Search Advanced

AIMS Mathematics

2020, Volume 5, Issue 1: 158-184. doi: 10.3934/math.2020010
Previous Article Next Article
Research article

Hippocrates of Chios – His Elements and His Lunes A critique of circular reasoning

  • Section for philosophy and Science Studies, Roskilde University, Denmark
  • In memory of Johan Rosing (1907–1978) and J. A. Bundgaard (1898–1976) teachers who shaped me but left me free
  • Received: 20 September 2019 Accepted: 24 September 2019 Published: 25 October 2019

  • Citation: Jens Høyrup. Hippocrates of Chios – His Elements and His Lunes A critique of circular reasoning[J]. AIMS Mathematics, 2020, 5(1): 158-184. doi: 10.3934/math.2020010

    Related Papers:



  • 加载中


    [1] Allman, George Johnston, 1889. Greek Geometry from Thales to Euclid. Dublin: Hodges, Figgis & Co./London: Longmans, Green & Co.
    [2] Aristotle, Works. Translated into English under the Editorship of W.D. Ross. 12 vols. Oxford: The Clarendon Press, 1908-1952.
    [3] Arrighi, Gino (ed.), 1989. Maestro Umbro (sec. XIII), Livero de l'abbecho. (Cod. 2404 della Biblioteca Riccardiana di Firenze). Bollettino della Deputazione di Storia Patria per l'Umbria 86, 5-140.
    [4] Barnes, Jonathan (ed.), 1984. The Complete Works of Aristotle. The Revised Oxford Translation. 2 vols. Princeton: Princeton University Press.
    [5] Becker, Oskar, 1936. Zur Textgestaltung des eudemischen Berichts über die Quadratur der Möndchen durch Hippokrates von Chios. Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik. Abteilung B: Studien 3 (1934-36), 411-419.
    [6] Bekker, Immanuel (ed.), 1831. Aristoteles graece. 2 vols. Berlin: Reimer.
    [7] Blanck, Horst, 2008. Il libro nel mondo antico. Bari: Dedalo.
    [8] Bretschneider, Carl Anton, 1870. Die Geometrie und die Geometer vor Euklides: Ein historischer Versuch. Leipzig: Teubner.
    [9] Bruins, Evert M., & Marguerite Rutten, 1961. Textes mathématiques de Suse. Paris: Paul Geuthner.
    [10] Bulmer-Thomas, Ivor, 1971. Eudemus of Rhodes, pp. 460-465 in Dictionary of Scientific Biography, vol. IV. New York: Scribner.
    [11] Burkert, Walter, 1959. ΣΤΟIΧΕIΟΝ: Eine semasiologische Studie. Philologus 103,167-197.
    [12] Burkert, Walter, 1962. Weisheit und Wissenschaft. Studien zu Pythagoras, Philolaos und Platon. Nürnberg: Hans Carl.
    [13] Cantor, Moritz, 1880. Vorlesungen über Geschichte der Mathematik. Erster Band, von den ältesten Zeiten bis zum Jahre 1200 n. Chr. Leipzig: Teubner.
    [14] Diels, Hermann (ed.), 1882. Simplicius, In Aristotelis physicorum libros quatuor priores commentaria. Reimer: Berlin.
    [15] Doxiadis, Apostolos, & Michalis Sialaros, 2013. Sing, Muse, of the Hypotenuse: Influences of Poetry and Rhetoric on the Formation of Greek Mathematics, pp. 367-409 in Markus Asper (ed.), 2013. Writing Science: Medical and Mathematical Authorship in Ancient Greece. Berlin & Boston: de Gruyter.
    [16] Easterling, P. E., & B. M. W. Knox (eds), 1985. The Cambridge History of Classical Literature. Ⅰ. Greek Literature. Cambridge: Cambridge University Press.
    [17] Friedlein, Gottfried (ed.), 1873. Procli Diadochi In primum Euclidis Elementorum librum commentarii. Leipzig: Teubner.
