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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
REFERENCES
Becker O., Critical Review of the English Edition of Archimedes by Dijksterhuis, Gnomon 29, 1957, pp. 329-332.
Becker O. and Hofmann J.E., Histoire des mathématiques, tr. R. Jouan, Paris, Lamarre,1956.
Dijksterhuis E.J., Archimedes, tr. C. Dikshoorn (with a new bibliographic essay by Wilbur R. Knorr), Princeton, NJ, Princeton University Press, 1987.
Knorr W.R., Archimedes and the Elements: Proposal for a Revised Chronological Ordering of the Archimedean Corpus, Archive for History of Exact Sciences 19, 1978, pp. 211-290.
Knorr W.R., Infinity and continuity: The interaction of mathematics and philosophy inantiquity, in N. Kretzmann (ed.), Infinity and continuity in ancient and medieval thought, Ithaca, N.Y., Cornell University Press, 1982, pp. 112-145.
Knorr W.R., The Ancient Tradition of Geometric Problems, New York, Dover, 1993.
Knorr W.R., The Method of Indivisibles in Ancient Geometry, in R. Calinger (ed.), Vita Mathematica. Historical research and integration with teaching, The Mathematical Association of America, 1996, pp. 67-86.
Netz R., Saito K. and Tchernetska N., A New Reading of Method Proposition 14: Preliminary Evidence from the Archimedes Palimpsest (Part 1), SCIAMVS 2, 2001, pp. 9-29.
Netz R., Acerbi F. and Wilson N., Towards a Reconstruction of Archimedes’ Stomachion, SCIAMVS 5, 2005, pp. 67-99.
Saito K., Between Magnitude and Quantity: Another Look at Archimedes’ Quadrature, Sugaku Expositions 19(1), 2006, pp. 35-52.
Thomas I., Selections Illustrating the History of Greek Mathematics, 2 vols, Cambridge,Mass., Harvard University Press, 1993.
Vitrac B., A propos de la chronologie des œuvres d’Archimède, in J.-Y. Guillaumin (ed.), Mathématiques dans l’Antiquité, Saint-Étienne, Publications de l’Université de Saint-Étienne, 1992, pp. 59-93.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer Netherlands
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-90-481-9091-1_5
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-9090-4
Online ISBN: 978-90-481-9091-1
eBook Packages: EngineeringEngineering (R0)