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Calculus, Part 1 Predecessors of Newton/Leibniz Area by Method of Exhaustion in antiquity Eudoxus Archimedes India Pedersen: “Many methods were developed to solve calculus problems; common to most of them was their ad hoc character. It is possible to find examples from the time before Newton and Leibniz which, when translated into modern mathematical language, show that differ- entiation and integration are inverse procedures; however, these examples are all related to specific problems and not to general theories.” Descartes’ Method for finding tangents Fermat’s Method of Maxima and Minima Cavalieri’s Principle: If cross-sections are in a constant ratio, areas are in that same ratio. Roberval’s quadrature of the cycloid Wallis’s “arithmetic” integration Fermat’s “logarithmic” integration Newton and Leibniz Pedersen: “The special merit of Newton and Leibniz was that they both worked out a general theory of the infinitesimal calculus. However, it cannot be said that either Newton or Leibniz
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