Skip to main content
SpringerLink
Log in

Cavalieri's method of indivisibles

  • Published:
Archive for History of Exact Sciences Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Literature

  • Stefano degli Angeli, 1659: De infinitis parabolis, Venezia.

  • Archimedes, On Conoids and Spheroids: An English paraphrase is published in The works of Archimedes (ed. T. L. Heath), New York 1897, pp. 99–150. A French translation is published in Les ouevres complètes d'Archimède (ed. P. Ver Eecke), vol. 1, second edition, Liège 1960, pp. 137–237.

  • Gino Arrighi, 1973: “La Geometria indivisibilibus continuorum di Bonaventura Cavalieri nella ritrovata stesura del 1627”, Physis, 15, pp. 133–147.

    Google Scholar 

  • Carl B. Boyer, 1941: “Cavalieri, Limits and Discarded Infinitesimals”, Scripta Mathematica, 8, pp. 79–91.

    Google Scholar 

  • Carl B. Boyer, 1968: A History of Mathematics, New York.

  • Ettore Carruccio, 1971: “Cavalieri”, Dictionary of Scientific Biography (ed. C. C. Gillispie), New York, vol. 3, pp. 149–153.

    Google Scholar 

  • Bonaventura Cavalieri, 16321: Directorium generale vranometricum, in quo trigonometriae logorithmicae fundamenta ..., Bologna.

  • Bonaventura Cavalieri, 16322: Lo Specchio vstorio ouero Trattato delle settioni coniche, Bologna. 2nd edition Bologna 1650.

  • Bonaventura Cavalieri 1635: Geometria indiuisibilibus continuorum noua quadam ratione promota, Bologna. 2nd edition Bologna 1653. See also Lombardo-Radice 1966 and Lur'e 1940. References in this paper are to the second edition.

  • Bonaventura Cavalieri, 1638: Compendio delle regole de triangoli, Bologna.

  • Bonaventura Cavalieri, 16391: Centuria di varii problemi. Per dimostrare l'uso e la facilità de' logaritmi nella gnomonica, astronomica, geograffia, altimetria, pianimetria, stereometria, & aritmetica prattica, Bologna.

  • Bonaventura Cavalieri, 16392: Nuoua pratica astrologica, Bologna.

  • Bonaventura Cavalieri, 1640: Appendice della nuoua pratica astrologica, Bologna.

  • Bonaventura Cavalieri, 1643: Trigonometria plana et sphaerica, Bologna.

  • Bonaventura Cavalieri, 1646: Silvio Filomantia, Trattato della ruota planetaria perpetua e dell'uso di quella, Bologna.

  • Bonaventura Cavalieri, 1647: Exercitationes geometricae sex. Bologna (Reprint Bologna 1980).

  • Bonaventura Cavalieri, n.d.: Tavola prima logarithmica. Tavola seconda logaritmica. Bologna.

  • G. Cellini, 19661: “Gli indivisibili nel pensiero matematico e filosofico di Bonaventura Cavalieri”, Periodico di matematiche, 4th ser., 44, pp. 1–21.

    Google Scholar 

  • G. Cellini, 19662: “Le dimostrazioni di Cavalieri del suo principio”, ibid., 4th ser., 44, pp. 85–105.

    Google Scholar 

  • Urbano Daviso, 1682: Trattato della Sfera, Roma. Introductory, the book contains “Vita del P. Buonaventura Cavalieri”.

  • G. W. Evans, 1917: “Cavalieri's Theorem in his own Words”, The American Mathematical Monthly, 24, pp. 447–451.

    Google Scholar 

  • Euclid: The Thirteen Books of Euclid's Elements (ed. Thomas L. Heath), 3 vols., 2nd ed. Cambridge 1925 (Reprint New York 1956).

  • Antonio Favaro, 1888: Bonaventura Cavalieri nello studio di Bologna, Bologna.

  • Antonio Favaro, 1905: “Bonaventura Cavalieri e la quadratura della spirale”, Rendiconti del Reale Istituto Lombardo di Scienze e Lettere, Serie II, 38, pp. 358–372.

    Google Scholar 

  • Emil A. Fellmann, 1959: “Die mathematischen Werke von Honoratus Fabry”, Physis, 1, pp. 6–25 and 73–102.

    Google Scholar 

  • Galileo Galilei: Le Opere di Galileo Galilei (ed. Antonio Favaro), 20 vols., 2nd edition, Firenze 1929–1939.

  • Galileo Galilei, 1914: Dialogues concerning two new Sciences (ed. Henry Crew et al.), New York.

  • M. Galuzzi & A. Guerraggio, “Some Interpretations of the Method of Indivisibles”, forthcoming in Jahrbuch Überblick Mathematik.

  • Enrico Giusti, 1980: Bonaventura Cavalieri and the Theory of Indivisibles, Bologna.

  • Paul Guldin, 1635–1641: Centrobaryca seu de centro grauitatis ..., 4 vols., Wien.

  • Johannes Hjelmslev, 1950: “Eudoxus' Axiom and Archimedes' Lemma”, Centaurus, 1, pp. 2–11.

    Google Scholar 

  • Christiaan Huygens: Oeuvres Complètes de Christiaan Huygens, 22 vols., La Haye, 1888–1950.