    [18] Gadamer, Hans-Georg, 1990. Hermeneutik. Ⅰ. Wahrheit und Methode. Grundzüge einer philosophischen Hermeneutik. Tübingen: J. C. B. Mohr (Paul Siebeck).
    [19] Gaiser, Konrad, 1963. Platons ungeschriebene Lehre. Studien zur systematischen und geschichtlichen Begründung der Wissenschaften in der platonischen Schule. Stuttgart: Ernst Klett.
    [20] GEL: Greek-English Lexicon. Compiled by Henry George Liddell and Robert Scott. Revised and Augmented Throughout... With a Supplement. Oxford: Oxford University Press, 1968.
    [21] Hankel, Hermann, 1874. Zur Geschichte der Mathematik in Alterthum und Mittelalter. Leipzig: Teubner.
    [22] Heath, Thomas L., 1921. A History of Greek Mathematics. 2 vols. Oxford: The Clarendon Press.
    [23] Heath, Thomas L. (ed., trans.), 1926. The Thirteen Books of Euclid's Elements. 2nd revised edition. 3 vols. Cambridge: Cambridge University Press/New York: Macmillan. 11908.
    [24] Heiberg, Johan Ludvig (ed., trans.), 1883. Euclidis Elementa. 5 vols. Leipzig: Teubner, 1883-1888.
    [25] Heiberg, Johan Ludvig, 1884. Griechische und römische Mathematik. Philologus 43,321-346,467-522.
    [26] Hon, Giora, & Bernard Goldstein, 2008. From Summetria to Symmetry: The Making of a Revolutionary Scientific Concept. New York: Springer.
    [27] Høyrup, Jens, 1990. Dýnamis, the Babylonians, and Theaetetus 147c7 - 148d7. Historia Mathematica 17,201-222.
    [28] Høyrup, Jens, 2000. Geometrical Patterns in the Pre-classical Greek Area. Prospecting the Borderland Between Decoration, Art, and Structural Inquiry. Revue d'Histoire des Mathématiques 6, 5-58.
    [29] Høyrup, Jens, 2001. On a Collection of Geometrical Riddles and Their Role in the Shaping of Four to Six "Algebras". Science in Context 14, 85-131.
    [30] Høyrup, Jens, 2002. Lengths, Widths, Surfaces: A Portrait of Old Babylonian Algebra and Its Kin. New York: Springer.
    [31] Høyrup, Jens, 2012. 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. Gaṇita Bhāratī 34,144-172.
    [32] Høyrup, Jens, 2019. From the Practice of Explanation to the Ideology of Demonstration: An Informal Essay, pp. 27-46 in Gert Schubring (ed.), Interfaces between Mathematical Practices and Mathematical Education. Cham etc.: Springer.
    [33] Junge, Gustav, 1907. Wann haben die Griechen das Irrationale Entdeckt?, pp. 221-264 in Novae symbolae joachimicae: Festschrift des Königlichen Joachimstalschen Gymnasiums auf Anlaßdes dreihundertjährigen Jubiläums der Anstalt. Halle, Verlag der Buchhandlung des Waisenhauses.
    [34] Kienast, Hermann J., 1995. Die Wasserleitung des Eupalinos auf Samos. Bonn: Deutsches Archäologisches Institut/Rudolf Habelt.
    [35] Kline, Morris, 1972. Mathematical Thought from Ancient to Modern Times. New York: Oxford University Press.
    [36] Lee, H. D. P. (ed., trans.), 1952. Aristotle, Meteorologica. Cambridge, Mass.: Harvard University Press/London: Heinemann.
    [37] Lloyd, Geoffrey E. R., 1987. The Alleged Fallacy of Hippocrates of Chios. Apeiron 20,103-128.
    [38] Longrigg, James, 1976. Thales, pp. 295-298 in Dictionary of Scientific Biography, vol. XIII. New York: Scribner.
    [39] Morrow, Glenn R. (ed., trans.), 1970. Proclus, A Commentary on the First Book of Euclid's Elements. Princeton, New Jersey: Princeton University Press.
