Heuristik und Geschichte der elementaren Volumenberechnung

Abstract

This text focuses on volume measurement in the realm of „higher elementary“ stereometry. It collects most of the material treatable with similarity arguments and Cavalieri‘s principle, but requiring no explicit knowledge of convergence, integral calculus and/or fundamentals of analysis. The main objective is an educational one: a synopsis and synthesis of the foremost ideas and strategies, which preceded modern analysis historically and psychologically. The main result is a space-oriented approach to several cubatures along historical lines and governed by Simpson’s rule, but all this in the informal and constructive spirit of Archimedes, Kepler, Cavalieri, or Jakob Steiner.