Jens Høyrup (Jens Hoyrup), Electronic texts on: abbacus mathematics

Cf. also Materials for the study of Fibonacci

(inter alia, the complete Boncompagni edition of his writings)

G:17	“VAT. LAT. 4826: Jacopo da Firenze, Tractatus algorismi”. Preliminary transcription of the manuscript, with occasional commentaries". Filosofi og Videnskabsteori på Roskilde Universitetscenter. 3. Række: Preprints og Reprints 1999 Nr. 3.

C:22

“The Founding of Italian Vernacular Algebra”, pp. 129–156 in Commerce et mathématiques du moyen âge à la renaissance, autour de la Méditerranée. Actes du Colloque International du Centre International d'Histoire des Sciences Occitanes (Beaumont de Lomagne, 13–16 mai 1999). Toulouse: Éditions du C.I.H.S.O., 2001.

B:43

“Lasciti sotto-scientifici alla matematica d'abbaco: quasi algebra ed altre strane specie / The Sub-Scientific Heritage in `abbaco´-Mathematics: Quasi-Algebra and Other Queer Species”. L'educazione matematica 22 (2001), 23-39, 94-103, 149-158.

B:53	“Leonardo Fibonacci and Abbaco Culture: a Proposal to Invert the Roles”. Revue d'Histoire des Mathématiques 11 (2005), 23-56. Preprint.

C:43

“L'algèbre de Jacopo de Florence : un défi à l'historiographie de l'algèbre presque-moderne”, pp. 257–272 in Frank Daelemans et al (eds), Mélanges offerts à Hossam Elkhadem par ses amis et ses élèves. Bruxelles: Archives et Bibliothèques de Belgique/Archief- en Bibliotheekwezen in Belgie, 2007 (written 2002). Manuscript.

B:54	“Jacopo da Firenze and the Beginning of Italian Vernacular Algebra”. Historia Mathematica 33 (2006), 4-42, doi: 10.1016/j.hm.2005.03.001. Preprint. The original publication is available at http://www.sciencedirect.com/science/journal/03150860.

B:56	“The 'Unknown Heritage': trace of a forgotten locus of mathematical sophistication”. Archive for history of Exact Sciences 62 (2008), 613-654. DOI 10.1007/s00407-008-0025-y. Preprint.

G:26	“Jacopo da Firenze, Tractatus algorismi: An edition of the manuscript Milan, Trivulziana MS 90, collated with Florence, Riccardiana MS 2236”. Filosofi og Videnskabsteori på Roskilde Universitetscenter. 3. Række: Preprints og Reprints 2007 Nr. 2.

G:29

“Über den italienischen Hintergrund der Rechenmeister-Mathematik”. Beitrag zur Tagung “Die Rechenmeister in der Renaissance und der frühen Neuzeit. Stand der Forschung und Perspektiven”, München, Deutsches Museum, 29. Februar 2008. Max-Planck-Institut für Wissenschaftsgeschichte, Preprint 349. http://www.mpiwg-berlin.mpg.de/Preprints/P349.PDF

C:39

“The Tortuous Ways toward a New Understanding of Algebra in the Italian Abbacus School (14th–16th Centuries)”, pp. 1–15 in O. Figueras, J. L. Corina, S. Alatorre, T.Rojano, A. Sepúlveda (eds), Proceedings of the Joint Meeting of PME 32 and PME-NA XXX. Morelia, Mexico, July 17–21, 2008, vol. I. México: Cinvestav–UMSNH, 2008.

B:70	“Explicit and Less Explicit Algorithmic Thinking, 1200-1500. Jordanus de Nemore, and the Contrast between Barthelemy de Romans et Chuquet”. Bollettino di Storia delle Scienze Matematiche 28 (2018), 9–30

E:74	[Review of Maryvonne Spiesser (ed.), Une arithmétique commerciale du XV^e siècle. Le Compendy de la praticque des nombres de Barthélemy de Romans. (De Diversis artibus, 70) Turnhout: Brepols, 2004]. Nuncius 20 (2005), 481–482. Manuscript.

