%E2%80%93Newton_calculus_controversy http://physics.wustl.edu/alford/general/newton.html http://pages.cs.wisc.edu/~sastry/hs323/calculus.pdf https://en.wikipedia.org/wiki/Leibniz%E2%80%93Newton_calculus_controversy http://www.juliantrubin.com/bigten/newtoninvent.html
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