    [40] Netz, Reviel, 2004. Eudemus of Rhodes, Hippocrates of Chios and the Earliest Form of a Greek Mathematical Text. Centaurus 46,243-286.
    [41] Nisard, Désiré (ed.), 1869. Oeuvres complètes d'Horace, de Juvénal, de Perse, de Sulpicia, de Turnus, de Catulle, de Properce, de Gallus et Maximien, de Tibulle de Phèdre et de Syrus. Avec une traduction française. Paris: Firmin Didot.
    [42] Osborne, Catherine (ed., trans.), 2006. Philoponus, On Aristotle Physics 1.1-3. London: Duckworth.
    [43] Robson, Eleanor, 1999. Mesopotamian Mathematics 2100-1600 BC. Technical Constants in Bureaucracy and Education. Oxford: Clarendon Press.
    [44] Rudio, Ferdinand (ed., trans.), ed. trans., 1907. Der Bericht des Simplicius über die Quadraturen des Antiphon und des Hippokrates. Griechisch und deutsch. Leipzig: Teubner.
    [45] Sachs, Eva, 1917. Die fünf platonischen Körper. Zur Geschichte der Mathematik und der Elementenlehre Platons und der Pythagoreer. Berlin: Weidmannsche Buchhandlung.
    [46] Saito, Ken, 1997. Pappus' Tool Box: Examination of the Use of the Elements Book Ⅱ in Book Ⅶ of the Collection, pp. 153-163 in Tasoula Berggren (ed.), Third International Conference on Ancient Mathematics. Proceedings of the Third International Meeting, Delphi, Greece, July 30-August 3, 1996. Burnaby, British Columbia: Simon Fraser University.
    [47] Shorey, Paul (ed., trans.), 1930. Plato, The Republic. 2 vols. (Loeb Classical Library). London: Heinemann/New York: Putnam, 1930, 1935.
    [48] Simpson, Peter L. P. (ed., trans.), 2013. The Eudemian Ethics of Aristotle. New Brunswick & London: Transaction.
    [49] Tannery, Paul, 1887. La géométrie grecque. Comment son histoire nous est parvenue et ce que nous en savons. Essai critique. Première partie, Histoire générale de la géométrie élémentaire. Paris: Gauthiers-Villars.
    [50] Tannery, Paul, 1912/1883. Le fragment d'Eudème sur la quadrature des lunules, pp. 339-370 in Paul Tannery, Mémoires scientifiques. Ⅰ. Sciences exactes dans l'Antiquité, 1876-1884. Toulouse: Édouard Privat/Paris: Gauthier-Villars.
    [51] Thomas, Ivor (ed., trans.), 1939. Selections Illustrating the History of Greek Mathematics. 2 vols. (Loeb Classical Library). London: Heinemann/New York: Putnam, 1939, 1941.
    [52] Timpanaro Cardini, Maria (ed.), 2010. Pitagorici antichi: Testimonianze e frammenti. Testo greco a fronte. Milano: Bompiani, 11958-1964.
    [53] Todd, Robert B. (ed., trans.), 2012. Themistius, On Aristotle Physics 1-3. London etc.: Bloomsbury.
    [54] Webster, E. W. (ed., trans.), 1931. Aristotle, Meteorologica, in Aristotle, Works (ed. W. D. Ross), vol. Ⅲ. Oxford: Clarendon Press.
    [55] Zeuthen, Hans Georg, 1896. Geschichte der Mathematik im Altertum und im Mittelalter. Vorlesungen. København: Høst & Søn.
    [56] Zhmud, Leonid, 2002. Eudemus' History of Mathematics, pp. 263-306 in István Bodnár & William W. Fortenbaugh (eds), Eudemus of Rhodes. New Brunswick & London: Transaction Publishers.
  • Reader Comments
  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
AIMS Mathematics
1.8 3.4

Metrics

Article views(4487) PDF downloads(658) Cited by(3)

Preview PDF
Download XML
Export Citation
Article outline

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog