Skip to main content
SpringerLink
Log in

The natures of numbers in and around Bombelli’s L’algebra

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

Abstract

The purpose of this article is to analyse the mathematical practices leading to Rafael Bombelli’s L’algebra (1572). The context for the analysis is the Italian algebra practiced by abbacus masters and Renaissance mathematicians of the fourteenth to sixteenth centuries. We will focus here on the semiotic aspects of algebraic practices and on the organisation of knowledge. Our purpose is to show how symbols that stand for underdetermined meanings combine with shifting principles of organisation to change the character of algebra.

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

Similar content being viewed by others

References

  • Bombello, Rafaello. 155?. L’algebra. Bologna, Biblioteca dell’Archiginnasio, B.1569.

  • Bombelli, Rafael. 1572. L’algebra. Bologna.

  • Bombelli, Rafael. 1929. L’algebra, Libri IV e V. Bortolotti, E., ed. Bologna. http://a2.lib.uchicago.edu/pip.php?/pres/2005/pres2005-188.pdf.

  • Bombelli, Rafael. 1966. L’algebra, Prima edizione integrale. Bortolotti, E., ed. Milano.

  • Benedetto (attributed to Pier Maria Calandri). 1974. Tractato d’abbacho, Arrighi, G., ed. Paris.

  • Cardano, Girolamo. 1545. Ars Magna sive de regulis algebraicis. Nürnberg.

  • Cardano, Girolamo. 1663. Hieronymo Cardani Mediolanensis Philosophi ac Medici celeberrimi Operum tomus quartus; quo continentur Arithmetica, Geometrica, Musica. Lyon.

  • Cardano, Girolamo. 1968. The rules of algebra (Ars Magna) (trans: Whitmer, T.R.). Mineola, NY.

  • Cifoletti, Giovanna. 1995. La question de l’algèbre: mathématiques et rhétorique des hommes de droit dans la France du 16e sicle. Annales. Histoire, Sciences Sociales 50(6): 1385–1416.

    Google Scholar 

  • Dardi. 2001. Aliabraa argibra, Franci, R., ed. Siena.

  • de Mazzinghi, Antonio. 1967. Trattato di Fioretti, Arrighi, G., ed. Paris.

  • della Francesca, Piero. 1970. Trattato d’abaco, Arrighi, G., ed. Paris.

  • Derrida Jacques. (1989) Edmund Husserl’s origin of geometry: An introduction. Lincoln, Nebraska

    Google Scholar 

  • Dieudonné, Jean. 1972. Review of J.E. Hofmann ‘R. Bombelli—Erstentdecker des Imaginären’. Praxis Math 14(9): 225–230. Math Review MR0484973 (58 #4832a).

  • Franci Rafaella, Laura Toti Rigatelli. (1985) Towards a history of algebra from Leonardo of Pisa to Luca Pacioli. Janus 72(1–3): 17–82

    MATH  MathSciNet  Google Scholar 

  • Giusti Enrico. (1991) L’algebra nel Trattato d’abaco di Piero della Francesca: osservazioni e congetture. Bollettino di storia delle scienze matematiche 11: 55–83

    MATH  MathSciNet  Google Scholar 

  • Giusti Enrico. (1992) Algebra and geometry in Bombelli and Viète. Bollettino di storia delle scienze matematiche 12: 303–328

    MATH  MathSciNet  Google Scholar 

  • Grosholz, Emily R. 2007. Representation and productive ambiguity in mathematics and the sciences. Oxford.

  • Heefer, Albrecht. 2005. The rhetoric of problems in algebra texbooks from Pacioli to Euler. Preprint. http://logica.ugent.be/albrecht/thesis/AlgebraRhetoric.pdf.

  • Heeffer Albrecht. (2008) The emergence of symbolic algebra as a shift in predominant models. Foundations of Science 13(2): 149–161

    Article  MathSciNet  Google Scholar 

  • Høyrup, Jens. 1994. In measure, number and weight. NY.

  • Høyrup, Jens. 2007. Jacopo Da Firenze’s Tractatus algorismi and early Italian abbacus culture. Basel.

  • Høyrup, Jens. 2009a. What did the abbacus teachers aim at when they (sometimes) ended up doing mathematics? An investigation of the incentives and norms of a distinct mathematical practice. In New Perspectives on mathematical practices, Van Kerkhove, B., ed. Singapore.

  • Høyrup, Jens. 2009b. Hesitating progress: The slow development toward algebraic symbolization in abbacus and related manuscripts, c. 1300 to c. 1550. Preprint presented at the PASR conference in Ghent, August 29, 2009.

