Early Middle Ages



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James Gregory (1638-1675) infinite series representations trigonometric functions and their inverse, like arctan x = x - x3/3 + x5/5 - x7/7 + ...

1668 Geometriae Pars Universalis the first published statement and proof of the fundamental theorem of the calculus (stated from a geometric point of view, and only for a special class of the curves considered by later versions of the theorem), acknowledged by Isaac Barrow



Johannes Hudde (1628-1704) mayor of Amsterdam between 1672 – 1703, a mathematician and governor of the Dutch East India Company

Newton and Leibniz mention Hudde many times and used some of his ideas in their own work on infinitesimal calculus. Hudde’s rule is a criterion for double roots.





Michel Rolle (1652-1719) French mathematician best known for Rolle's theorem (1691); invented notation n√x and introduced in France sign “=”; also the co-inventor in Europe of Gaussian elimination (1690).





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