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The Social Relations of Physics, Mysticism, and Mathematics pp 253–266Cite as

Mathematics in Europe, 1200–1700

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Part of the book series: A Pallas Paperback ((EPIS,volume 10))

Abstract

The problem of passing from commensurable to incommensurable magnitudes led eventually to the development of the method of exhaustion. Here the Greeks took steps toward the creation of the calculus.1 Already Antiphon in the fifth century BC had worked on “exhausting” the area between a circle and an inscribed regular polygon. This is a crude approach to integration. The fullest development of this method by the Greeks and the nearest approach to integration as we understand it is credited to Archimedes.

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Notes

  1. Smith, 1958, Vol. II, op. cit., pp. 676–702.

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  2. Farrington, 1961, op. cit., pp. 204–205.

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  3. Farrington, 1961, op. cit., pp. 214–215, 309.

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  4. Cf. Marx, 1973, op. cit., p. 103.

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  5. Marx, 1967, op. cit., p. 77.

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  6. D. Hayes, Europe in the Fourteenth and Fifteenth Centuries, Holt, Rinehart, and Winston, New York, 1966; F. Braudel, Capitalism and Material Life 1400–1800, Harper Torchbooks, New York, 1974; P. Sweezy et al, The Transition to Capitalism, Verso, London,1978.

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  7. J. Merrington, ‘Town and Country in the Transition to Capitalism’, in Sweezy, op. cit., pp. 180–181.

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  8. Struik, 1967, op. cit., p. 86.

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  9. Boyer, 1949, op. cit.

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  10. G. Galilei, Le opere di Galilei Galilei, edizione nazionale (20 vols.), Vol. 18, Barbera, Florence, 1890–1909, pp. 153–154.

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  11. Braudel, op. cit., p. 336; McNeill, op. cit., pp. 645–647; Smith, 1958, Vol. I, op. cit., pp. 437–442.

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  12. Work on the calculus was by no means absent: see D. B. Wagner, ‘Liu Hui and Tsu Keng-chin on the Volume of a Sphere’, Chinese Science, Vol. III (March), 1978, pp. 59–79.

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Authors and Affiliations

  1. Science and Technology Studies Division, Rensselaer Polytechnic Institute, 12181, Troy, NY, USA

    Sal Restivo

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  1. Sal Restivo
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© 1985 D. Reidel Publishing Company, Dordrecht, Holland

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Restivo, S. (1985). Mathematics in Europe, 1200–1700. In: The Social Relations of Physics, Mysticism, and Mathematics. A Pallas Paperback, vol 10. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7058-8_15

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  • DOI: https://doi.org/10.1007/978-94-009-7058-8_15

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-277-2084-9

  • Online ISBN: 978-94-009-7058-8

  • eBook Packages: Springer Book Archive

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