  • Jayawardene S.A. (1963) Unpublished Documents relating to Rafael Bombelli in the archives of Bologna. Isis 54(3): 391–395

    Article  MATH  Google Scholar 

  • Jayawardene S.A. (1965) Rafael Bombelli, engineer-architect: Some unpublished documents of the Apostolic Camera. Isis 56(3): 298–306

    Article  Google Scholar 

  • Jayawardene S.A. (1973) The influence of practical arithmetics on the algebra of Rafael Bombelli. Isis 64(4): 510–523

    Article  MATH  MathSciNet  Google Scholar 

  • La Nave Federica, Barry Mazur. (2002) ‘Reading Bombelli’. The Mathematical Intellegencer 24(1): 12–21

    Article  MATH  Google Scholar 

  • Leonardo Pisano. 1862. Boncompagni, B., ed. Scritti di Leonardo Pisano: mathematico del secolo decimoterzo, Vol. II. Roma.

  • Malet Antoni. (2006) Renaissance notions of number and magnitude. Historia Mathematica 33: 63–81

    Article  MATH  MathSciNet  Google Scholar 

  • Netz, Reviel. 2004. The transformation of mathematics in the early Mediterranean world. Cambridge.

  • Paolo dell’Abbaco. 1964. Trattato d’aritmetica, Arrighi, G., ed. Paris.

  • Radford Luis. (1997) Before the other unknowns were invented: Didactic inquiries on the methods and problems of mediaeval Italian algebra. For the Learning of Mathematics 15(3): 28–38

    MathSciNet  Google Scholar 

  • Radford Luis. (2003) On the epistemological limits of language: Mathematical knowledge and social practice during the Renaissance. Educational Studies in Mathematics 52: 123–150

    Article  Google Scholar 

  • Rivolo M.T., Simi A. (1998) The computation of square and cube roots in Italy from Fibonacci to Bombelli. Archives for the History of Exact Science 52(2): 161–193

    Article  MATH  MathSciNet  Google Scholar 

  • Rose, Paul L. 1975. The Italian Renaissance of mathematics. Studies on humanists and mathematicians from Petrarch to Galileo. Genève.

  • Tanner R.C.H. (1980) The alien realm of the minus: Deviatory mathematics in Cardano’s writings. Annals of Science 37(2): 159–178

    Article  MATH  MathSciNet  Google Scholar 

  • Tartaglia, Niccolo Fontana. 1543. Euclide megarense philosopho: solo introduttore delle scientie mathematice: diligentemente reassettato, et alla integrita ridotto ...Secondo le due Tradottioni. Venice.

  • Tartaglia, Niccolo Fontana. 1560. General Trattato di Numeri et Misure, Part VI. Venice.

  • Van Egmond, Warren. 1980. Practical mathematics in the Italian Renaissance: A catalog of Italian abbacus manuscripts and printed books to 1600. Firenze.

  • Wagner, Roy. 2009a. S(z p , z p ): Post structural readings of Gödel’s proof. Milano.

  • Wagner Roy. (2009) Mathematical variables as indigenous concepts. International Studies in the Philosophy of Science 32(1): 1–18

    Article  Google Scholar 

  • Wagner, Roy. 2010. For a thicker semiotic description of mathematical practice and structure. In Philosophy of mathematics: Philosophical aspects and mathematical practice, Löwe, B. and T. Müller, eds. London.

  • Wagner, Roy. Forthcoming. The geometry of the unknown: Bombelli’s Algebra Linearia. In Philosophical aspects of symbolic reasoning in early modern science and mathematics, Heeffer, A. and M. Van Dyck eds. London.

Download references

Author information

Authors and Affiliations

  1. The Edelstein Center for the History and Philosophy of Science, Technology and Medicine, The Hebrew University in Jerusalem, Givat Ram, 91904, Jerusalem, Israel

    Roy Wagner

Authors
  1. Roy Wagner
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Roy Wagner.

Additional information

Communicated by Niccolo Guicciardini.

Part of the research for this article was conducted whilst visiting Boston University’s Center for the Philosophy of Science, the Max Planck Institute for the History of Science and the Edelstein Center for the History, and Philosophy of Science, Technology and Medicine.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wagner, R. The natures of numbers in and around Bombelli’s L’algebra . Arch. Hist. Exact Sci. 64, 485–523 (2010). https://doi.org/10.1007/s00407-010-0062-1

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00407-010-0062-1

Keywords

Search

Navigation