Linked bibliography for the SEP article "Continuity and Infinitesimals" by John L. Bell
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- Aristotle, Physics, 2 volumes (Loeb Classical Library,
228 and 255), P. H. Wickstead and F. M. Cornford (trans), Cambridge,
MA: Harvard University Press and Heinemann, 1980.
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Moralia, 2 volumes (Loeb Classical Library, 271 and 287), Hugh
Tredinnick and G. Cyril Armstrong (trans), Cambridge, MA: Harvard
University Press, 1996.
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Prior Analytics (Loeb Classical Library, 325), H. P. Cooke and
Hugh Tredinnick (trans), Cambridge, MA: Harvard University Press,
1996a.
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Leibniz’s Early Thought”, in The Philosophy of the
Young Leibniz (Studia Leibnitziana Sonderhefte 35), Mark Kurstad,
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11–28. (Scholar)
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Infinitesimal Calculus, Oxford: Pergamon Press. Reprinted New
York: Dover, 1987. (Scholar)
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London. Translated in The Geometrical Lectures of Isaac
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- Bell, John L., 1998, A Primer of Infinitesimal Analysis, Cambridge: Cambridge University Press. doi:10.1017/cbo9780511619625 (Scholar)
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- –––, 2001, “The Continuum in Smooth Infinitesimal Analysis”, in Schuster, Berger, and Osswald 2001: 19–24. doi:10.1007/978-94-015-9757-9_2">10.1007/978-94-015-9757-9_2 (Scholar)
- –––, 2003, “Hermann Weyl’s Later Philosophical Views: His Divergence from Husserl”, in Husserl and the Sciences: Selected Perspectives, Richard A. Feist (ed.), Ottawa: University of Ottawa Press. (Scholar)
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- –––, 2019, The Continuous, the Discrete and the Infinitesimal in Philosophy and Mathematics (The Western Ontario Series in Philosophy of Science 82), Cham, Switzerland: Springer International Publishing. doi:10.1007/978-3-030-18707-1 (Scholar)
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accounts of the continuum today”, in Shapiro and Hellman 2020:
476–501. doi:10.1093/oso/9780198809647.003.0018 (Scholar)
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Evolution of the Concept of Real Number”, in Bharath Sriraman
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Practice, Cham, Switzerland: Springer.
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- Bishop, Errett, 1967, Foundations of Constructive Analysis, New York: McGraw-Hill. (Scholar)
- Bishop, Errett and Douglas S. Bridges, 1985, Constructive Analysis, Berlin: Springer. doi:10.1007/978-3-642-61667-9 (Scholar)
- Bolzano, Bernard, 1817, “Rein analytischer Beweis des
Lehrsatzes, dass zwischen je zwey Werthen, die ein entgegengesetzes
Resultat gewähren, wenigstens eine reelle Wurzel der Gleichung
liege” (Purely Analytic Proof of the Theorem That Between Any
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“A Translation of Bolzano’s Paper on the Intermediate
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- Bos, H. J. M., 1974, “Differentials, Higher-Order Differentials and the Derivative in the Leibnizian Calculus”, Archive for History of Exact Sciences, 14(1): 1–90. doi:10.1007/bf00327456 (Scholar)
- Boyer, Carl Benjamin, 1939 [1959], The Concepts of the Calculus: a Critical and Historical Discussion of the Derivative and the Integral, New York: Columbia University Press; second edition 1949. Second edition reprinted as The History of the Calculus and its Conceptual Development, New York: Dover, 1959. (Scholar)
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- Boyer, Carl B. and Uta C. Merzbach, 1989, A History of
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- Bradwardine, Thomas, c. 1330, Tractatus de Continuo,
published in Murdoch 1957: 339–471. (Scholar)
- Brentano, Franz, 1905 [1966], “Draft of a letter from Brentano to Husserl: Florence, 30 April, 1905”, in Franz Brentano, The True and the Evident, Oskar Kraus (ed.), Roderick M. Chilsholm (English Edition ed.), Roderick M. Chisholm, Ilse Politzer, and Kurt R. Fischer (trans.), London: Routledge and Kegan Paul, pp. 94–95. (Scholar)
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- Bridges, Douglas S., 1994, “A Constructive Look at the Real
Number Line”, in Ehrlich 1994a: 29–92.
