Abstracts
Abstract
In this paper, I examine aspects of the methodological debate that originated in 2010, when the distinguished historian of mathematics Sabetai Unguru reviewed Roshdi Rashed’s edition of the Arabic translation of Apollonius’ Conics. In his review, Unguru criticized what Rashed calls “l’usage instrumental d’une autre mathématique pour commenter une oeuvre ancienne”. I consider this debate very important and will try to place it within in the discussion of the so-called “geometric algebra” that goes back to the seventies, by tracing the contributions of the main figures who took part in it.
Keywords:
- History of mathematics,
- Translation,
- Sabetai Unguru,
- Roshdi Rashed
Appendices
Bibliography
- Berggren, J. L. 1984. “History of Greek Mathematics: A Survey of Recent Research”. Historia Mathematica 11: 394–410.
- Christianidis, J. 2004. ed. Classics in the History of Greek Mathematics. New York.
- Freudenthal, H. 1977. “What Is Algebra and What Has It Been in History”. Archive for the History of Exact Science 15: 189–200.
- Høyrup, J. 2016. “What Is ‘Geometric Algebra’, and What Has It Been in Historiography?” Preprint 15 January 2016. http://akira.ruc.dk/ jensh/Publications 2016_What%20is%20'Geometric%20Algebra'_S.pdf. In print: AIMS Mathematics 2 (2019) 128–160. Citations are from the preprint.
- Montelle, C. 2011. Review of Rashed and Bellosta 2010. Aestimatio os 8: 183–187.
- Oaks, J. 2014. Review of Rashed 2009. Aestimatio os 11: 24–49.
- Oaks, J. 2015. Review of Rashed 2012. Aestimatio os 12: 105–109.
- Rashed, R. 2007. Al-Khwārizmi. Le commencement de l’algèbre. Paris.
- Rashed, R. 2008. Apollonius de Perge. Coniques. Tome 1.1: Livre I texte grec et arabe établi, traduit et commenté. Berlin
- Rashed, R. 2009. Apollonius de Perge. Coniques. Tome 2.2. Livre IV: Commentaire historique et matématique. Berlin.
- Rashed, R. 2012. Abū Kāmil. Algèbre et analyse diophantienne. Berlin.
- Rashed, R. 2013a. Histoire de l’analyse diophantienne classique. D’Abū Kāmil à Fermat. Berlin.
- Rashed, R. 2013b. Ibn al-Haytham and Analytical Mathematics. Translated by S.Glynn and R. Wareham. Abingdon, UK/New York. Translation of the French edition of 1993.
- Rashed, R. and H. Bellosta. 2010. Apollonius de Perge. La section des droits selon des rapports. Berlin.
- Rowe, D. 2012. “Otto Neugebauer and Richard Courant: On Exporting the Göttingen Approach to the History of Mathematics”. Mathematical Intelligencer 34: 29–37.
- Sidoli, N. 2011. “Apollonius’ Conics: The Greek and Arabic Traditions”. ISIS 102: 537–542.
- Schneider, I. 2016. Archimedes. New York.
- Unguru, S. 1975. “On the Need to Rewrite the History of Greek Mathematics”. Archive for the History of Exact Science 15: 67–114.
- Unguru, S. 2004. “Methodological Issues in the Historiography of Greek Mathematics”. See Christianidis 2004, 383–461.
- Unguru, S. 2010. Review of Rashed 2009. Aestimatio os 7: 29–42.
- Weil, A. 1980. “The History of Mathematics: Why and How”. Proceedings of the International Congress of Mathematics, Helsinki 1978. Academia Scientiarum Finnica 1: 227–236.