Kilström Tomas: Area och volymberäkningar före infinitesimalkalkylen  

Abstract: We will take a look at the different methods of calculating area and volume predating the infinitesimal calculus developed in the late 17th century by Newton and Leibniz. This paper will primarily look at four methods of calculating areas and volumes: Eudoxus method of exhaustion, Cavalieri's principle, series and their sums, and some strictly geometrical proofs. We will discover some of the problems early geometers had, and the tools they used in order to circumvent them, all the while building the foundation of what would become the infinitesimal calculus.