doi:10.1007/978-94-015-8248-3_2">10.1007/978-94-015-8248-3_2 (Scholar)
- –––, 1999, “Constructive Mathematics: A Foundation for Computable Analysis”, Theoretical Computer Science, 219(1–2): 95–109. doi:10.1016/s0304-3975(98)00285-0 (Scholar)
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gleichmässig stetig ist”, Koninklijke Akademie van
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- Cajori, Florian, 1919, A History of the Conceptions of Limits
and Fluxions in Great Britain, from Newton to Woodhouse, Chicago:
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lineare Punktmannichfaltigkeiten”, Mathematische
Annalen, 21(4): 545–591. Separately published in the same
year as Grundlagen einer allgemeinen Mannigfaltigkeitslehre,
Leipzig: Teubner. Translated as “Foundations of a General Theory
of Manifolds: A Mathematico-Philosophical Investigation”, in
Ewald 1999: II, pp. 878–919. doi:10.1007/BF01446819 (German,
first publication) (Scholar)
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Begrüngung der transfiniten Mengenlehre”, Mathematische
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Translated as Contributions to the Founding of the Theory of
Transfinite Numbers, Philip E.B. Jourdain (trans.), New York:
Dover, 1961 (original translation date 1952). See also Dauben 1979:
chapter 8. doi:10.1007/bf02124929 (German, part I)
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- Carnot, Lazare, 1797 [1832], Reflexions sur la Métaphysique du Calcul Infinitesimal, Paris: Duprat. Translated as Reflexions on the Metaphysical Principles of the Infinitesimal Analysis, W. R. Browell (trans.), Oxford: J. H. Parker, 1832. (Scholar)
- Cauchy, Augustin-Louis, 1821, Cours d’Analyse de
l’École Royale Polytechnique; I.re Partie. Analyse
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- Chevalier, G., (ed.), 1929, “Continu et Discontinu”,
special issue of Cahiers de la Nouvelle Journée, 15,
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- Child, J. M., 1916, “Introducion” to the 1916 edition
of Barrow 1670 [1916: 1–32. (Scholar)
- Cusanus, Nicolas, 1440 [1954], De Docta Ignorantia,
manuscript. Translated as Of Learned Ignorance, Germain Heron
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- D’Alembert, Jean le Rond and Denis Diderot, 1751–1766,
Encyclopédie, ou, Dictionnaire raisonné des
sciences, des arts et des métiers /, mis en ordre et
publié par Diderot, quant à la partie
mathématique, par d’Alembert, Paris. Reprinted
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- Dauben, Joseph W., 1979, Georg Cantor: His Mathematics and Philosophy of the Infinite, Cambridge, MA: Harvard University Press. (Scholar)
- Dedekind, Richard, 1872 [1999], Stetigkeit und irrationale
Zahlen (Continuity and Irrational Numbers), Braunschweig: F.
Vieweg & Sohn. Translated in Essays on the Theory of Numbers:
I. Continuity and Irrational Numbers. II. The Nature and Meaning of
Numbers, Wooster Woodruff Beman (trans.), Chicago: Open Court,
1901. Reprinted New York: Dover, 1963. A revised version of the
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- Descartes, René, 1637, Discours de la Méthode Pour bien conduire sa raison, et chercher la vérité dans les sciences, Leiden. Translated as Discourse on Method, Meditations, and Principles of Philosophy (Everyman’s Library), London: Dent, 1927. (Scholar)
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- Euclid, The Thirteen Books of Euclid’s Elements, 3
volumes, T. L. Heath (trans.), Cambridge: Cambridge University Press,
1908. Second edition in 1926. (Scholar)
- Euler, Leonhard, 1748, Introductio in analysin
infinitorum, 2 volumes, Lausanne. Translated as Introduction
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Springer, 1988. (Scholar)
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princesse d’Allemagne sur divers sujets de physique et de
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Frankfurt (1774, last volume); letters originally written between 1760
and 1762. Translated as Letters of Euler on Different Subjects in
Natural Philosophy: Addressed to a German Princess, 2 volumes,
Henry Hunter (trans.), second edition, London, 1802. Reprinted New
York: Harper and Brothers, 1835. (Scholar)
- Evans, Melbourne G., 1955, “Aristotle, Newton, and the Theory of Continuous Magnitude”, Journal of the History of Ideas, 16(4): 548–557. doi:10.2307/2707510 (Scholar)
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- Fermat, Pierre de, c. 1638, Methodus ad Disquirendam Maximam
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(Scholar)
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