Skip to main content
SpringerLink
Log in

The appearance of negative solutions in mediaeval mathematics

  • 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

Bibliography

  • Abū Kāmil: [Algebra, i.e.] Kitāb fī'l-jabr wa'l-muqābala. Ms Beyazıt 19046 (olim Kara Mustafa Paşa 379). See also Sesiano, J.

  • Abū'l-Wafā': Kitāb al-manāzil fī mā ya\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\cdot}$}}{h} \)tāju ilaihi 'l-kuttāb wa'l-`ummāl min `ilm al-\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\cdot}$}}{h} \)isāb, ed. A. Saidan [= Tārīkh `ilm al-\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\cdot}$}}{h} \)isāb al-`arabī, I]. `Ammān, 1971. See also Medovoy, M.

  • Alcuin: Propositiones ad acuendos iuvenes, (latest edition), by M. Folkerts, in: Denkschriften d. österr. Akad. d. Wiss., math.-naturwiss. Kl., 116,6 (1978).

  • Boncompagni, B.: Scritti di Leonardo Pisano, I [Liber abbaci] - II [Practica geometriae, Opera minora]. Roma, 1857–62.

  • The Flos has recently been translated into Italian by E. Picutti in Physis, 25 (1983), pp. 293–387.

    Google Scholar 

  • Chuquet, N.: [Triparty, et applications, in:] Ms Bibl. Nationale, fonds français 1346. See also l'Huillier, H.; Marre, A.

  • Colebrooke, H.: Algebra, with Arithmetic and Mensuration, from the Sanscrit of Brahmegupta and Bháscara. London, 1817.

  • Diophantus: See Sesiano, J.; Tannery, P.

  • Folkerts, M.: Pseudo-Beda: De arithmeticis propositionibus. Eine mathematische Schrift aus der Karolingerzeit, in: Sudhoffs Archiv, 56 (1972), pp. 22–43. See also Alcuin.

    Google Scholar 

  • Franci, R., & Toti Rigatelli, L.: La trattatistica matematica del Rinascimento senese, in: Atti Accad. Fisiocritici di Siena, ser. XIV, vol. 13 (1981), pp. 1–71.

    Google Scholar 

  • Heath, Th.: A History of Greek Mathematics (2 vols). Oxford, 1921.

  • Hochheim, A.: Kâfî fîl Hisâb (Genügendes über Arithmetik) des ... Alkarkhî, I–III [3 Hefte]. Halle (Saale), 1878–80.

  • Iamblichus: In Nicomachi arithmeticam introductionem liber, ed. H. Pistelli. Lipsiae, 1894.

  • Juschkewitsch, A.: Geschichte der Mathematik im Mittelalter. Leipzig, 1964.

  • al-Karajī: See Hochheim, A.; Sesiano, J.; Vogel, K.; Woepcke, F.

  • Leonardo of Pisa: See Boncompagni, B.

  • l'Huillier, H.: Nicolas Chuquet: La Géométrie. Paris, 1979.

  • Marre, A.: Notice sur Nicolas Chuquet et son Triparty en la science des nombres, in Bullettino di bibliografia e di storia delle scienze matem. e fis., 13 (1880), pp. 555–659, 693–814.

    Google Scholar 

  • Appendice au Triparty en la science des nombres de Nicolas Chuquet parisien, in ibid.,, 14 (1881), pp. 413–460.

    Google Scholar 

  • Medovoy, M. (Медовой, М.): Об одном случае применения отрицательных чицел у Абу-л-Вафы, in: Историко-математические исследования, XI (1958), pp. 593–598.

    Google Scholar 

  • Pacioli, L.: [Aritmetica, in] Cod. Vat. lat. 3129.

  • Summa de Arithmetica, Geometria, Proportioni e Proportionalita. Vinegia, 14941; Toscolano, 15232.

  • Pellos, Fr.: Compendion de lo abaco. Thaurino, 1492.

  • Saidan, A.: See Abū'l-Wafā'.

  • Sesiano, J.: Books IV to VII of Diophantus' “Arithmetica” in the Arabic Translation Attributed to Qus \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\cdot}$}}{t} \)ā ibn Lūqā. New York/Heidelberg/Berlin, 1982.

  • Les Méthodes d'analyse indéterminée chez Abū Kāmil, in Centaurus, 21 (1977), pp. 89–105.

    Google Scholar 

  • Le Traitement des équations indéterminées dans le Badi' fī'l-150-3isāb d'Abū Bakr al-Karajī, in Archive for Hist. of Ex. Sciences, 17 (1977), pp. 297–379.

    Google Scholar 

  • Une Arithmétique médiévale en langue provençale, in Centaurus, 27 (1984), pp. 26–75.

    Google Scholar 

  • Tannery, P.: Diophanti Alexandrini Opera omnia cum graecis commentariis (2 vols). Lipsiae, 1893–95.

  • Tropfke, J.: Geschichte der Elementarmathematik. Berlin, 19804.

  • Vogel, K.: Neun Bücher arithmetischer Technik [= Oswalds Klassiker d. exakten Wiss., N.F., Bd. 4]. Braunschweig, 1968.

  • Zur Geschichte der linearen Gleichungen mit mehreren Unbekannten, in Deutsche Mathematik, 5 (1940), pp. 217–240.

    Google Scholar 

  • Ein unbestimmtes Problem al-Kara\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{g} \)īs in Rechenbüchern des Abendlandes, in Sudhoffs Archiv, 61 (1977), pp. 66–74.

    Google Scholar 

  • Volodarsky, A. (Володарский, А.): Очерки истории средневековой индийской математики. Москва, 1977.

  • Woepcke, F.: Extrait du Fakhrî. Paris, 1853.

Download references

Author information

Authors and Affiliations

  1. Département de Mathématiques, École polytechnique fédérale de Lausanne, Lausanne

    Jacques Sesiano

Authors
  1. Jacques Sesiano
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by B. L. van der Waerden

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sesiano, J. The appearance of negative solutions in mediaeval mathematics. Arch. Hist. Exact Sci. 32, 105–150 (1985). https://doi.org/10.1007/BF00329870

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00329870

Keywords

Search

Navigation