REFERENCES
Andersen, Kirsti: 1986. ‘The Method of Indivisibles: Changing Understandings’, in A. Heinekamp (ed.), 300 Jahre “Nova Methodus” von G. W. Leibniz (1684-1984), Special issue of Studia Leibnitiana 14, 14–25.
Babbage, Charles: [1830] 1989. ‘Notation’, in M. Campbell-Kelly (ed.), The Works of Charles Babbage, Vol. 1. Mathematical Papers, New York University Press, New York, pp. 394–399.
Barabashev, A. G.: 1997. ‘In Support of Significant Modernization of Original Mathematical Texts (In Defense of Presentism)’, Philosophica Mathematica III 5, 21–41.
Baron, Margaret E.: 1969. The Origins of the Infinitesimal Calculus, Dover, New York.
Bos, H. J. M.: 1974. ‘Differentials, Higher-Order Differentials and the Derivative in the Leibnizian Calculus’, Archive for History of Exact Sciences 14, 1–90.
Bos, Henk J. M.: 1991. ‘The Fundamental Concepts of the Leibnizian Calculus’, Lectures in the History of Mathematics, Mathematical Association of America, Washington, DC, pp. 83–99.
Bosmans, H.: 1922. ‘Un chapitre de l'oeuvre de Cavalieri. Les propositions XVI-XXVII de l'Exercitio quarta’, Mathesis 36, 365–373, 446-456.
Boyer, Carl B.: [1949] 1959. The History of the Calculus and its Conceptual Development, Dover, New York.
Boyer, Carl B.: 1946. ‘Proportion, Equation, Function: Three Steps in the Development of a Concept’, Scripta Mathematica 12, 5–13.
Brown, James Robert: 1994. Smoke and Mirrors. How Science Reflects Reality, Routledge, London.
Butterfield, Herbert: [1931] 1965. The Whig Interpretation of History, Norton, New York.
Cajori, Florian: [1928-1929] 1993. A History of Mathematical Notations. Two Volumes Bound as One, Dover, New York.
Cavalieri, Bonaventura: [1635] 1653. Geometria indivisibilibus continuorum nova quadam ratione promota, Bononiae.
Cavalieri, Bonaventura: 1647. Exercitationes geometricae sex, Bononiae.
DeGandt, François: 1987. ‘Les Indivisibles de Torricelli’, L'oeuvre de Torricelli: Science Galiléenne et Nouvelle Géométrie, Publications de la Faculté des Lettres et Sciences Humaines de Nice, Nice, pp. 147–206.
DeGandt, François: 1991. ‘Cavalieri's Indivisibles and Euclid's Canons’, in P. Barker and R. Ariew (eds.), Revolution and Continuity, Catholic University Press, Washington, DC, pp. 157–182.
Frege, Gottlob: ([1879] 1967). Begriffsschrift, a Formula Language, Modeled up on that of Arithmetic, for Pure Thought, Stephan Bauer-Mengelberg, (trans.), in J. van Heijenoort (ed.), From Frege to Gödel, Harvard University Press, Cambridge, MA.
Frege, Gottlob: [1884] 1980. The Foundations of Arithmetic, 2nd rev. edn., J. L. Austin (trans.), Northwestern University Press, Evanston.
Frege, Gottlob: [1893] 1997. ‘Grundgesetze der Arithmetik’, Vol. I, in M. Beaney (trans. and ed.), The Frege Reader, Blackwell, Oxford, pp. 194–223.
Freudenthal, Hans: 1977. ‘What is Algebra and What has it been in History?’, Archive for History of Exact Sciences 16, 189–200.
Hill, Katherine: 1996. ‘Neither Ancient nor Modern: Wallis and Barrow on the Composition of Continua’, Part One: ‘Mathematical Styles and the Composition of Continua’, Notes and Records of the Royal Society London 50(2), 165–178.
Kitcher, Philip: 1988. ‘Mathematical Naturalism’, in W. Aspray and P. Kitcher (eds.), History and Philosophy of Modern Mathematics, University of Minnesota Press, Minneapolis, pp. 293–325.
Lakatos, Imre: 1976. Proofs and Refutations. J. Worrall and E. Zahar (eds.), Cambridge University Press, Cambridge.
Mancosu, Paolo: 1996. Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century, Oxford University Press, New York.
Muntersbjorn, Madeline M: 1999. ‘Naturalism, Notation, and the Metaphysics of Mathematics’, Philosophia Mathematica 7(3), 178–199.
Pycior, Helena: 1997. Symbols, Impossible Numbers, and Geometric Entanglements, Cambridge University Press, Cambridge.
Resnik, Michael D. (ed.): 1995. Mathematical Objects and Mathematical Knowledge, Dartmouth, Aldershot.
Smith, David Eugene: 1963. Mathematics. New York: Cooper Square.
Struik, D. J.: 1969. A Source Book in Mathematics 1200-1800, Harvard University Press, Cambridge, MA.
Tappenden, Jamie: 1995. ‘Extending Knowledge and ‘Fruitful Concepts’: Fregean Themes in the Foundations of Mathematics’, Noûs 29(4), 427–467.
Unguru, Sabetai: 1975. ‘On the Need to Rewrite the History of Greek Mathematics’, Archive for History of Exact Sciences 15: 67–114.
Van Bendegem and Jean Paul: 1993. ‘Foundations of Mathematics or Mathematical Practice: Is One Forced to Choose?’, in S. Restivo, J.P. Bendegem and R. Fischer (eds.), Math Worlds. Philosophical and Social Studies of Mathematics and Mathematics Education, pp. 21–38.
Wallis, John: 1685. A Treatise of Algebra, Both Historical and Practical, London.
Wallis, John: 1695-1699. Opera Mathematica, 3 vols, Oxoniae.
Whiteside, D. T.: 1962. ‘Patterns of Mathematical Thought in the later Seventeenth Century’, Archive for History of Exact Sciences 1, 179–388.
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Muntersbjorn, M.M. Representational Innovation and Mathematical Ontology. Synthese 134, 159–180 (2003). https://doi.org/10.1023/A:1022139715092
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DOI: https://doi.org/10.1023/A:1022139715092