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Archive for History of Exact Sciences

, Volume 63, Issue 4, pp 433–470 | Cite as

Between Viète and Descartes: Adriaan van Roomen and the Mathesis Universalis

  • Paul Bockstaele
Article

Abstract

Adriaan van Roomen published an outline of what he called a Mathesis Universalis in 1597. This earned him a well-deserved place in the history of early modern ideas about a universal mathematics which was intended to encompass both geometry and arithmetic and to provide general rules valid for operations involving numbers, geometrical magnitudes, and all other quantities amenable to measurement and calculation. ‘Mathesis Universalis’ (MU) became the most common (though not the only) term for mathematical theories developed with that aim. At some time around 1600 van Roomen composed a new version of his MU, considerably different from the earlier one. This second version was never effectively published and it has not been discussed in detail in the secondary literature before. The text has, however, survived and the two versions are presented and compared in the present article. Sections 1–6 are about the first version of van Roomen’s MU the occasion of its publication (a controversy about Archimedes’ treatise on the circle, Sect. 2), its conceptual context (Sect. 3), its structure (with an overview of its definitions, axioms, and theorems) and its dependence on Clavius’ use of numbers in dealing with both rational and irrational ratios (Sect. 4), the geometrical interpretation of arithmetical operations multiplication and division (Sect. 5), and an analysis of its content in modern terms. In his second version of a MU van Roomen took algebra into account, inspired by Viète’s early treatises; he planned to publish it as part of a new edition of Al-Khwarizmi’s treatise on algebra (Sect. 7). Section 8 describes the conceptual background and the difficulties involved in the merging of algebra and geometry; Sect. 9 summarizes and analyzes the definitions, axioms and theorems of the second version, noting the differences with the first version and tracing the influence of Viète. Section 10 deals with the influence of van Roomen on later discussions of MU, and briefly sketches Descartes’ ideas about MU as expressed in the latter’s Regulae.

