Skip to main content Accesibility Help

Two Approaches to Foundations in Greek Mathematics: Apollonius and Geminus

  • Fabio Acerbi (a1)

This article is the sequel to an article published in the previous issue of Science in Context that dealt with homeomeric lines (Acerbi 2010). The present article deals with foundational issues in Greek mathematics. It considers two key characters in the study of mathematical homeomery, namely, Apollonius and Geminus, and analyzes in detail their approaches to foundational themes as they are attested in ancient sources. The main historiographical result of this paper is to show that there was a well-established mathematical field of discourse in “foundations of mathematics,” a fact that is by no means obvious. The paper argues that the authors involved in this field of discourse set up a variety of philosophical, scholarly, and mathematical tools that they used in developing their investigations.

Hide All
Acerbi, Fabio. 2007. “Una scuola matematica alessandrina?” In La Matematica, Vol. 1. I luoghi e i tempi, edited by Bartocci, Claudio, Odifreddi, Piergiorgio, 6589. Turin: Einaudi.
Acerbi, Fabio. 2008. “Hero of Alexandria.” In New Dictionary of Scientific Biography, edited by Koertge, Noretta III:283286. Detroit: Ch. Scribner's Sons.
Acerbi, Fabio. 2010. “Homeomeric Lines in Greek Mathematics.” Science in Context 23 (1):137.
Acerbi, Fabio. Forthcoming. “Perché una dimostrazione geometrica greca è generale.” In Atti degli incontri di Gargnano, edited by Repellini, Ferruccio Franco and Nenci, Elio. Milan: LED.
Anaritius' Commentary on Euclid. The Latin Translation I-IV. 1994. Edited by Tummers, Paul M. J. E.. Nijmegen: Ingenium Publishers.
Barnes, Jonathan. 1990. “Logical Form and Logical Matter.” In Logica, mente e persona, edited by Alberti, Antonina, 7119. Florence: Leo S. Olschki.
Barnes, Jonathan. 1993. “‘Third Sort of Syllogism’: Galen and the Logic of Relations.” In Modern Thinkers and Ancient Thinkers, edited by Sharples, Robert W., 172194. London: UCL Press.
Barnes, Jonathan. 2007. Truth, etc: Six lectures in ancient logic. Oxford: Clarendon Press.
Blass, Friedrich. 1883. Dissertatio de Gemino et Posidonio. Kiel: C. F. Mohr.
Bowen, Alan C. and Todd, Robert B.. 2004. Cleomedes’ Lectures on Astronomy: a Translation of The Heavens with an Introduction and Commentary. Berkeley and Los Angeles: University of California Press.
Caston, Victor. 1999. “Something and Nothing: The Stoics on Concepts and Universals.” Oxford Studies in Ancient Philosophy 17:145213.
Euclide. 1990–2001. Les Éléments. Translated with commentary by Bernard Vitrac. 4 vols. Paris: Presses Universitaires de France.
Evans, James and Berggren, J. Lennart. 2006. Geminos's Introduction to the Phenomena. Princeton: Princeton University Press.
The Fihrist of al-Nadīm. A Tenth-century Survey of Muslim Culture. 1970. Translated by Dodge, Bayard. New York: Columbia University Press.
Fortenbaugh, William W., Huby, Pamela M., Sharples, Robert W., and Gutas, Dimitri, eds. 1993. Theophrastus of Eresus. Sources for His Life, Writings, Thought and Influence. 2 vols. Leiden: New York; Cologne: Brill.
Fried, Michael N. and Unguru, Sabetai. 2001. Apollonius of Perga's Conica. Text, Context, Subtext. Leiden, Boston, Cologne: Brill.
von Fritz, Kurt. 1955. “Die APXAI in der griechischen Mathematik.” Archiv für Begriffsgeschichte 1:13103.
Hankinson, Robert James. 1994. “Galen and the Logic of Relations.” In Aristotle in Late Antiquity, edited by Schrenk, Lawrence P., 5775. Washington: Catholic University of America Press.
Heiberg, Johan Ludwig. 1884. “Griechische und römische Mathematik.” Philologus 43:321346, 467–522.
Hogendijk, Jan P. 2000. “Traces of the Lost Geometrical Elements of Menelaus in Two Texts of al-Sijzī.Zeitschrift für Geschichte der arabisch-islamischen Wissenschaften 13:129164.