  • Jean Itard, 1953: “Quelques remarques historiques sur l'axiomatique du concept de grandeur”, La Revue Scientifique, 91, pp. 3–14.

    Google Scholar 

  • Johannes Kepler, 1615: Noua stereometria doliorum vinariorum, Linz.

  • Johannes Kepler: Gesammelte Werke, München 1937-.

  • Helmut Krieger, 1971: “Konstruktion bogengleicher algebraischer Kurven in historischer Sicht”, Centaurus, 16, pp. 92–162.

    Google Scholar 

  • G. W. Leibniz, 1920: The Early Mathematical Manuscripts of Leibniz (ed. J. M. Child), Chicago and London.

  • Lucio Lombardo-Radice, 1966: Geometria degli indivisibili di Bonaventura Cavalieri, Torino. This book contains an annotated Italian translation of Geometria and Exercitationes, Book III.

  • S. J. Lur'e, 1940: Bonaventura Kavalieri Geometrija izlozennaja novym sposobom, Moscow and Leningrad 1940. This book contains a Russian translation of Geometria Books I and II, and Exercitationes, Book IV with comments.

  • Colin MacLaurin, 1742: A Treatise of Fluxions, 2 vols., Edinburgh.

  • Maximilien Marie, 1883–1888: Histoire des sciences mathématiques et physiques, 12 vols., Paris (Reprint New York 1977).

  • Arnaldo Masotti, 1948: “Commemorazione di Bonaventura Cavalieri”, Rendiconti dell'Istituto Lombardo di scienze e lettere, parte generale e atti ufficiali, 81, pp. 43–86. Also as separate print, Milano 1949. The treatise contains an extensive list of the literature up to 1948 on Cavalieri.

    Google Scholar 

  • Mersenne: Correspondance du P. Marin Mersenne, Vol. 1-, Paris 1945-.

  • Guidobaldo del Monte, 1588: Guidi Ubaldo, In duos Archimedis aequeponderantium libros paraphrasis ..., Pesaro.

  • Jean Etienne Montucla, 1758: Histoire des Mathématiques, 2 vols., Paris, second edition 4 vols., Paris 1799–1802 (Reprint Paris 1968).

  • Blaise Pascal: Oeuvres de Blaise Pascal, 14 vols., Paris 1904–1914.

  • Kirsti M. Pedersen, 1970: “Roberval's Comparison of the Arclength of a Spiral and a Parabola”, Centaurus, 15, pp. 26–43.

    Google Scholar 

  • Kirsti M. Pedersen, 1980: “Techniques of the Calculus, 1630–1660”, in From the Calculus to Set Theory 1630–1910 (ed. I. Grattan-Guinness), London, pp. 10–48.

  • Gabrio Piola, 1844: Elogio di Bonaventura Cavalieri, Milano.

  • C. Renaldinus, 1668: De resolutione et compositione mathematica, Padua.

  • Gilles P. Roberval, 1730: “Traité des indivisibles” in Mémoires de l'Académie Royale des Sciences depuis 1666 jusqu'a 1699, vol. 6, Paris. There are two editions with this title; I have used the one starting in the following way: On a rassemblé dans ce Sixième Tome les Ouvrages de Mr. DE ROBERVAL. Ce Volume contient ...

  • D. E. Smith, 1929: A Source Book in Mathematics, 2 vols. (Reprint New York 1959).

  • Bartholomeus Sover, 1630: Curvi ac recti proportio promota, Padua.

  • Edward Stamm, 1936. “Tractatus de Continuo von Thomas Bradwardina”, Isis, 26, pp. 13–32.

    Google Scholar 

  • D. J. Struik, 1969: A Source Book in Mathematics 1200–1800, Cambridge, Massachusetts.

  • J. C. Sturm, 1700: Mathesis enucleata: or the elements of mathematicks, London. Translation of Mathesis enucleata, Nüremberg 1687.

  • Evangelista Torricelli: Opere di Evangelista Torricelli (ed. Gino Loria e Giuseppe Vassura), 4 vols., Faenza 1919–1944.

  • Luca Valerio, 1604: De centro gravitatis solidorum, Roma.

  • Evelyn Walker, 1932: A Study of the Traité des indivisibles of Gilles Persone de Roberval, New York.

  • John Wallis, 1972: Opera mathematica (ed. C. J. Scriba), vol. 1, Hildesheim and New York (Reprint of Oxford 1695).

  • C. R. Wallner, 1903: “Die Wandlungen des Indivisibilienbegriffs von Cavalieri bis Wallis”, Bibliotheca Mathematica, Dritte Folge, 4, pp. 28–47.

    Google Scholar 

  • H. G. Zeuthen, 1903: Geschichte der Mathematik im XVI. und XVII. Jahrhundert, Leipzig (Reprint New York 1966).

Download references

Author information

Authors and Affiliations

  1. History of Science Department, University of Aarhus, Denmark

    Kirsti Andersen

Authors
  1. Kirsti Andersen
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by C. J. Scriba & Olaf Pedersen

Rights and permissions

Reprints and permissions

About this article

Cite this article

Andersen, K. Cavalieri's method of indivisibles. Arch. Hist. Exact Sci. 31, 291–367 (1985). https://doi.org/10.1007/BF00348519

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00348519

Search

Navigation