Keywords

Regular Polygon Rational Proportion Modern Term Algebraic Term Book Versus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Alsted, Johann Heinrich. 1613. Methodus admirandorum mathematicorum complectens novem libros matheseos universae, Herborn.Google Scholar
  2. Andreas Valerius. (1643) Bibliotheca Belgica: De Belgis vita scriptisque claris. Jacob Zegers, LeuvenGoogle Scholar
  3. Apollonius. 1566. Conicorum libri priores quattuor, una cum Pappi Alexandrini lemmatibus et commentariis Eutocii Ascalonitae, Sereni Antissensis philosophi libri de sectione cylindri et coni nunc primum in lucem editi. Quae omnia nuper Federicus Commandinus Urbinas mendis quamplurimis expurgata e Graeco convertit, et commentariis illustravit (tr. annot. ed. F. Commandino), 2 vols. Bologna: Ex officina Alexandri Benatii.Google Scholar
  4. Apollonius. 1710. Conicorum libri octo, et Sereni. Antissensis De Sectione Cylindri et coni libri duo (also Pappus’ Lemmata and Eutocius’ Commentaries, ed. Edm. Halley, OxfordGoogle Scholar
  5. Archimedes. 1558. Opera non nulla (tr. ed. F. Commandino). Venice: apud P. Manutium.Google Scholar
  6. Archimedes. The Works of Archimedes, ed. intr. tr. Thomas L. Heath, reprint of ed. 1897, with suppl.: ‘the method’ of 1912. New York: Dover.Google Scholar
  7. Aristotle. 1952. The Works of Aristotle. Encyclopaedia Brittanica.Google Scholar
  8. Beeckman, Isaac. 1939–1953. Journal tenu par Isaac Beeckman de 1604 à 1634, ed. annot. introd. C. de Waard, 4 vols. The Hague: Martinus Nijhoff.Google Scholar
  9. Benedetti Giovanni Battista. (1585) Io Baptistae Benedicti Patritii Veneti philosophi diversarum speculationum mathematicarum et physicarum liber. Turin, apud Haeredem Nicolai BevilaquaeGoogle Scholar
  10. Bockstaele, Paul. 1963. Adriaan van Roomen en Polen : Zijn onderwijs te Zamosz en zijn invloed op Jan Broszek. Mededeelingen Kon. Vlaamse Academie voor Wetenschappen, Letteren en Schone Kunsten van België, Klasse der Wetenschappen, 25, 8.Google Scholar
  11. Bockstaele Paul. (19760. The correspondence of Adriaan van Roomen. Lias 3:85–129, 249–299Google Scholar
  12. Bockstaele Paul. (1992) The correspondence of Adriaan van Roomen: corrections and additions, 1594–1615. Lias 19: 3–20Google Scholar
  13. Bosmans Henri. (1906) Le fragment du commentaire d’Adrien Romain sur l’Algèbre de Mahumed ben Musa el-Chowârezmî. Annales de la Société scientifique de Bruxelles 30: 267–287Google Scholar
  14. Boncompagni, Baldassare. 1851–52. Della vita e delle opere di Leonardo Pisano, matematico del secolo decimoterze. Atti dell’ Academia Pontifica de Nuovi Lincei 5: 5–91, 208–246.Google Scholar
  15. Cardano Girolamo. (1545) Artis magnae sive de regulis algebraicis liber unus. Nürnberg, Johann PetraeusGoogle Scholar
  16. Crapulli Giovanni. (1969). Mathesis Universalis; genesi di una idea nel XVI secolo. Rome: Edizioni dell’AteneoGoogle Scholar
  17. Descartes, René. 1964–74. Regulae ad directionem ingenii. In (Descartes 1964–74b), vol. 10, 359–469.Google Scholar
  18. Descartes, René. 1964–74. Oeuvres de Descartes nouvelle présentation, eds. Adam, Charles, & Tannery, Paul, Paris, 1897–1913, 12 vols, Paris: Vrin.Google Scholar
  19. Descartes, René. 1998. Regulae ad directionem ingenii : Rules for the direction of the natural intelligence. In Studies in the history of ideas in the Low Countries, ed. tr. George Hefferman (bilingual edition), 3. Amsterdam: Rodopi.Google Scholar
  20. Diophantus. 1575. Rerum arithmeticarum libri sex, quorum duo adjecta habent scholia Maximi Planudis, item liber de numeris polygonis seu multangulis, ed. G. Xylander. (W. Holzmann), Basel.Google Scholar
  21. Egmond, Warren van. 1985. A catalog of Viète’s printed and manuscript works. In Mathemata: Festschrift für Helmuth Gericke, eds. Menso Folkerts, Uta Lindgren, 59–396. Stuttgart: Franz Steiner.Google Scholar
  22. Euclid. 1533. Eukleidou stoicheioon. Euclidis Elementorum XV ex Theonis coloquiis. Primum ejus librum commentarium Procli libri IV Graece. Adiecta praefatiuncula in qua de disciplinis mathematicis nonnihil, ed. S. Grynaeus, Basel.Google Scholar
  23. Euclid. 1591. Euclidis elementorum libri XV accessit XVI de solidorum regularium cuiuslibet intra quodlibet comparatione. Omnes perspicuis demonstrationibus, accuratisque scholiis illustrati, ac multarum rerum accessione locupletati. Nunc tertio editi, summaque diligentia recogniti, atque emendati, ed. Chr. Clavius, 2 vols. Cologne: Expensis Ioh. Baptistae Ciotti.Google Scholar
  24. Euclid. 1956. The thirteen books of Euclid’s Elements (tr. intr. comm. Thomas L. Heath; reprint of ed. 1926), 3 vols. New York: Dover.Google Scholar
