<P> Anders Hald writes that, "The basis of Fermat's mathematics was the classical Greek treatises combined with Vieta's new algebraic methods ." </P> <P> Fermat's pioneering work in analytic geometry (Methodus ad disquirendam maximam et minimam et de tangentibus linearum curvarum) was circulated in manuscript form in 1636 (based on results achieved in 1629), predating the publication of Descartes' famous La géométrie (1637), which exploited the work . This manuscript was published posthumously in 1679 in Varia opera mathematica, as Ad Locos Planos et Solidos Isagoge (Introduction to Plane and Solid Loci). </P> <P> In Methodus ad disquirendam maximam et minimam and in De tangentibus linearum curvarum, Fermat developed a method (adequality) for determining maxima, minima, and tangents to various curves that was equivalent to differential calculus . In these works, Fermat obtained a technique for finding the centers of gravity of various plane and solid figures, which led to his further work in quadrature . </P> <P> Fermat was the first person known to have evaluated the integral of general power functions . With his method, he was able to reduce this evaluation to the sum of geometric series . The resulting formula was helpful to Newton, and then Leibniz, when they independently developed the fundamental theorem of calculus . </P>

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