zbMATH — the first resource for mathematics

Geminus and the concept of mean motion in Greco-Latin astronomy. (English) Zbl 0856.01002
A methodological reasoning is presented of how Ptolemy’s predecessor Geminus attacked the problem of introducing elements of arithmetics into the interpretation of lunar data. His main concern was the representation of the anomalistic month in particular, and the arithmetic principles and parameters organising the content of tables for daily lunar motion in longitude in general. The authors label Geminus’ lunar theory as a genetic arithmetical reconstruction.
Reviewer: H.Eelsalu (Tartu)
01A20 History of mathematics in Ancient Greece and Rome
85-03 History of astronomy and astrophysics
Full Text: DOI
[1] Aaboe, A. 1965. ’On Period Relations in Babylonian Astronomy’Centaurus 10: 213–231. · Zbl 0207.28102
[2] Aaboe, A.;Britton, J. P.;Henderson, J. A.;Neugebauer, O.; &Sachs, A. J. 1991.Saros Cycle Dates and Related Babylonian Astronomical Texts. Transactions of the American Philosophical Society 81.6. Philadelphia: American Philosophical Society.
[3] Allan, D. J. 1995. ed.Aristotelis de caelo. Oxford: Clarendon Press.
[4] Archimedes.De lineis spiralibus. SeeHeiberg 1910–1923, ii (with Latin trans.);Mugler 1970–1972, ii (with French trans.).
[5] Aristotle.De caelo. SeeAllan, 1995.
[6] Aristotle.Physica. SeeRoss 1955.
[7] Astronomical Cuneiform Texts. SeeNeugebauer 1955.
[8] Aujac, G. 1975. ed. & trans.Géminos: Introduction aux phénomènes. Paris: Les Belles Lettres.
[9] Aujac, G. 1979. ed. & trans.Autolycos de Pitane: La sphère en mouvement, Levers et couchers, testimonia. Paris: Les Belles Lettres.
[10] Autolycus.De sphaera quae movetur. SeeMogenet. 1950,Aujac 1979 (with French trans.).
[11] Babylonian Astronomical Diaries. SeeSachs &Hunger 1989–1989.
[12] Berggren, J. L. 1991. ’The Relation of Greek Sphaerics to Early Greek Astronomy’. SeeBowen. 227–248.
[13] Berggren, J. L., &Thomas, R. S. D. 1992. ’Mathematical Astronomy in the Fourth Century B.C. as Found in Euclid’sPhaenomena’.Physis 39: 7–33. · Zbl 0772.01001
[14] Blass, F. W. 1887. ed. & trans.Eudoxi ars astronomica. Kiel.
[15] Bowen, A. C. 1991. ed.Science and Philosophy in Classical Greece. Institute for Research in Classical Philosophy and Science: Sources and Studies in the History and Philosophy of Classical Science 2. New York/London: Garland Publishing.
[16] Bowen, A. C. 1993. rev.Hunger &Pingree 1989.Ancient Philosophy 13: 139–142.
[17] Bowen, A. C. 1994. rev.Taub 1993.Isis 85: 140–141.
[18] Bowen, A. C. 1996. ’The Exact Sciences in Hellenistic Times: Texts and Issues’. SeeFurley 1996 (in press).
[19] Bowen, A. C., &Bowen, W. R. 1996. ’The Translator as Interpreter: Euclid’sSectio canonis and Ptolemy’s Harmonica in the Latin Tradition’. SeeManiates 1988 (in press).
[20] Bowen, A. C., &Goldstein, B. R. 1988. ’Meton of Athens and Astronomy in the Late Fifth Century B.C.’ SeeLeichty, Ellis, &Gerardi 1988, 39–81.
[21] Bowen, A. C., &Goldstein, B. R. 1991. ’Hipparchus’ Treatment of Early Greek Astronomy: The Case of Eudoxus and the Length of Daytime’Proceedings of the American Philosophical Society 135: 233–254.
[22] Censorinus,De die natali. SeeSallman, 1983Rocca-Serra 1980 (French trans.)
[23] Cicero.De fato. SeeRackham. 1942 (with trans.).
[24] Cleomedes,De motu circulari corporum caelestium. SeeTodd, 1990Goulet 1980 (with French trans.).
[25] De Falco, V., &Krause!,M. K. 1966. edd. & trans.Hypsikles: Die Aufgangszeiten der Gestirne mit einer Einführung von O. Neugebauer. Abhandlungen der Akademie der Wissenschaften in Göttingen, philologisch-historische Klasse, Dritte Folge, Nr. 62. Göttinger: Vandenhoeck & Ruprecht.
[26] Eastwood, B. S. 1992. ’Heraclides and Heliocentrism: Texts, Diagrams, and Interpretations’Journal for the History of Astronomy 23: 233–260.
[27] Euclid.Phaenomena. SeeMenge 1916 (with Latin trans.).
[28] Furley, D. J. 1997. ed.Routledge History of Philosophy ii. London/New York: Routledge (in press).
[29] Geminus.Introductio astronomiae. SeeManitius. 1898 (with German trans.),Aujac 1975 (with French trans.).
[30] Gillispie, C. C. 1970–1980. ed.Dictionary of Scientific Biography New York: Scribners.
[31] Goldstein, B. R. 1967. ed. and trans.The Arabic Version of Ptolemy’s Planetary Hypotheses. Transactions of the American hilosophical Society, New Series57. 4. Philadelphia: American Philosophical Society.
[32] Goldstein, B. R. 1988. ’A New Set of Fourteenth Century Planetary Observations’Proceedings of the American Philosophical Society 132: 371–399.
[33] Goldstein, B. R., &Bowen, A. C. 1991. ’The Introduction of Dated Observations and Precise Measurement in Greek Astronomy’Archive for History of Exact Sciences 43: 93–132. · Zbl 0767.01004
[34] Goold, G. P. 1977. ed. & trans.Manilius: Astronomica. Loeb Classical Library. London: Heinemann.
[35] Goulet, R. 1980. ed. & trans.Cléomède: Théorie élémentaire. Paris: Vrin.
[36] Granger, F. 1931–1934. ed. & trans.Vitruvius: De architectura. 2 vols. Loeb Classical Library. London: Heinemann.
[37] Grenfell, B. P., &Hunt, A. S. 1906. edd. & trans.The Hibeh Papyri. Part 1. London: Egypt Exploration Fund.
[38] Hayduck, I. L. 1894. ed.Simplicii in Aristotelis de caelo commentaria. Commentaria in Aristotelem Graeca 7. Berlin: Academia Litterarum Regia Borussica.
[39] Heath, T. L. 1960.A History of Greek Mathematics. 2 vols. Oxford: Clarendon Press.
[40] Heiberg, J. L. 1898–1907. ed.Claudii Ptolemaei opera quae exstant omnia. 3 vols. Leipzig: Teubner.
[41] Heiberg, J. L. 1910–1923. ed. & trans.Archimedis opera omnia cum commentariis Eutocii. 4 vols. Leipzig: Teubner.
[42] Hiller, E. 1878. ed.Theonis Smyrnaei philosophi expositio rerum mathematicarum ad legendum Platonem utilium. Leipzig: Teubner.
[43] Hipparchus. InArati et Eudoxi phaenomena. SeeManitius. 1894 (with German trans.). · JFM 25.1913.04
[44] Hunger, H., &Pingree, D. 1989. edd. & trans.MUL.APIN: An Astronomical Compendium in Cuneiform. Archiv für Orientforschung, Beiheft 24. Horn, Austria: Ferdinand Berger & Söhne.
[45] Hyginus.Astronomia. SeeLe Boeffle 1983 (with French trans.).
[46] Hypsicles.Anaphoricus. Seede Falco &Krause 1966.
[47] Jones, A. 1983. ’The Development and Transmission of 248-Day Schemes for Lunar Motion in Ancient Astronomy’Archive for History of Exact Sciences 19: 1–36. · Zbl 0541.01002
[48] Jones A. 1991. ’Hipparchus’s Computations of Solar Longitudes’Journal for the History of Astronomy 22: 101–125.
[49] Le Boeffle, A. 1983. ed. & trans.Hygin: L’astronomie Paris: Les Belles Lettres.
[50] Leichty, E.;Ellis, M. de J.; &Gerardi, P. 1988. edd. AScientific Humanist: Studies in Memory of Abraham Sachs. Occasional Publications of the Samuel Noah Kramer Fund 9. Philadelphia: The University Museum.
[51] Letronne, M. (&Brunet de Presle, W.) 1865. ed.Traité d’astronomie d’après Eudoxe. Notices et extraits des manuscripts de la Bibliothèque impériale,18.2: 25–76.
[52] Maniates, M. R. 1996. ed.Music Discourse from Classical to Early Modern Times: Editing and Translating Texts. Conference on Editorial Problems 26. New York: AMS Press (in press).
[53] Manilius.Astronomica. SeeGoold 1977 (with trans.).
[54] Manitius, C. 1894. ed. & trans.Hipparchi in Arati et Eudoxi phaenomena commentariorum libri iii. Leipzig: Teubner.
[55] Manitius. 1898. ed. & trans.Geminus: Elementa astronomiae. Leipzig: Teubner.
