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date: 22 September 2019

Abstract and Keywords

This chapter discusses the history of Leibniz's work on infinitesimal calculus of which a considerable part is still unknown. His new method, emerging from studies in the summing of infinite number series and the quadrature of curves, combines two procedures with opposite orientation, differentiation and integration. These two procedures are united in a common formalism introducing in 1675 the symbols d and ∫ for differentiation and integration. Subsequently, Leibniz and his followers developed new rules and solution methods, and applied the calculus to physics. During Leibniz’s lifetime the public success of his calculus was overshadowed by discussions over the foundations of his methods and the priority dispute with Newton. While infinitesimals were eliminated from the calculus during the 19th century, non-standard analysis reinstated them again. The status of infinitesimals in Leibniz’s own philosophy of mathematics is still disputed.

Keywords: Leibniz, calculus, infinite series, differentiation, integration, priority dispute, Newton, problem of foundations, non-standard analysis

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