  25. Gemma Frisius, Reiner. 1581. Arithmeticae Practicae methodus facilis, per Gemmam Frisium, Medicum et Mathematicum conscripta, iam recens ab Auctore pluribus locis aucta et recognita. In eandem Ioannis Steinii et Jacobi Peletarii Annotationes (based on an edition Cologne 1571). Antwerp: J. van der Loo, P. van Tongeren.Google Scholar
  26. Gilbert, Philippe. 1859. Notice sur le mathématicien Louvaniste Adrianus Romanus, professeur à l’ancienne Université de Louvain. Revue Catholique 17: 277–286, 394–409.Google Scholar
  27. Gosselin, G. 1577. De arte magna seu de occulta parte numerorum quae et algebra et almucabala vulgo dicitur, libri quattuor. In quibus explicantur aequationes Diophanti, regulae quantitatis simplicis et quantitatis surdae. Paris: Apud Aegidium Beys.Google Scholar
  28. Kepler Johannes. (1619) Harmonices mundi libri V. Linz, Ioannes PlancusGoogle Scholar
  29. Maurolico, Franceso. 1575. Arithmetica Google Scholar
  30. du Mans Peletier, Jacques. (1560) De occulta parte numerorum, quam Algebram vocant, libri duo. Guillaume Cavellat, ParisGoogle Scholar
  31. Pereira Benito. (1576) De communibus omnium rerum naturalium principiis et affectionibus libri quindecim. apud Franciscum et Bartholomaeum Tosium, RomeGoogle Scholar
  32. Proclus. 1533. Commentariorum Procli editio prima quae Simonis Grynaei opera addita est Euclidis elementis graece editis, ed. S. Grynaeus, Basel.Google Scholar
  33. Proclus. 1560. In primum Euclidis Elementorum librum commentariorum ad universam mathematicam disciplinam principium eruditionis tradentium libri III, ed. F. Barozzi, Padua.Google Scholar
  34. Proclus. 1970. A commentary on the first book of Euclid’s Elements tr. intr. Glenn R. Morrow. Princeton: Princeton University Press.Google Scholar
  35. Romanus, Adrianus. 1593. Ideae mathematicae pars prima sive methodus polygonorum qua laterum, perimetrorum et arearum cujuscunque polygoni investigandorum ratio exactissima et certissima una cum circuli quadratura continetur. Antwerp.Google Scholar
  36. Romanus, Adrianus. 1597. In Archimedis circuli dimensionem expositio et analysis: Apologia pro Archimede ad Clariss. virum Josephum Scaligerum: Exercitationes cyclicae contra Iosephum Scaligerum, Orontium Finaeum et Raymarum Ursum, in decem dialogos distinctae. Würzburg.Google Scholar
  37. Romanus, Adrianus. After 1600. In Mahumedis arabis algebram prolegomena. Würzburg: Georg Fleischmann, c. 1602 (At present, no extant copies of this item are known, see section 7, esp footnote 75).Google Scholar
  38. Romanus Adrianus. 1602. Universae mathesis idea, qua mathematicae universim sumptae natura, praestantia, usus et distributio brevissime proponuntur. Würzburg: Georg FleischmannGoogle Scholar
  39. Romanus Adrianus. (1605). Mathesis Polemica. Frankfurt: Laevinus HulsiusGoogle Scholar
  40. Scaliger, Joseph. 1594. Cyclometrica elementa duo. Leiden: Ex officina Plantiniana, apud Franciscum Raphelengium.Google Scholar
  41. Scaliger, Joseph. 1594. Mesolabium ad nobiles academiae Lugdunensis Batavorum Curatores et magnifices eiusdem civitatis consules. Leiden: Ex officina Plantiniana, apud Franciscum Raphelengium.Google Scholar
  42. Scaliger, Joseph. 1594. Appendix ad cyclometrica sua: in qua asseritur quadratio circuli, contra oblationes quorundam, et castigantur quaedam errata in demonstrationibus cyclometricis. Leiden: Ex officina Plantiniana, apud Franciscum Raphelengium.Google Scholar
  43. Stevin, Simon. 1585. L’Arithmetique ...: aussi l’algèbre ... les quatre premiers livres d’Algebre de Diophante d’Alexandrie ... un livre particulier de la Pratique d’arithmetique ... Et une traicté des Incommensurables grandeurs: avec l’explication du Dixiesme Livre d’Euclide. Leiden: Christophe Plantin.Google Scholar
  44. Viète, François. 1591. In artem analyticen isagoge: seorsim excussa ab opere restitutae mathematicae analyseos seu algebra nova. Tours: Jamet Mettayer.Google Scholar
  45. Viète, François. 1592. Effectionum geometricarum canonica recensio, Tours.Google Scholar
  46. Viète François. (1593) Supplementum geometriae : ex opere restitutae mathematicae analyseos seu algebra nova. Tours, Jamet MettayerGoogle Scholar
  47. Viète François. (1593) Variorum de rebus mathematicis responsorum liber VIII cuius praecipua capita sunt de duplicatione cubi et quadratione circuli. Tours, J. MettayerGoogle Scholar
  48. Viète, François. 1593–1600. Zeteticorum libri quinque. Tours: Jamet Mettayer/David le Clerc.Google Scholar
  49. Viète, François. 1594. Munimen adversus nova cyclometrica, Paris.Google Scholar
  50. Viète, François. 1595. Pseudo-Mesolabum & alia quaedam adiuncta, Paris.Google Scholar
  51. Viète, François. 1595. Ad problema quod omnibus mathematicis totius orbis construendum proposuit Adrianus Romanus Responsum. Paris.Google Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Paul Bockstaele
    • 1
  1. 1.Oud-HeverleeBelgium

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