Servois' 1817 "Memoir on Quadratures"

François-Joseph Servois (1767–1847) was a French priest, artillery officer, professor of mathematics, and museum curator. Servois conducted research in many areas of mathematics, including geometry and the differential calculus. In 1817, after a three-year period with no publications, Servois published his "Memoir on Quadratures," where he tackled a new area of mathematics: numerical integration. This paper examines the "Quadratures" paper, in which Servois addressed a debate on numerical integration techniques among the mathematicians Christian Kramp (1760–1826), Joseph-Diez Gergonne (1771–1859), and Joseph-Balthazard Bérard (1763–1844?). Our paper provides a readers' guide to Servois' 1817 paper and concludes with several student activities that can be incorporated into a numerical analysis course. We also offer readers a complete English translation of Servois' "Memoir on Quadratures" (pdf).