Skip to main content

On the Shoulders of Hipparchus

This is a preview of subscription content, access via your institution.

References

  1. Abu'l-Wafa' 1971, The Arithmetic of Abu al-Wafa' al-Buzajani, ed. A. S. Saidan. Amman.

  2. Acerbi F. 2000, Plato: Parmenides 149a7–c3. A Proof by Complete Induction? Archive for History of Exact Sciences 55, pp. 57–76.

  3. Alexander of Aphrodisias, In Aristotelis analyticorum priorum librum I commentarium, in Commentaria in Aristotelem Graeca, vol. II.1, ed. M. Wallies. Berlin (Academia litterarum regia borussica), G. Reimer 1883 (reprint ed.: Berlin, De Gruyter 1957).

  4. Aristotle 1989, Prior Analytics. Translated, with introduction, notes, and commentary, by R. Smith. Indianapolis/Cambridge, Hackett Publishing Company.

  5. Aristotle 1949, Aristotle's Prior and Posterior Analytics. A Revised Text with Introduction and Commentary by W. D. Ross. Oxford, Oxford University Press.

  6. Aulus Gellius, Noctes Atticae, ed. P. K. Marshall, 2 vols. Oxford, Oxford University Press 1968.

  7. Barnes J. 1982, Medicine, Experience and Logic, in Science and Speculation, ed. J. Barnes, J. Brunschwig, M. F. Burnyeat, M. Schofield. Cambridge, Cambridge University Press, pp. 24–68.

  8. Becker O. 1936, Die Lehre vom Geraden und Ungeraden im Neunten Buch der Euklidischen Elemente, Quellen und Studien zur Geschichte der Mathematik, Astronomie, und Physik B3, pp. 533–553.

  9. Biermann K.-R., Mau J. 1958, Überprüfung einer frühen Anwendung der Kombinatorik in der Logik, The Journal of Symbolic Logic 23, pp. 129–132.

  10. Biggs N. L. 1979, The roots of combinatorics, Historia Mathematica 6, pp. 109–136.

  11. Bobzien S. 1996, Stoic Syllogistic, Oxford Studies in Ancient Philosophy 14, pp. 133–192.

  12. Bobzien S. 1999, The Stoics, in The Cambridge History of Hellenistic Philosophy, part II, Logic and Language, ed. K. Algra, J. Barnes, J. Mansfeld, M. Schofield. Cambridge, Cambridge University Press, pp. 92–157.

  13. Boethius, Porphyrii Isagoge a Boethio translata, in Commentaria in Aristotelem Graeca, vol. IV.1, ed. A. Busse. Berlin (Academia litterarum regia borussica), G. Reimer 1887 (reprint ed.: Berlin, De Gruyter 1957).

  14. Boethius, In Porphyrium Commentariorum libri V, in Patrologiae cursus completus, Manlii Severini Boethii Opera Omnia, accurante J.-P. Migne, Patrologiae Latinae Tomus 64. Paris 1847 (reprint ed.: Turnhout (BE), Brepols 1979).

  15. Boethius, In Categorias Aristotelis libri IV, in Patrologiae cursus completus, Manlii Severini Boethii Opera Omnia, accurante J.-P. Migne, Patrologiae Latinae Tomus 64. Paris 1847 (reprint ed.: Turnhout (BE), Brepols 1979).

  16. Boethius 1969, De hypotheticis syllogismis. Testo, traduzione, introduzione e commento di L. Obertello. Brescia, Paideia Editrice.

  17. Bonitz H. 1870, Index Aristotelicus, in Aristotelis Opera, vol. V, ex recensione I. Bekker. Berlin (Academia litterarum regia borussica), G. Reimer (reprint ed.: Berlin, De Gruyter 1961).

  18. Busard H. L. L. 1983, The First Latin Translation of Euclid's Elements Commonly Ascribed to Adelard of Bath. Toronto, Pontifical Institute of Mediaeval Studies.

  19. Busard H. L. L. 1984, The Latin translation of the Arabic version of Euclid's Elements commonly ascribed to Gerard of Cremona. Leiden, Brill.

  20. De Falco V., Krause M. (eds.) 1966, Hypsikles. Die Aufgangszeiten der Gestirne. Abhandlungen der Akademie der Wissenschaften in Gottingen, Philologisch-Historische Klasse, Dritte Folge, Nr. 62. Göttingen, Vandenhoek & Ruprecht.

  21. Dexippus, In Aristotelis categorias commentarium, in Commentaria in Aristotelem Graeca, vol. IV.2, ed. A. Busse. Berlin (Academia litterarum regia borussica), G. Reimer 1888 (reprint ed.: Berlin, De Gruyter 1957).

