Infinite sums and the calculation of 𝝅, as presented by the Swedish mathematician Anders Gabriel Duhre in the early 18th century

Paper in proceeding, 2019

Anders Gabriel Duhre, an important mathematician and mathematics educator in Sweden during the 18th century, contributed with two textbooks in mathematics, one in algebra and one in geometry. Among others, he treats infinitesimals based on Nieuwentijts’ theories from Analysis infinitorum and infinite sums based on Wallis’ method of induction from Arithmetica infinitorum. Based on these results, Duhre develops an ingenious method to determine the area enclosed by curves by constructing a corresponding curve. He applies his method to the circle in order to find an expression of 𝜋 as an infinite series. The series he finds is a modified version of the Gregory-Leibniz’ series. In the present paper we consider in detail Duhre’s presentation in order to further investigate the influence upon him as well as his influence on the Swedish mathematical society of his time.