Review of Maria do Céu Silva, “The Algebraic Content of Bento Fernandes’s Tratado da arte de arismetica (1555)”. Historia Mathematica 35 (2008), 190–219. Written for Zentralblatt für Mathematik und ihre Grenzgebiete.

C:44

“How to transfer the conceptual structure of Old Babylonian Mathematics: solutions and inherent problems. With an Italian Parallel”, pp. 385–117 in Annette Imhausen & Tanja Pommerening (eds), Writings of Erly Scholars in the Ancient Near East, Egypt, Rome and Greece: Translating Ancient Scientific Texts. (Beiträge zur Altertumskunde, 296). Berlin & New York: De Gruyter, 2010. Preprint.

G:35

“Hesitating progress – the slow development toward algebraic symbolization in abbacus and related manuscripts, c. 1300 to c. 1550”. Contribution to the conference “Philosophical Aspects of Symbolic Reasoning in Early Modern Science and Mathematics”, Ghent, 27–29 August 2009. Max-Planck-Institut für Wissenschaftsgeschichte, Preprint 390

C:45	“A Diluted al-Karaji in Abbacus Mathematics”, pp. 187–197 in Actes du 10ième Colloque Maghrébin sur l'Histoire des mathématiques Arabes, Tunis, 29–30–31 mai, 2010. Tunis: Publications de l'Association Tunisiennes des Sciences mathématiques, 2011. Preprint.

G:39	“Fibonacci – Protagonist or Witness? Who Taught Catholic Christian Europe about Mediterranean Commercial Arithmetic?”. Paper presented at the workshop “Borders and Gates or Open Spaces? Knowledge Cultures in the Mediterranean During the 14th and 15th Centuries”, . Preprint, 26 December 2010 ”.

G:40

“The Fifteenth-Seventeenth Century Transformation of Abbacus Algebra: Perhaps – Though Not Thought of by Edgar Zilsel and Joseph
Needham – the Best Illustration of the ‘Zilsel-Needham thesis’”. Summer School on the History of Algebra, Institute for the History of the Natural Sciences, Chinese Academy of Science, 1–2 September 2011. Preprint, 17 September 2011.

B:63	“Sanskrit-Prakrit Interaction in Elementary Mathematics as Reflected in Arabic and Italian Formulations of the Rule of Three – and Something more on the Rule Elsewhere”. Ganita BhāratÌ 34 (2012; actually 2014), 144–172.

G:48	“Embedding: Another Case of Stumbling Progress”. Contribution to the workshop “Mathematics in the Renaissance: Language, Methods, and Practices”, ETSEIB, Barcelona, 23 January 2015. Roskilde University, 27.1.2015.

B:64	“Fibonacci – Protagonist or Witness? Who Taught Catholic Christian Europe about Mediterranean Commercial Arithmetic?”. Journal of Transcultural Medieval Studies 1 (2014), 219–247

C:61	“From the Practice of Explanation to the Ideology of Demonstration: An Informal Essay”, pp. 27–46 in G. Schubring (ed.), Interfaces between Mathematical Practices and Mathematical Education. Cham: Springer, 2018.

D:17	“Abbacus School”, in Marco Sgarbi (ed.), Encyclopedia of Renaissance Philosophy. Cham: Springer, 2018. https://doi.org/10.1007/978-3-319-02848-4_1135-1

B:72	“Reinventing or Borrowing Hot Water: Early Latin and Tuscan Algebraic Operations with Two Unknowns”. Gaṇita Bhāratī 41 (2019; published 2021), 115–159.

B74	“Fifteenth-Century Italian Symbolic Algebraic Calculation with Four or Five Unknowns”.2020{c}_Fifteenth-century Italian symbolic algebraic calculation with four or five unknowns_S.pdf Gaṇita Bhāratī 42 (2020, published 2022), 161–192.

E:99

Review of Stephan Deschauer, Die große Arithmetik aus dem Codex Vind. phil. gr. 65. Eine anonyme Algorismusschrift aus der Endzeit des byzantinischen Reiches.Denkschriften Österreichische Akademie der Wissenschaften, Philosophisch-Historische Klasse, 461. Verlag der Österreichischen Akademie der Wissenschaften, Vienna, 2014. Mathematical Reviews MR3308969.