[56] Martin, T. H. 1849. ed. & trans.Theonis Smyrnaei liber de astronoma. Paris: Dezorby et E. Magdeleine.
[57] Mayhoff, C. 1906. ed.C. Plinii Secundi naturalis historia i. Teubner: Leipzig.
[58] Menge, H. 1916. ed. & trans.Euclidis phaenomena et scripta musica. Leipzig: Teubner.
[59] Mogenet, J. 1950. ed.Autolycus de Pitane: Histoire du texte, suivie de l’édition critique des traités, De la sphère en mouvement et Des levers et couchers. Louvain: Publications Universitaires de Louvain. · Zbl 0041.33718
[60] Mugler, C. 1970–1972. ed. & trans.Archimède. 3 vols. Paris: Les Belles Lettres.
[61] MUL.APIN. SeeHunger &Pingree. 1989 (with trans.).
[62] Neugebauer, O. 1934.Vorlesungen über Geschichte der antiken mathematischen Wissenschaften: I. Vorgriechische Mathematik. Berlin: Springer-Verlag. · JFM 60.0002.01
[63] Neugebauer, O. 1955. ed.Astronomical Cuneiform Texts: Babylonian Ephemerides of the Seleucid Period for the Motion of the Sun, the Moon, and the Planets. London: Lund Humphries. Repr. Sources in the History of Mathematics and Physical Sciences 5. New York/Heidelberg/Berlin: Springer-Verlag. · Zbl 1372.01100
[64] Neugebauer, O. 1968. ’The Origin of ystem Bof Babylonian Astronomy’Centaurus 12: 265–270. Repr.Neugebauer 1986, 265–270.
[65] Neugebauer, O. 1969.The Exact Sciences in Antiquity. 2nd edn. New York: Dover. · Zbl 0049.00201
[66] Neugebauer, O. 1975.A History of Ancient Mathematical Astronomy. 3 vols. Studies in the History of Mathematics and Physical Sciences 1. Berlin/Heidelberg/New York: Springer-Verlag. · Zbl 0323.01002
[67] Neugebauer, O. 1986.Astronomy and History: Selected Essays. New York: Springer-Verlag. · Zbl 0543.01011
[68] P. Hibeh 27. SeeGrenfell &Hunt 1906 138–157 (with trans.).
[69] P. Michigan 149. SeeRobbins, 62–117 1936 (with trans.).
[70] P. Parisinus graecus 1. SeeLetronne 1865,Blass 1887 (with Latin trans.)
[71] Pliny.Historia naturalis ii. SeeMayhoff 1906.
[72] Ptolemy.Almagest. SeeHeiberg, 1898–1907Toomer 1984 (trans.).
[73] Ptolemy.Planetary Hypotheses. SeeGoldstein 1967 (with trans.)
[74] Rackham, H. 1942. trans.Cicero. iv. Loeb Classical Library. London: Heinemann.
[75] Robbins, F. E. 1936. SeeWinter 1936, 62–117.
[76] Rocca-Serra, G. 1980. trans.Censorinus: Le jour natal. Paris: Vrin.
[77] Ross, D. (1955)Aristotle’s Physics: A Revised Text with Introduction and Commentary. Oxford: Clarendon Press.
[78] Sachs, A. J., &Hunger, H. 1988–1989. edd. & trans.Astronomical Diaries and Related Texts from Babylonia. 2 vols. Vienna: Österreichischen Akademie der Wissenschaften.
[79] Sallman, N. 1983. ed.Censorini de die natali liber ad Q. Caerillium. Leipzig: Teubner.
[80] Simplicius. InAristotelis de caelo. SeeHayduck. 1894.
[81] Taub, L. C. 1993.Ptolemy’s Universe: The Natural Philosphical and Ethical Foundations of Ptolemy’s Astronomy. Chicago/La Salle: Open Court.
[82] Theon of Smyrna.Expositio rerum mathematicarum ad legendum Plantonem utilium. SeeMartin. 1849 (with Latin trans.), Hiller 1878.
[83] Todd, R. 1990. ed.Cleomedis caelestia. Leipzig: Teubner.
[84] Toomer, G. J. 1978. ’Ptolemy’. SeeGillispie 1970–1980, xi 186–206.
[85] Toomer, G. J. 1984. trans.Ptolemy’s Almagest. New York/Berlin: Springer-Verlag.
[86] Vitruvius.De architectura. SeeGranger, 1931–1934, (with trans.).
[87] Winter, J. G. 1936. ed.Papyri in the University of Michigan Collection: III. Miscellaneous Papyri. Ann. Arbor: University of Michigan Press. · JFM 62.1017.02
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.