Abstract
In the paper we discuss the three methods that Archimedes employs to deal with the problem of the quadrature of a parabolic segment. We characterize the three approaches as heuristic, mechanical and geometric respectively. We investigate Archimedes’ own attitude towards the three methods, and we conclude with a critical presentation of the prevalent views concerning the matter, which have been expressed in the past by historians of mathematics.
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Christianidis, J., Demis, A. (2010). Archimedes’ Quadratures. In: Paipetis, S., Ceccarelli, M. (eds) The Genius of Archimedes -- 23 Centuries of Influence on Mathematics, Science and Engineering. History of Mechanism and Machine Science, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9091-1_5
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DOI: https://doi.org/10.1007/978-90-481-9091-1_5
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