Jaouiche, Khalil. 1986. La théorie des parallèles en pays d'Islam. Paris: Vrin.
Knorr, Wilbur Richard. 1986. The Ancient Tradition of Geometric Problems. Boston, Basel, Berlin: Birkhäuser.
Knorr, Wilbur Richard. 1989. Textual Studies in Ancient and Medieval Geometry. Boston, Basel, Berlin: Birkhäuser.
Kouremenos, Theokritos. 1994. “Poseidonius and Geminus on the Foundations of Mathematics.” Hermes 122:437450.
Lloyd, Geoffrey Ernest Richard. 1978. “Saving the Appearances.” Classical Quarterly 28:202222.
Mueller, Ian. 1981. Philosophy of Mathematics and Deductive Structure in Euclid's Elements. Cambridge, MA and London: MIT Press.
Pappus of Alexandria. 1986. Book 7 of the Collection. Edited with Translation and Commentary by Jones, Alexander, 2 vols. New York, Berlin, Heidelberg, Tokyo: Springer-Verlag.
Poseidonius. 1982. Die Fragmente. Edited by Herausgegeben von Willy Theiler. Berlin, New York: De Gruyter.
Posidonius. 1989. I. The Fragments. Edited by Edelstein, Ludwig and Kidd, Ian Gray. 2nd ed.Cambridge: Cambridge University Press.
Rabouin, David. 2009. Mathesis universalis. L'idée de « mathématique universelle » d'Aristote à Descartes. Paris: Presses Universitaires de France.
Rashed, Roshdi, and Houzel, Christian. 2005. “Thâbit ibn Qurra et la théorie des parallèles.” Arabic Science and Philosophy 15:955.
Reinhardt, Karl. 1921. Poseidonios. Munich: C. H. Beck.
Sabra, Abdelhamid I. 1968. “Thâbit ibn Qurra on Euclid's Parallels Postulate.” Journal of the Warburg and Courtauld Institutes 31:1232.
Schmidt, Max C. P. 1886. “Philologische beiträge zu griechischen mathematikern. III. Was schrieb Geminos?Philologus 45:6381.
Tannery, Paul. [1881] 1912–1950. “Quelques fragments d'Apollonius de Perge.” Bulletin des Sciences mathématiques 2nd series, V:124–136. Reprinted in idem, Mémoires Scientifiques, edited by Heiberg, Johan Ludwig & Zeuthen, Hieronymus Georg, 17 vols., I:124138. Toulouse: Privat; Paris: Gauthier-Villars.
Tannery, Paul. 1882a. “Sur les fragments d'Eudème de Rhodes.” Annales de la Faculté des Lettres de Bordeaux, IV:70–76. Reprinted in idem, Mémoires Scientifiques I:168–177.
Tannery, Paul. 1882b. “Sur Sporos de Nicée.” Annales de la Faculté des Lettres de Bordeaux, IV:257–261. Reprinted in idem, Mémoires Scientifiques I:178–184.
Tannery, Paul. 1883–4. “Pour l'histoire des lignes et surfaces courbes dans l'antiquité.” Bulletin des Sciences mathématiques 2nd series, VII:278–291 and VIII:19–30, 101–112. Reprinted in idem, Mémoires Scientifiques II:1–47.
Tannery, Paul. 1901. “Le philosophe Aganis est-il identique à Géminus?” Bibliotheca Mathematica 3rd series, II:9–11. Reprinted in idem Mémoires Scientifiques III:37–41.
Tannery, Paul. 1887. La géométrie grecque. Paris: Gauthier-Villars.
Thabit ibn Qurra. 2009. Science and Philosophy in Nineteenth-Century Bagdad. Edited by Rashed, Roshdi. Berlin and New York: De Gruyter.
Tittel, Karl. 1895. De Gemini Stoici studiis mathematicis quaestiones philologae. Leipzig: Typis M. Hoffmanni.
Tittel, Karl. 1910. “Geminos (1).” In Paulys Real-Encyclopädie der classischen Altertumswissenschaft, edited by Wissowa, Georg et al. , VII.1:1026–1050. Stuttgart: J.B. Metzler 18941963.
Todd, Robert B. 2000. “Géminos.” In Dictionnaire des Philosophes Antiques, edited by Goulet, Richard III:472477. Paris: CNRS Editions.
Vitrac, Bernard. 2005. “Les classifications des sciences mathématiques en Grèce ancienne.” Archives de Philosophie 68:269301.
Vitrac, Bernard. Forthcoming. “Faut-il réhabiliter Héron?” In L'homme et la science, Actes du XVIe Congrès de l'Association Guillaume Budé, Montpellier, Septembre 1–4, 2008. Paris: Les Belles Lettres.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Science in Context
  • ISSN: 0269-8897
  • EISSN: 1474-0664
  • URL: /core/journals/science-in-context
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed