Skip to main navigation menu Skip to main content Skip to site footer

Artículos

Vol. 24 No. 2 (2021): July

ANAMNESIS OF THE THEORY OF THE INDIVISIBLES OF CAVALIERI

DOI
https://doi.org/10.12802/relime.21.2422
Submitted
November 7, 2022
Published
2021-07-01

Abstract

In their specific social and cultural circumstance, the Cavalerian indivisibles constitute an understandable theory that seeks the symbols of the infinite-continuous at the dawn of European Modernity. Many of the key notions of this theory survive in mathematics today.

References

  1. Andersen, K. (1985). Cavalieri’s Method of Indivisibles. Archive for the History of Exact Sciences, 31, 291-367.
  2. Assis, A. K. T. y Magnaghi, C. P. (2012). The Ilustrated Method of Archimedes: Utilizing the Law of the Lever to Calculate Areas, Volumes, and Centers of Gravity. Montreal: Apeiron.Berkeley, G. (1734). The Analyst; or a Discourse Addressed to an Infidel Mathematician [...] Londres: Printed for J. Tonson in the Strand.
  3. Boyer, C. (1959). The History of the Calculus and its Conceptual Development. New York: Dover.
  4. Boyer, C. (1968). A History of Mathematics. New York: John Wiley & Sons.
  5. Brunschvicg, L. (1912). Les étapes de la philosophie mathématique. París: Librairie Félix Alcan.
  6. Cavalieri, B. (1647). Exercitationes geometricae sex. Bolonia: Typis Iacobi Montij.
  7. Cavalieri, B. (1653). Geometria indivisibilibus continuorum nova quadam ratione promota. Bolonia: Ex Typographia de Lucijs.
  8. Clagett, M. (Ed.). (1968). Nicole Oresme and the Medieval Geometry of Qualities and Motions. Madison: The University of Wisconsin Press
  9. Do Carmo, M. P. (1976). Differential Geometry of Curves and Surfaces. Englewood Cliffs, NJ: Prentice-Hall Inc.
  10. Dupuis, N. F. (1914). Elementary Synthetic Geometry of the Point, Line and Circle in the Plane.London: MacMillan & Co., Ltd.
  11. Edwards, C. H. (1979). The Historical Development of the Calculus. New York: Springer.
  12. Hairer, E. y Wanner, G. (1996). Analysis by Its History. New York: Springer.
  13. Hall, A. R. (2002). Philosophers at War. The Quarrel between Newton and Leibniz. Cambridge: Cambridge University Press.
  14. Heath, T. L. (1912). The Method of Archimedes. Cambridge: Cambridge University Press.
  15. Heiberg, J. L. y Menge H. (Eds.) (MDCCCLXXXIV). Euclidis Opera Omnia. Vol. II. Libros V-IX continens. Lipsiae: in aedibus B. G. Teubneri.
  16. Heiberg, J. L. (1907). Eine neue Archimedeshandschrift. Hermes : Zeitschrift für klassische Philologie, 42 (2), 235-303.
  17. Heiberg, J. L. (Trad.) (1909). Geometric Solutions Derived from Mechanics. A Treatise of Archimedes. Chicago: The Open Court Publishing Company.
  18. Jones, F. (2001). Lebesgue Integration on Euclidean Space. Sudbury, Massachusetts: Jones and Bartlett Publishers.
  19. Koyré, A. (1978). Estudios de historia del pensamiento científico (E. Pérez y E. Bustos, Trans). México: Siglo veintiuno editores. (Obra original publicada en 1973).
  20. Kunz, E. (1976). Ebene Geometrie. Axiomatische Begründung der euklidischen und nichteuklidischen Geometrie. Hamburg: ro ro ro vieweg.
  21. Lakatos, I. (1978). Mathematics, Science and Epistemology-Philosophical Papers. Volume 2. Cambridge: Cambridge University Press.
  22. Leibniz, G. W. (1956). Studies in Physics and the Nature of Body, 1671. En L. E. Loemker. (Ed.), Philosophical Papers and Letters (139-145). Dordrecht: Kluwer Academic Publishers. (Obra original publicada en 1671).
  23. Lombardo-Radice, L. (Ed.). (1966). Geometria degli indivisibili di Bonaventura Cavalieri. Turín: Unione Tipografico-Editrice Torinese.
  24. Marsden, J. E. y Tromba, A. J. (1988). Vector Calculus. Third Edition. New York: W. H. Freeman and Company.
  25. Mengoli, P. (1659). Geometriae speciosae elementa. Bolonia: Typis Io. Baptistae Ferronij.
  26. Newton, I. (1687). Philosophia naturalis principia mathematica. Londres: Jussu Societatis Regiae ac Typis Josephi Streater.
  27. Pascal, B. (1658). Lettres de A. Dettonville [...] París.
  28. Porée, M. (2000). La «méthode Serres».Sillages critiques 1. Online since 11.01.2013, connection on 04.04.2019. http://journals.openedition.org/sillagescritiques/3155
  29. Radford, L. (2008, julio). Semiotic Reflections on Medieval and Contemporary Graphic Representations of Motion. Ponencia presentada en la History and Pedagogy of MathematicsConference, México D. F.
  30. Raffo, F. (2016). Continuo e infinito. Influencias y génesis del tratamiento leibniziano del laberintodel continuo (Tesis doctoral). Universidad Nacional de La Plata, La Plata, Argentina.
  31. Roberval, G. P. (1693). Traité des indivisibles. En Messieurs de l’Académie Royale des Sciences. Divers ouvrages de mathématiques et de physique (190-245). París: L’Imprimerie Royale.
  32. Robinson, A. (1966). Non-standard Analysis. Amsterdam: North-Holland Publishing Company.
  33. Smith, D. E. (1929). A Source Book in Mathematics. New York: McGraw-Hill Book Company, Inc.
  34. Solère, J. L. (s. f.). Scotus Geometres. The longetivity of Duns Scotus’s geometric arguments against indivisibilism. https://www2.bc.edu/jeanluc-solere/docs/PAPERS/Solere_Scotus%20Geometres%202.pdf, Recuperado 21.03.2019.
  35. Tamayo, A. C. (2018). Escenas de la representación matemática de los indivisibles en el siglo XVII (Tesis doctoral no publicada). Universidad Nacional de Colombia, Medellín, Colombia.
  36. Torricelli, E. (1969). On the Acute Hyperbolic Solid. En D. J. Struik. A Source Book in Mathematics, 1200-1800 (227-232). Princeton: Princeton University Press. (Obra original publicada ca. 1643).Wentworth, G. y Smith, D. E. (Revs.) (1910).
  37. Wentworth’s Plane Geometry. Boston: Ginn and Company.

Downloads

Download data is not yet available.

Similar Articles

1 2 3 4 5 6 7 8 9 10 > >> 

You may also start an advanced similarity search for this article.

Most read articles by the same author(s)