One of Berkeley's arguments on compensating errors in the calculus

Historia Mathematica

Volumn 38, Issue 2, 2011, Pages 219-231

  Andersen, Kirsti ^a  

^a AARHUS UNIVERSITY   (Denmark)

Author keywords

Berkeley; Carnot; Compensating errors

Indexed keywords

EID: 79952250831     PISSN: 03150860     EISSN: 1090249X     Source Type: Journal    
DOI: 10.1016/j.hm.2010.07.001     Document Type: Article

References (24)

1. Arthur, Richard T.W., 2008. Leery bedfellows: Newton and Leibniz on the status of infinitesimals. In: Ursula Goldenbaum, & Douglas, Jesseph, (Eds.). Infinitesimal Differences. Controversies between Leibniz and his Contemporaries. New York, pp. 7-30.
2. Barreau Hervé Lazare Carnot defenseur des infinitesimaux. Cahiers d'histoire & philosophie des sciences, nouvelle série 1987, 20:1-10.
3. Berkeley, George, 1734. The Analyst or a Discourse Addressed to an Infidel Mathematician, London.
4. Blay Michel Deux moment de la critique du calcul infinitesimal: Michel Rolle et George Berkeley. Revue d'histoire des sciences 1986, 39:223-253.
5. Bos Henk J.M. Differentials, higher order differentials and the derivative in the Leibnizian calculus. Archive for History of the Exact Sciences 1974, 14:1-90.
6. Breidert,Wolfgang, 1989. George Berkeley 1685-1753, Basel.
7. Cantor Geoffrey Berkeley's The Analyst revisited. Isis 1984, 75:668-683.
8. Carnot, Lazare, 1797. Réflexions sur la Métaphysique Du Calcul Infinitesimal, Paris. Second edition Paris 1813.
9. Dhombres, Jean, Dhombres, Nicole, 1997. Lazare Carnot, Paris.
10. Gillispie, Charles Coulston, 1971a. Lazare Carnot. In: Gillispie, Charles Coulston (Ed.), Dictionary of Scientific Biography, vol. 3. New York, pp. 70-79.
11. Gillispie, Charles Coulston, 1971b. Lazare Carnot Savant, Princeton. French edition Paris 1979.
12. Grabiner, Judith V., 1981. The Origin of Cauchy's Rigorous Calculus, Cambridge, Massachusetts.
13. Grattan-Guinness Ivor Criticism of the calculus as a study in the theory of limits. Janus 1969, 56:215-227.
14. Guiccardini, Niccolò, 1989. The Development of Newtonian Calculus in Britain 1700-1800, Cambridge.
15. Jesseph, Douglas M., 1992. Introduction to The Analyst. In: George Berkeley, De motu and The Analyst, edited and translated by Douglas M. Jesseph, Dordrecht, pp. 111-155.
16. Jesseph, Douglas M., 1993. Berkeley's Philosophy of Mathematics, Chicago.
17. Jesseph Douglas M. Leibniz on the foundations of the calculus: the question of reality of infinitesimal magnitudes. Perspectives on Science 1998, 6:121-130.
18. Jesseph, Douglas M., 2005. George Berkeley, The Analyst (1734). In: Ivor Grattan-Guinness, (Ed.), Landmark Writings in Western Mathematics 1640-1940. pp. 6-40. (Chapter 8).
19. Jesseph, Douglas M., 2008. Faith and fluxions: Berkeley on theology and mathematics. In: Daniel, Steve, (Ed.), New Interpretations of Berkeley's Thought, New York, pp. 247-260.
20. L'Hospital, Guillaume François Antoine, 1696. Analyse des Infiniments Petits, Paris. Facsimile reprint Paris 1988.
21. Pycior, Helena M., 1997. Symbols, Impossible Numbers, and Geometric Entanglements: British Algebra through the Commentaries on Newton's Universal Arithmetick, Cambridge.
22. Schubring, Gert, 2005. Conflicts between Generalization, Rigor and Intuition. Number Concepts Underlying the Development of Analysis in 17-19th Century France and Germany, New York.
23. Thiele, Rüdiger, 1990. Carnots betrachtungen über die grundlagen der analysis. In: Spalt, Detlef, (Ed.), Rechnen mit dem Unendlichen, Basel, pp. 69 -94.
24. Youschkevitch, Adolf P., 1971. Lazare Carnot and the competition of the Berlin academy on the mathematical theory of the infinite in Gillispie 1971, pp. 149-168.