  22. Diogenes Laertius, Vitae Philosophorum, ed. H. S. Long, 2 vols. Oxford, Oxford University Press 1964.

  23. Einarson B. 1936, On Certain Mathematical Terms in Aristotle's Logic, The American Journal of Philology LVII, pp. 33–54; 151–172.

  24. Euclide 1998, Les Éléments. Traduction et commentaires par Bernard Vitrac. Paris, Presses Universitaires de France. Vol. 3, livre X.

  25. Euclides, Elementa. Post I. L. Heiberg edidit E. S. Stamatis. 5 vols. Leipzig-Stuttgart, B. G. Teubner, 1969–1977.

  26. Euclides 1916, Euclidis Phaenomena et Scripta Musica. Edidit H. Menge. Fragmenta. Collegit et disposuit I. L. Heiberg. in Euclidis Opera Omnia, vol. VIII, ediderunt I. L. Heiberg et H. Menge. Leipzig, B. G. Teubner.

  27. Frede M. 1974, Die stoische Logik. Abhandlungen der Akademie der Wissenschaften in Göttingen Philologisch-Historische Klasse, Dritte Folge, Nr. 88. Göttingen, Vandenhoek & Ruprecht.

  28. Galenus, Institutio logica, ed. K. Kalbfleisch. Leipzig, B. G. Teubner 1896.

  29. Habsieger L., Kazarian M., Lando S. 1998, On the Second Number of Plutarch, The American Mathematical Monthly 105, p. 446.

  30. Hardy G. H., Wright E. M. 1979, An Introduction to the Theory of Numbers. 5th ed. Oxford, Oxford University Press.

  31. Heath T. L. 1921, A History of Greek Mathematics. 2 vols. Oxford, Oxford University Press (reprint ed.: New York, Dover 1981).

  32. Heiberg J. L. (ed.) 1927, Theodosius Tripolites Sphaerica. Abhandlungen der Gesellschaft der Wissenschaften zu Göttingen, Philologisch-Historische Klasse, Neue Folge bd. XIX, 3. Berlin, Weidmannsche Buchhandlung.

  33. Heron 1903, Heronis Alexandrini opera quae supersunt omnia. Volumen III. Rationes Dimetiendi et Commentatio Dioptrica. Edidit H. Schoene. Leipzig, B. G. Teubner (reprint ed.: Stuttgart and Leipzig, Teubner 1976).

  34. Hilbert D., Ackermann W. 1950, Principles of Mathematical Logic. New York, Chelsea Publishing Company.

  35. Høyrup J. 2002, Lenghts, Widths, Surfaces. A Portrait of Old Babylonian Algebra and Its Kin. New York/Berlin/Heidelberg, Springer-Verlag.

  36. Høyrup J. (forthcoming), Conceptual Divergence – Canons an Taboos – and Critique. Reflections on Explanatory Categories, paper presented at the Sixth International Conference on Ancient Mathematics, Delphi 2002.

  37. Hülser K. (ed.) 1987–1988, Die Fragmente zur Dialektik der Stoiker. 4 vols. Stuttgart/Bad Cannstatt, Frommann-Holzboog.

  38. Iamblichus, In Nichomachi arithmeticam introductionem liber, ed. H. Pistelli. Leipzig, B. G. Teubner 1894 (reprint ed.: Stuttgart and Leipzig, B. G. Teubner 1975).

  39. Ibn An-Nadim 1871–72, Kitab al-Fihrist, ed. G. Fülgel, J Rödiger, A Müller, 2 vols. Leipzig, B. G. Teubner.

  40. Junge G., Thomson W. 1930, The Commentary of Pappus on Book X of Euclid's Elements. Cambridge (Mass.), Harvard University Press.

  41. Klein J. 1968, Greek Mathematical Thought and the Origin of Algebra. Cambridge (Mass.), MIT Press. (English translation of: Die griechische Logistik und die Entstehung der Algebra, Quellen und Studien zur Geschichte der Mathematik, Astronomie, und Physik B3 (1934–1936), pp. 18–105; 122–235)

  42. Kneale W. C., Kneale M. 1971, The Development of Logic. 2nd ed. Oxford, Oxford University Press.

  43. Knorr W. R. 1975, The Evolution of the Euclidean Elements. Dordrecht/Boston, Reidel.

  44. LSJ, Liddell H. G., Scott R., Jones H. S., A Greek-English Lexicon. With a revised supple- ment 1996. Oxford, Clarendon Press.

  45. Lukasiewicz J. 1957, Aristotle's Syllogistic. Oxford, Oxford University Press (reprint ed. 1998).

  46. Mahoney M. S. 1971, Babylonian Algebra: Form vs. Content, Studies in History and Philosophy of Science 1, pp. 369–380.

