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While trying to teach myself calculus, I stumbled upon a BBC documentary called The Birth of Calculus. In the documentary, the narrator explains that Newton and other contemporary mathematicians were trying to find a universal method for finding tangents to polynomial curves.

Why was that a problem of interest to Newton and his contemporaries? What were they studying? Instantaneous velocities? Rates of change? Mechanical motion?

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    Since Newton also formulated basic laws of physics, I'd guess he was studying mechanincal motion.2012-07-25
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    Finding tangents was also a rather important component of that method named after him for numerically approximating roots of nonlinear equations...2012-07-25
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    Fermat, Descartes, Sluse, others were interested in the problem of tangents and subtangents, and largely solved it, at least for the kinds of curves they cared about. Newton showed no particular interest in solving an already solved problem. The authors are confusing the structure of elementary calculus courses with the history of the subject.2012-07-25

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