Hostname: page-component-76fb5796d-zzh7m Total loading time: 0 Render date: 2024-04-27T13:12:47.878Z Has data issue: false hasContentIssue false
  • English
  • Français

Ancient Rhetoric and Greek Mathematics: A Response to a Modern Historiographical Dilemma

Published online by Cambridge University Press:  01 September 2003

Alain Bernard
Alain Bernard
Affiliation:
Dibner Institute, Boston
Get access Rights & Permissions [Opens in a new window]

Abstract

Argument

In this article, I compare Sabetai Unguru’s and Wilbur Knorr’s views on the historiography of ancient Greek mathematics. Although they share the same concern for avoiding anachronisms, they take very different stands on the role mathematical readings should have in the interpretation of ancient mathematics. While Unguru refuses any intrusion of mathematical practice into history, Knorr believes this practice to be a key tool for understanding the ancient tradition of geometry. Thus modern historians have to find their way between these opposing views while avoiding an unsatisfactory compromise. One approach to this, I propose, is to take ancient rhetoric into account. I illustrate this proposal by showing how rhetorical categories can help us to analyze mathematical texts. I finally show that such an approach accommodates Knorr’s concern about ancient mathematical practice as well as the standards for modern historical research set by Unguru 25 years ago.

Type
Articles
Information
Science in Context , Volume 16 , Issue 3 , September 2003 , pp. 391 - 412
Copyright
2003 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ancient sources

Coll. Math. Pappi Alexandrini collectionis quæ supersunt. Edition and Latin translation of Friedrich Hultsch. 3 vol. Berlin:Weidmann. 1876-1878. Coll. Math. 39.3 = page 39, line 3.
Arch. Archimedes: Opera omnia, cum commentariis Eutocii. Edition and Latin translation of Johan Heiberg. Leipzig: Teubner. 1910-1915. Arch. III 67.3 = volume III, page 67, line 3.
In Eucl. Proclus diadochi in Primum Euclidis Elementorum Librum commentarii. Edition of Godfried Friedlein. Leipzig: Teubner. 1873 (reprint Georg Olms 1967). In Eucl. 54.5 = page 54, line 5.

Modern References

Berggren, J. L.1984. “History of Greek Mathematics: A Survey of Recent Research.” Historia Mathematica 11:394-410.Google Scholar
Bernard, A.2003a. “Sophistic Aspects of Pappus’s Collection.” Archive for History of Exact Sciences 57::93-150.Google Scholar
Bernard, A.2003b. “Comment définir la nature des textes mathématiques de l‘antiquité grecque tardive?” Revue d‘histoire des mathématiques.Google Scholar
Brown, P.1992. Power and Persuasion in Late Antiquity: Towards a Christian Empire. Madison, Wis.: University of Wisconsin Press.
Cifoletti, G.1992. “Mathematics and Rhetoric, Peletier, Gosselin and the Making of the French Algebraic Tradition.” Ph.D. thesis, Princeton University. To be published.
Cifoletti, G.1995. “La question de l’algèbre. Mathématiques et rhétorique des hommes de droit dans la France du 16e siècle.” Annales EHSS (1995):1385-1416.Google Scholar
Cuomo, S.2000. Pappus of Alexandria and the Mathematics of Late Antiquity. Cambridge: Cambridge University Press.
Fried, M.and S. Unguru. 2001. Apollonius of Perga’s ‘Conica’, Text, Context, Subtext. Leiden: Brill.
Heath, M.1995. Hermogenes’ On Issues: Strategies of Argument in Later Greek Rhetoric. Oxford: Clarendon Press.
Jones, A.1986. Pappus: Book 7 of the Collection. Edition, English translation, commentary. 2 vol. Berlin, New York: Springer Verlag.
Kaster, R. A.1988. Guardians of Language: the Grammarian and Society in Late Antiquity. Berkeley: University of California Press.
Klein, J.[1968] 1992. Greek Mathematical Thought and the Origin of Algebra. Translated by Eva Brann. New York: Dover.
Knorr, W. R.1975. The Evolution of the Euclidean Elements, Dordrecht, Boston: Reidel.
Knorr, W. R.[1986] 1993. The ancient tradition of geometric problems. New York: Dover.
Knorr, W. R.1989. Textual studies in ancient and medieval geometry. Basel: Birkhaüser.
Lloyd, G. E. R.[1996] 1999. Adversaries and Authorities. Cambridge/New York: Cambridge University Press.
Mahoney, M.1968. “Another Look at Greek Mathematical Analysis.“ Archive for History of Exact Sciences 5:319-348.Google Scholar
Marrou, H. I.1948. Histoire de l’éducation dans l’Antiquité. Paris: Seuil.
Netz, R.1998. “Deuteronomic Texts: Late Antiquity and the History of Mathematics.” Revue d’histoire des mathématiques 4:261-288.Google Scholar
Netz, R.1999. “Archimedes Transformed: The Case of a Result Stating a Maximum for a Cubic Equation.” Archive for the History of Exact Sciences 54:1-47.Google Scholar
Netz, R.K. Saito, and N. Tchernetska2001/2. “A new reading of Method Proposition 14: preliminary evidence from the Archimedes palimpsest.” SCIAMVS 2 (2001):9-29and SCIAMVS 3 (2002):109-125.
Porter, S. E.1997. Handbook of Classical Rhetoric in the Hellenistic Period, 330 B.C.–A.D. 400. Edited by S. E. Porter. Leiden: Brill.
Unguru, S. 1975. “On the need to rewrite the history of Greek mathematics.” Archive for the History of Exact Sciences 15:67-114.Google Scholar
Unguru, S.1979. “History of Ancient Mathematics: Some Reflections on the State of the Art.” Isis 70:555-565.Google Scholar
Unguru, S.and D. Rowe. 1981. “Does the Quadratic Equation Have Greek Roots?” Libertas Mathematica, vol.1.Google Scholar
Zeuthen, H. G.[1886] 1966. Die Lehre von den Kegelschnitten im Altertum. Hildesheim: Olms.