  47. Mates B. 1953, Stoic Logic. Berkeley/Los Angeles, University of California Press.

  48. Mendell H. 1998, Making Sense of Aristotelian Demonstration, Oxford Studies in Ancient Philosophy 16, pp. 161–225.

  49. Nesselmann G. H. F. 1842, Versuch einer kritischen Geschichte der Algebra. Nach den Quellen bearbeitet. Erster Theil, Die Algebra der Griechen. Berlin, G. Reimer.

  50. Netz R. (forthcoming), It's not that they couldn't.

  51. Neugebauer O. 1975, A History of Ancient Mathematical Astronomy. 3 vols. New York/Berlin/Heidelberg, Springer-Verlag.

  52. Nicomachus, Introductio arithmetica, ed. R. Hoche. Leipzig, B. G. Teubner 1866.

  53. Pappus 1876–78, Collectionis quae supersunt. Edidit F. Hultsch. 3 vols. Berlin, Weidmann (reprint ed.: Amsterdam, Hakkert 1965).

  54. Pappus 1986, Book 7 of the Collection. Edited with Translation and Commentary by Alexander Jones, 2 vols. New York/Berlin/Heidelberg/Tokio, Springer-Verlag.

  55. Plutarch 1938, Quaestionum convivialium libri IX, in Plutarchi moralia, vol. IV, ed. C. Hubert. Leipzig, B. G. Teubner.

  56. Plutarch 1976, Moralia, vol. XIII, part II, with an English translation by Harold Cherniss, Loeb Classical Library 470. London, Cambridge (Mass.), Harvard University Press.

  57. Porphyry, Isagoge sive quinque voces, in Commentaria in Aristotelem Graeca, vol. IV.1, ed. A. Busse. Berlin (Academia litterarum regia borussica), G. Reimer 1895 (reprint ed.: Berlin, De Gruyter, 1957).

  58. Rome A. 1930, Procédés anciens de calcul des combinaisons. Annales de la Societé scientifique de Bruxelles A 50, pp. 97–104.

  59. Schröder E. 1870, Vier combinatorische Probleme, Zeitschrift für Mathematik und Physik, 15, pp. 361–376.

  60. Sesiano J. 1998, An Early Form of Greek Algebra, Centaurus 40, pp. 276–302.

  61. Sextus Empiricus, Pyrrhoneion Hypotyposeon libri tres, in Opera, vol. I, ed. H. Mutschmann, J. Mau. 2nd and corrected ed. Stuttgart and Leipzig, B. G. Teubner 1958.

  62. Sextus Empiricus, Adversus Dogmaticos libri quinque (Adv. math. VII–XI), in Opera, vol. II, ed. H. Mutschmann. Leipzig, B. G. Teubner 1914 (reprint ed.: Stuttgart and Leipzig, Teubner 1958).

  63. Simplicius, In Aristotelis physicorum libros quattuor priores commentaria, in Commentaria in Aristotelem Graeca, vol. IX, ed. H. Diels. Berlin (Academia litterarum regia borussica), G. Reimer 1882 (reprint ed.: Berlin, De Gruyter 1957).

  64. Stanley R. P. 1997, Hipparchus, Plutarch, Schröder, and Hough, The American Mathematical Monthly 104, pp. 344–350.

  65. Suter H. 1892, Das Mathematiker-Verzeichniss im Fihrist des Ibn Abî Ja'kûb an-Nadîm (Muhammad Ibn Ishak), Abhandlungen zur Geschichte der Mathematik 6, pp. 1–87.

  66. Theon Smyrnaeus, Expositio rerum mathematicarum ad legendum Platonem utilium, ed. E. Hiller. Leipzig, B. G. Teubner 1878 (reprint ed.: Stuttgart and Leipzig, B. G. Teubner 1995).

  67. Toomer G. J. 1978, Hipparchus, in Dictionary of Scientific Biography, ed. C. C. Gillispie, 16 vols. New York, C. Schribner's Sons 1970–1980, XV, supplement I, pp. 207–224.

  68. Waitz TH. 1844–46, Organon graece, novis codicum auxiliis adiutus recognovit, scholiis ineditis et commentario instruxit Th. Waitz, 2 vols, Leipzig (reprint ed.: Aalen 1965).

  69. Ziegler K. 1951, Plutarchos, in Paulys Real-Encyclopädie der classischen Altertumswissenschaft, 2nd ed., ed. G. Wissowa et al., 24 vols in 43. Stuttgart, J. B. Metzler 1894–1963, XXI 1, cc. 636–962.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to F. Acerbi.

Additional information

Communicated by A. Jones

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Acerbi, F. On the Shoulders of Hipparchus. Arch. Hist. Exact Sci. 57, 465–502 (2003). https://doi.org/10.1007/s00407-003-0067-0

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00407-003-0067-0