The Forgotten Gifts of Hermes: The Latin Reception of Proclus’ Commentary on Euclid’s Elements
Contenido principal del artículo
Resumen
The present work offers an account of the Latin reception of Proclus’ Commentary in the first book of Euclid’s Elements (In Euclidem). The overall goal of this paper is to offer a unified historical and philological map as a ground-tool for understanding the Latin reception of In Euclidem from the early 16th century to the 17th century, which includes manuscript sources hitherto overlooked. I will deal with the three known complete translations produced by Bartolomeo Zamberti (1473–1543), Giovanni Battista Gabia (c.1500–1590), and Francesco Barozzi (1537–1604), as well as with five fragmentary translations embedded in the works of Giorgio Valla (1447–1500), Jerónimo Muñoz (1520–1591), Conrad Dasypodius (1532–1600), Federico Borromeo (1564–1631), and Johannes Kepler (1571–1630). Each of these translations and the intentions of their authors are discussed in chronological order. Five of them (following the fragment chosen by Kepler) are partially edited in the Appendix.
Descargas
Detalles del artículo
Política propuesta para las revistas que ofrecen acceso abierto
Los autores que publican en esta revista aceptan las siguientes condiciones:
a. Desde el número IV y para los números futuros, la política de la editorial es que los autores conserven los derechos de autor y concedan a la revista el derecho de primera publicación con el trabajo licenciado simultáneamente bajo una Licencia de Atribución Creative Commons que permita a otros compartir el trabajo con un reconocimiento de la autoría del trabajo y la publicación inicial en esta revista.
b. Los autores pueden establecer acuerdos contractuales adicionales para la distribución no exclusiva de la versión publicada del trabajo en la revista (por ejemplo, enviarlo a un repositorio institucional o publicarlo en un libro), con un reconocimiento de su publicación inicial en esta revista.
c. Se permite y anima a los autores a publicar su trabajo en línea (por ejemplo, en repositorios institucionales o en su sitio web) antes y durante el proceso de presentación, ya que puede dar lugar a intercambios productivos, así como a una citación más temprana y mayor del trabajo publicado (Véase The Effect of Open Access).
Bibliografía
Manuscripts
Bologna, Biblioteca Universitaria, 2293, fol. 1–149v.
Milan, Biblioteca Ambrosiana P. 51 sup.
Milan, Biblioteca Ambrosiana R 181 (16) inf. 1.
Modena, Biblioteca Estense, α. T. 9. 11, fol. 67–241v.
Munich, Bayerische Staatsbibliothek, A. gr. b. 954.
Munich, Bayerische Staatsbibliothek, Clm 10674, fol. 337r–340v.
Munich, Bayerische Staatsbibliothek, Clm 6, fol. 1r–154v.
Munich, Bayerische Staatsbibliothek, Cod. Graec. 427, fol. 1–234v.
Naples, Biblioteca Nazionale di Napoli, VIII, 33, fol. 21r–300r.
Oxford, Bodleian Library, Barocci 161.
Oxford, Corpus Christi College Library, 97.
Paris, Bibliothèque nationale de France, Baluze 281.
Paris, Bibliothèque nationale de Paris, Latin 7218.
Salamanca, Biblioteca de la Universidad de Salamanca, 2320, fol. 3v–133v.
Vatican City, Biblioteca Apostolica Vaticana, Vat. Barb. Gr. 101.
Vatican City, Biblioteca Apostolica Vaticana, Urb. Gr. 71.
Vatican City, Biblioteca Apostolica Vaticana, Vat. Lat. 4575, fol. 1r–19r.
Vatican City, Biblioteca Apostolica Vaticana, Vat. Lat. 6996, fol. 2r–159r.
Vatican City, Biblioteca Apostolica Vaticana, Vat. Lat. 6998, fol. 3r–116r.
Vatican City, Biblioteca Apostolica Vaticana, Vat., Barb. Gr. 145.
Venice, Biblioteca Marciana VI. 11.
Venice, Biblioteca Marciana, Gr. Z. 306.
Primary Sources
Alessandro Piccolomini, De certitudine mathematicarum scientiarum, Antonio Blado, Roma 1547.
Conrad Dasypodius, Mathematicum, complectens praecepta mathematica, astronomica, logistica, Volumen II, J. Rihel, Strasbourg 1570.
— Protheoria Mathematica in qua non solum disciplinae mathematicae omnes, ordine convenienti enumerantur, verum etiam universalia Mathematica praecepta, explicantur, Iodocus Martinus, Strabourg 1593.
Euclid, Proclus, Εὐκλείδου Στοιχεíων βιβλία 15 ἐκ τοῦ Θέωνος συνουσíων. Εἰς τοῦ ἑαυτοῦ τὸ πρῶτον ἐξηγημáτων Πρóκλου βιβλία 4, I, ed. Simon Grynaeus, Hervagium, Basel 1533.
Federico Borromeo, De Pythagoricis numeris libri tres, ed. Manuel Bertolini, Bulzoni, Roma 2017 (Biblioteca Ambrosiana/Fonti e Studi 26).
Francesco Barozzi, Procli Diadochi Lycii philosophi platonici ac matematici probatissimi in primum Euclidis Elementorum librum commentariorum ad uniuersam mathematicam disciplinam principium eruditionis tradentium libri IV, Gratiosus Perchacinus, Padova 1560.
— Opusculum in quo una oratio et duae quaestiones, altera de certitudine, et altera de medietate mathematicarum, continentur, E.G.P., Padova 1560.
Giorgio Valla, De expetendis et fugiendis rebus opus, Manutius, Venezia 1501.
Giovanni Aurispa, Carteggio di Giovanni Aurispa, ed. Remigio Sabbadini, Istituto storico italiano, Roma 1931 (Fonti per la storia d’Italia).
Johannes Kepler, Harmonices mundi libri V, Ioannes Plancus, Linz 1619.
— Opera omnia, ed. Christian Frisch, vol. II, Heyder & Zimmer, Frankfurt and Erlangen 1859.
Proclus, Procli Diadochi in Primum Euclidis Elementorum Librum Commentarii, ed. Godfried Friedlein, B. G. Teubneri, Leipzig 1874.
Secondary Sources
Adamson, Peter, Filip Karfík, « Proclus’ Legacy », in Pieter D’Hoine, Marije Martijn (eds.), All From One: A Guide to Proclus, Oxford University Press, Oxford 2016, p. 290–332.
Aurivillius, Pehr Fabian, Catalogus librorum impressorum Bibliothecae Regiae Academiae Upsaliensis, Stenhammar et Palmblad, Upsala 1814.
Boncompagni, Baldassarre, Intorno al comento di Proclo sul primo libro degli Elementi di Euclide, Tipografia delle Scienze Matematiche e Fisiche, Roma 1784.
Brach, Jean Pierre, « Pythagorean Number Mysticism in the Renaissance. An Overview », in Irene Caiazzo, Constantonos Macris, Aurélien Robert (eds.), Brill’s Companion to the Reception of Pythagoras and Pythagoreanism in the Middle Ages and the Renaissance, Brill, Boston 2021 (Brill’s Companions to Classical Reception, 24), p. 457–488.
Valentino Capocci, Bibliothecae Apostolicae Vaticanae, Codices Barberiniani graeci, Tomus I. Codices 1–163, Bibliotheca Vaticana, Città del Vaticano 1958.
Luis Miguel Carolino, « Mathematics and the Late Aristotelian Theory of Science: The Quaestio de Certitudine Mathematicarum in Seventeenth–century Portuguese Universities », in Victor Navarro-Brotons, William Eamon (eds.), Beyond the Black Legend: Spain and the Scientific Revolution, Publicacions de la Universitat de València, Valencia 2007, p. 399–412
Guy Claessens, « Clavius, Proclus, and the Limits of Interpretation: Snapshot–idealization versus Projectionism», History of Science, 47/3 (2009), p. 317–336.
— « Het denken verbeeld. De vroegmoderne receptie (1533–1650) van Proclus’ Commentaar op het eerste boek van Euclides’ Elementen », Ph.D. Diss. KU Leuven 2011.
— Imagination as Self–knowledge: Kepler on Proclus’ Commentary on the First Book of Euclid’s Elements », Early Science and Medicine, 16/3 (2011), p. 179–199.
— « Proclus in the Renaissance », in Marco Sgarbi (ed.), Encyclopedia of Renaissance Philosophy, Springer, Cham 2018. <https://link.springer.com/referenceworkentry/10.1007/978-3-319-02848-4_412-1>.
— « Reception and the Textuality of History: Ramus and Kepler on Proclus’ History and Philosophy of Geometry », in André Lardinois, Sophie Levie, Hans Hoeken, Christoph Lüthy (eds.), Texts, Transmissions, Receptions: Modern Approaches to Narratives, Brill, Boston 2015 (Radboud Studies in Humanities, 1), p. 281–294.
— « The Drawing Board of Imagination: Federico Commandino and John Philoponus », Journal of the History of Ideas, 76/4 (2015), p. 499–515.
Cozzoli, Daniele, « Alessandro Piccolomini and the Certitude of Mathematics », History and Philosophy of Logic, 28/2 (2007) p. 151–171.
Crapulli, Giovanni, Mathesis universalis: Genesi di una idea nel XVI secolo, Edizioni dell’Ateneo, Roma 1969 (Lessico intellettuale europeo, 3).
De Caro, Mario, « Galileo e il platonismo fisico–matematico », in Riccardo Chiaradonna (ed), Il platonismo e le scienze, Carocci, Roma 2012 (Colloquium philosophicum, Nuova serie, 3), p. 119–138.
— « Galileo’s Mathematical Platonism », in Johannes Czermak (ed.), Philosophy of Mathematics, Holder – Pichler – Tempsky, Wien 1993, p. 1–9.
— « Sul platonismo di Galileo », Rivista di filosofía, 82 (1996), p. 25–40.
De Pace, Anna, Le matematiche e il mondo. Ricerche su un dibattito in Italia nella seconda metà del Cinquecento, Francoangeli, Milano 1993 (Filosofia e scienza – Studi).
De Risi, Vincenzo, Leibniz on the Parallel Postulate and the Foundations of Geometry, The Unpublished Manuscripts, Birkhäuser, Berlin 2018 (Sciences Networks Historical Studies 51).
Del Gallo, Elena, « Gabia, Giovan Battista », in Dizionario Biografico degli Italiani, Volume 51, 1998. .
Dubouclez, Olivier, Descartes et la voie de l’analyse, Presses Universitaires de France, Paris 2013 (Épiméthé essais philosophique).
Escobar, Jorge M., « Kepler’s theory of the soul: a study on epistemology », Studies in History and Philosophy of Science Part A, 39/1 (2008) p. 15–41.
Ferraro, Giovanni, « Dimostrazioni Matematiche e Conoscenza Scientifica in Alessandro Piccolomini », in Howard Burns, Francesco Paolo Di Teodoro, Giorgio Bacci (eds.), Saggi di Letteratura architettonica da Vitruvio a Winckelmann III, Olschki, Firenze 2010, p. 215–233.
Field, Judith Veronica, Kepler’s Geometrical Cosmology, Athalone, London 1988 (Bloomsbury Academic Collections: Philosophy).
Giacobbe, Giulio Cesare, « Il Commentarium De Certitudine Mathematicarum Disciplinarum di Alessandro Piccolomini », Physis, 14/2 (1972), p. 162–193.
— « Francesco Barozzi e la quaestio de certitudine mathematicarum », Physis, 14/4 (1972), p. 162–193.
Giacomelli, Ciro, « I libri greci di Matteo Macigni. Contributo allo studio di una biblioteca umanistica », La parola del passato, 407/2 (2019), p. 361–420.
Goulding, Robert, « