«Combustion Tables» in Twelfth-Century Latin Europe: A Preliminary Study

Contenido principal del artículo

Carl Philipp Emanuel Nothaft

Resumen

The Latin manuscript sources studied in this article jointly document the existence and erstwhile circulation of a highly atypical set of computational tables for planetary longitudes, coupled with extensive tables for ascensions, which served astrologers in Latin Europe as early as the 1130s. An associated text of c.1220 refers to the tables for the five planets as « combustion tables » (tabule combustionis), which reflects the way the tables in question use the time and position of the last conjunction between a planet and the Sun - known in medieval terminology as combustio - as an anchor for calculating the planet’s true ecliptic longitude at a later date within its synodic period. Multiple lines of evidence suggest that the combustion tables as well as the associated solar and ascension tables originally circulated alongside the pseudo-Ptolemaic Iudicia, an astrological work of probable Arabic origin (pre-1138). Overall, the surviving manuscript material raises the possibility that the tables and the Iudicia were at one point a single work that supported astrological computations and judgments at an early stage of their respective development in Latin Europe.

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Cómo citar
Nothaft, C. P. E. (2024). «Combustion Tables» in Twelfth-Century Latin Europe: A Preliminary Study. Mediterranea, International Journal on the Transfer of Knowledge, 9, 107–164. https://doi.org/10.21071/mijtk.v9i.16441
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Artículos

Bibliografía

Manuscripts

Cambridge, Fitzwilliam Museum, McClean 165

Chartres, Bibliothèque municipale, 213†

Chartres, Bibliothèque municipale, 214†

Darmstadt, Universitäts- und Landesbibliothek, 765

Dijon, Bibliothèque municipale, 448

Erfurt, Universitätsbibliothek, Dep. Erf. CA 8o 81

London, British Library, Cotton Appendix VI

London, British Library, Royal 7.F.VIII

Munich, Bayerische Staatsbibliothek, Clm 18927

Oxford, Bodleian Library, Digby 40

Oxford, Corpus Christi College, 233

Oxford, Corpus Christi College, 283

Paris, Bibliothèque nationale de France, lat. 7291

Paris, Bibliothèque nationale de France, lat. 16208

St Petersburg, Biblioteka Akademii Nauk, F. 8 (XXAb/IIII)

Vatican City, Biblioteca Apostolica Vactiana, Pal. lat. 1410

Vatican City, Biblioteca Apostolica Vaticana, Vat. lat. 5714

Vienna, Österreichische Nationalbibliothek, 2385

Wolfenbüttel, Herzog-August-Bibliothek, Cod. Guelf. 51.9 Aug. 4o

Printed Sources

Abraham Ibn Ezra, Liber de rationibus tabularum, ed. José María Millás Vallicrosa, El libro de los fundamentos de las Tablas astronómicas de R. Abraham Ibn ʽEzra, CSIC, Madrid 1947 (Instituto Arias Montano, Ser. D, 2).

Adelard of Bath, De opere astrolapsus, in Bruce George Dickey, « Adelard of Bath: An Examination Based on heretofore Unexamined Manuscripts », Ph.D. Diss., University of Toronto 1982, p. 147–229.

al-Battānī, Opus astronomicum, ed. Carlo Alfonso Nallino, 3 vol., Hoepli, Milan 1899–1907 (Pubblicazioni del Reale Osservatorio di Brera in Milano, 40).

Ezich Elkaurezmi, trans. Adelard of Bath, ed. Heinrich Suter, Die astronomischen Tafeln des Muḥammed ibn Mūsā al-Khwārizmī in der Bearbeitung des Maslama ibn Aḥmed al-Madjrīṭī und der latein. Übersetzung des Athelhard von Bath, A. F. Høst & Søn, København 1914 (Det Kongelige Danske Videnskabernes Selskab, Skrifter, 7th Ser., Historisk og filosofisk Afd., 3.1).

John of Pavia, Canones super tabulas Humeniz philosophi summi egipciorum, in José María Millás Vallicrosa, Estudios sobre Azarquiel, CSIC, Madrid 1943–1950, p. 379–392.

Petrus Alfonsi, Epistola ad peripateticos, in John Tolan, Petrus Alfonsi and His Medieval Readers, University Press of Florida, Gainesville 1993, p. 164–180.

Pseudo-Ptolemy, Iudicia, ed. David Juste, « Transcription of Pseudo-Ptolemy, Iudicia (update 25.05.2021) », Ptolemaeus Arabus et Latinus. Texts,

<https://ptolemaeus.badw.de/text/M106> (Accessed 29 Nov. 2023).

Raymond of Marseilles, Liber cursuum planetarum, in Opera omnia, vol. I, ed. and trans. Marie-Thérèse d’Alverny, Charles Burnett, Emmanuel Poulle, CNRS Éditions, Paris 2009 (Sources d’histoire médiévale, 40).

The Toledan Tables, ed. Fritz S. Pedersen, 4 vol., C. A. Reitzel, København 2002 (Det Kongelige Danske Videnskabernes Selskab, Historisk-filosofiske Skrifter, 24/1–4).

Walcher of Malvern, De Dracone, in C. Philipp E. Nothaft, Walcher of Malvern: De lunationibus and De Dracone; Study, Edition, Translation, and Commentary, Brepols, Turnhout 2017 (De Diversis Artibus, 101 [N.S. 64]), p. 194–217.

— De lunationibus, in C. Philipp E. Nothaft, Walcher of Malvern: ‘De lunationibus’ and ‘De Dracone’; Study, Edition, Translation, and Commentary, Turnhout 2017 (De Diversis Artibus, 101 [N.S. 64]), p. 90–191.

Modern authors (after 1789)

Bernhard, Ludger, Die Chronologie der Syrer, Böhlau, Vienna 1969 (Sitzungsberichte der Österreichischen Akademie der Wissenschaften, phil.-hist. Kl., 264.3).

Birkenmajer, Aleksander, « À propos de l’‘Abrahismus’ », Archives internationales d’histoire des sciences, 3 (1950), p. 378–390. Reprinted in Id., Études d’histoire des sciences et de la philosophie du Moyen Âge, Wydawnictwo Polskiej Akademij Nauk, Wrocław 1970, p. 237–249.

Blume, Dieter, Mechthild Haffner, Wolfgang Metzger, Sternbilder des Mittelalters: Der gemalte Himmel zwischen Wissenschaft und Phantasie, vol. I: 800–1200, Akademie Verlag, Berlin 2012.

Borst, Arno, Schriften zur Komputistik im Frankenreich von 721 bis 818, vol. I, Hahnsche Buchhandlung, Hannover 2006 (Quellen zur Geistesgeschichte des Mittelalters, 21).

Boudet, Jean-Patrice, « Chartres, BM, ms. 213 (ancien 169) – détruit (1944) », <https://www.manuscrits-de-chartres.fr/sites/default/files/fileviewer/documents/notices-detaillees/chartres-bm-ms-213_notice_jp-boudet.pdf> (Accessed 29 Nov. 2023).

— Entre science et nigromance: astrologie, divination et magie dans l’Occident médiéval (XIIe–XVe siècle), Publications de la Sorbonne, Paris 2006.

Burnett, Charles, « Advertising the New Science of the Stars circa 1120–50 », in Françoise Gasparri (ed.), Le XIIe siècle: mutations et renouveau en France dans la première moitié du XIIe siècle, Le Léopard d’Or, Paris 1994 (Cahiers du Léopard d’Or, 3), p. 147–157.

— « A New Source for Dominicus Gundissalinus’s Account of the Science of the Stars? », Annals of Science, 47 (1990), p. 361–374.

— « Astrology, Astronomy and Magic as the Motivation for the Scientific Renaissance of the Twelfth Century », in Angela Voss, Jean Hinson Lall (eds.), The Imaginal Cosmos: Astrology, Divination and the Sacred, University of Kent, Canterbury 2007, p. 55–61.

— « Nīranj: A Category of Magic (Almost) Forgotten in the Latin West », in Claudio Leonardi, Francesco Santi (eds.), Natura, scienze e società medievali: Studi in onore di Agostino Paravicini Bagliani, SISMEL–Edizioni del Galluzzo, Florence 2008 (Micrologus Library, 28), p. 37–66.

— « The Contents and Affiliation of the Scientific Manuscripts Written at, or Brought to, Chartres in the Time of John of Salisbury », in Michael Wilks (ed.), The World of John of Salisbury, Blackwell, Oxford 1984 (Studies in Church History: Subsidia, 3), p. 127–160.

Burnett, Charles, David Juste, « A New Catalogue of Medieval Translations into Latin of Texts on Astronomy and Astrology », in Faith Wallis, Robert Wisnovsky (eds.), Medieval Textual Cultures: Agents of Transmission, Translation and Transformation, de Gruyter, Berlin 2016 (Judaism, Christianity, and Islam – Tension, Transmission, Transformation, 6), p. 63–76.

Casulleras, Josep, « Las Tablas astronómicas de Pedro Alfonso », in María Jesús Lacarra (ed.), Estudios sobre Pedro Alfonso de Huesca, Instituto de Estudios Altoaragonenses, Huesca 1996 (Estudios Altoaragonenses, 41), p. 349–366.

Chabás, José, Computational Astronomy in the Middle Ages: Sets of Astronomical Tables in Latin, CSIC, Madrid 2019 (Estudios sobre la ciencia, 72).

Chabás, José, Bernard R. Goldstein, A Survey of European Astronomical Tables in the Late Middle Ages, Brill, Leiden 2012 (Time, Astronomy, and Calendars: Texts and Studies, 2).

— « John of Murs’s Tables of 1321 », Journal for the History of Astronomy, 40 (2009), p. 297–320.

Clark, Charles W., « A Christian Defense of Astrology in the Twelfth Century: The Liber cursuum planetarum of Raymond of Marseilles », International Social Science Review, 70 (1995), p. 93–102.

d’Alverny, Marie-Thérèse, « Abélard et l’astrologie », in René Louis, Jean Jolivet, Jean Châtillon (eds.), Pierre Abelard – Pierre le Venerable: les courants philosophiques littéraires et artistiques en Occident au milieu du XIIe siecle; abbaye de Cluny, 2 au 9 juillet 1972, Éditions du CNRS, Paris 1975, p. 611–630 (Actes et mémoires des colloques internationaux du Centre National de la Recherche Scientifique, 546). Reprinted as Chapter XV in Ead., La transmission des textes philosophiques et scientifiques au Moyen Âge, ed. Charles Burnett, Variorum, Aldershot 1994.

— « Astrologues et théologiens au XIIe siècle », in André Duval (ed.), Mélanges offerts à M.-D. Chenu, maître en théologie, Vrin, Paris 1967, p. 31–50 (Bibliothèque Thomiste, 37). Reprinted as Chapter XVI in Ead., La transmission des textes philosophiques et scientifiques au Moyen Âge, ed. Charles Burnett, Variorum, Aldershot 1994.

Grumel, Venance, La chronologie, Presses universitaires de France, Paris 1958 (Traité d’Études Byzantines, 1).

Haskins, Charles Homer, Studies in the History of Mediaeval Science, Harvard University Press, Cambridge (Mass.) 1924.

Honigmann, Ernst, Die sieben Klimata und die ΠΟΛΕΙΣ ΕΠΙΣΗΜΟΙ: Eine Untersuchung zur Geschichte der Geographie und Astrologie im Altertum und Mittelalter, Winter, Heidelberg 1929.

Jeudy, Colette, Yves-François Riou, Les manuscrits classiques latins des bibliothèques publiques de France, vol. I: Agen–Évreux, Éditions du Centre National de la Recherche Scientifique, Paris 1989.

Juste, David, « Anonymous, Commentary on Pseudo-Ptolemy’s Iudicia (update: 05.12.2022) », Ptolemaeus Arabus et Latinus. Works,

<http://ptolemaeus.badw.de/work/119> (Accessed 29 Nov. 2023).

— « Horoscopic Astrology in Early Medieval Europe (500–1100) », in La conoscenza scientifica nell’Alto Medioevo: Spoleto, 25 aprile – 1 maggio 2019, vol. I, Fondazione Centro Italiano di Studi sull’Alto Medioevo, Spoleto 2020 (Settimane di studio della Fondazione Centro Italiano di Studi sull’Alto Medioevo, 67), p. 311–333.

— Les Alchandreana primitifs: études sur les plus anciens traités astrologiques latins d’origine arabe (Xe siècle), Brill, Leiden 2007 (Brill’s Studies in Intellectual History, 152).

— « Les textes astrologiques latins attribués à Aristote », Micrologus, 21 (2013), p. 145–164.

— « MS London, British Library, Cotton Appendix VI (update: 20.02.2022) », Ptolemaeus Arabus et Latinus. Manuscripts, <http://ptolemaeus.badw.de/ms/49> (Accessed 29 Nov. 2023).

— « MS Munich, Bayerische Staatsbibliothek, Clm 18927 (update: 24.02.2022) », Ptolemaeus Arabus et Latinus. Manuscripts, <http://ptolemaeus.badw.de/ms/87> (Accessed 29 Nov. 2023).

— « MS Oxford, Corpus Christi College, 233 (update: 01.03.2022) », Ptolemaeus Arabus et Latinus. Manuscripts, <http://ptolemaeus.badw.de/ms/483> (Accessed 29 Nov. 2023).

— « MS Vatican, Biblioteca Apostolica Vaticana, Vat. lat. 5714 (update: 15.11.2022) », Ptolemaeus Arabus et Latinus. Manuscripts, <http://ptolemaeus.badw.de/ms/294> (Accessed 29 Nov. 2023).

— « Pseudo-Ptolemy, Iudicia (update: 10.03.2022) », Ptolemaeus Arabus et Latinus. Works, <http://ptolemaeus.badw.de/ms/483> (Accessed 29 Nov. 2023).

— « Neither Observation nor Astronomical Tables: An Alternative Way of Computing the Planetary Longitudes in the Early Western Middle Ages », in Charles Burnett, Jan P. Hogendijk, Kim Plofker, Michio Yano (eds.), Studies in the History of the Exact Sciences in Honour of David Pingree, Brill, Leiden, 2004 (Islamic Philosophy, Theology, and Science: Texts and Studies, 54), p. 181–222.

— « The Impact of Arabic Sources on European Astrology: Some Facts and Numbers », Micrologus, 24 (2016), p. 173–194.

Kennedy, E. S., M. H. Kennedy, Geographical Coordinates of Localities from Islamic Sources, Institut für Geschichte der Arabisch-Islamischen Wissenschaften an der Johann Wolfgang Goethe-Universität, Frankfurt/Main 1987 (Veröffentlichungen des Institutes für Geschichte der Arabisch-Islamischen Wissenschaften, Reihe A: Texte und Studien, 2).

Lemay, Richard, Abu Ma‘shar and Latin Aristotelianism in the Twelfth Century: The Recovery of Aritotle’s Natural Philosophy through Arabic Astrology, American University of Beirut, Beirut 1962 (American University of Beirut, Publication of the Faculty of Arts and Sciences: Oriental Series, 38).

Lipton, Joshua David, « The Rational Evaluation of Astrology in the Period of Arabo-Latin Translation ca. 1126–1187 AD », Ph.D. diss., University of California, Los Angeles, 1978.

Malewicz, Małgorzata Hanna, « Libellus de efficatia artis astrologice: traité astrologique d’Eudes de Champagne, XIIe siècle », Mediaevalia Philosophica Polonorum, 20 (1974), p. 3–95.

Mercier, Raymond, « Astronomical Tables in the Twelfth Century », in Charles Burnett (ed.), Adelard of Bath: An English Scientist and Arabist of the Early Twelfth Century, Warburg Institute, London 1987 (Warburg Institute Surveys and Texts 14), p. 87–118. Reprinted as Chapter VII in Id., Studies on the Transmission of Medieval Mathematical Astronomy, Ashgate, Aldershot 2004 (Variorum Collected Studies Series, 787).

— « Astronomical Tables of Abraham Bar Ḥiyya », in Sacha Stern, Charles Burnett (eds.), Time, Astronomy, and Calendars in the Jewish Tradition, Brill, Leiden 2014 (Time, Astronomy, and Calendars: Texts and Studies, 3), p. 155–207.

Millás Vallicrosa, José María, Estudios sobre Azarquiel, CSIC, Madrid 1943–1950.

— « Sobre la autenticidad de una obra astronómica de R. Abraham ibn ‘Ezra », Isis, 40 (1949), p. 32–33.

Neugebauer, Otto, A History of Ancient Mathematical Astronomy, 3 vol., Springer, Berlin 1975 (Studies in the History of Mathematics and Physical Sciences, 1).

— An Astronomical Almanac for the Year 348/9 (P. Heid. inv. no. 34), Munksgaard, Copenhagen 1956 (Historisk-filologiske Meddelelser udgivet af Det Kongelige Danske Videnskabernes Selskab, Bind 36, no. 4).

— The Astronomical Tables of Al-Khwārizmī: Translation with Commentaries of the Latin Version ed. by H. Suter, Supplemented by Corpus Christi College MS 283, Munksgaard, København 1962 (Det Kongelige Danske Videnskabernes Selskab, Historisk-filosofiske Skrifter, 4.2).

North, John D., Richard of Wallingford: An Edition of His Writings with Introductions, English Translation and Commentary, 3 vol., Clarendon Press, Oxford 1976.

Nothaft, C. Philipp E., « Ephemerides in High Medieval Europe: The Textual Evidence », Journal for the History of Astronomy, 52 (2021), p. 33–52.

— Graeco-Arabic Astronomy for Twelfth-Century Latin Readers: Ptolomeus et multi sapientum (Abraham Ibn Ezra Latinus) — Robert of Chester, Liber canonum, pt. ii, Brill, Leiden 2023 (Time, Astronomy, and Calendars: Texts and Studies, 12).

— Walcher of Malvern: De lunationibus and De Dracone; Study, Edition, Translation, and Commentary, Brepols, Turnhout 2017 (De Diversis Artibus, 101 [N.S. 64]).

Omont, H., A. Molinier, C. Couderc, E. Coyecque, Catalogue général des manuscrits des bibliothèques publiques de France: Départements, vol. XI: Chartres, Plon, Paris 1890.

Palmer, Andrew (trans.), The Seventh Century in the West-Syrian Chronicles, Liverpool University Press, Liverpool 1993.

Runciman, David, « Bishop Bartholomew of Exeter (d. 1184) and the Heresy of Astrology », Journal of Ecclesiastical History, 70 (2019), p. 265–282.

Samsó, Julio, « ‘Dixit Abraham Iudeus’: algunas observaciones sobre los textos astronómicos latinos de Abraham Ibn ‘Ezra », Iberia Judaica, 4 (2012), p. 171–200.

— Las ciencias de los antiguos en Al-Andalus, Editorial MAPFRE, Madrid 1992.

— On Both Sides of the Strait of Gibraltar: Studies in the History of Medieval Astronomy in the Iberian Peninsula and the Maghrib, Brill, Leiden 2020 (Handbook of Oriental Studies, Section One, 144).

Sela, Shlomo, Abraham Ibn Ezra and the Rise of Medieval Hebrew Science, Brill, Leiden 2003 (Brill’s Series in Jewish Studies, 32).

— « Algunos puntos de contacto entre el Libro de las tablas astronómicas en su versión latina y las obras literarias hebreas de Abraham Ibn Ezra », Miscelánea de Estudios Árabes y Hebraicos, Sección de Hebreo, 46 (1997), p. 37–56.

— « Contactos científicos entre judíos y cristianos en el siglo XII: el caso del Libro de las tablas astronómicas de Abraham Ibn Ezra en su versión latina y hebrea », Miscelánea de Estudios Árabes y Hebraicos, Sección de Hebreo, 45 (1996), p. 185–222.

Smithuis, Renate, « Science in Normandy and England under the Angevins: The Creation of Abraham Ibn Ezra’s Latin Works on Astronomy and Astrology », in Giulio Busi (ed.), Hebrew to Latin, Latin to Hebrew: The Mirroring of Two Cultures in the Age of Humanism; Colloquium Held at the Warburg Institute, London, October 18–19, 2004, Aragno, Turin 2006 (Berlin Studies in Judaism, 1), p. 23–59.

Tibbets, Gerald R., « The Beginnings of a Cartographic Tradition », in J. B. Harley, David Woodward (eds.), The History of Cartography, vol. I.1: Cartography in the Traditional Islamic and South Asian Societies, Chicago University Press, Chicago 1992, p. 90–107.

Thorndike, Lynn, The Sphere of Sacrobosco and Its Commentators, University of Chicago Press, Chicago 1949.

Tolan, John, « Reading God’s Will in the Stars: Petrus Alfonsi and Raymond de Marseille Defend the New Arabic Astrology », Revista Española de Filosofía Medieval, 7 (2000), p. 13–30.

von Heinemann, Otto, Die Augusteischen Handschriften, vol. V: Codex Guelferbytanus 34.1 Aug. 4° bis 117 Augusteus 4°, Klostermann, Frankfurt/Main 1966 [1903] (Kataloge der Herzog-August-Bibliothek Wolfenbüttel: Die alte Reihe, 8).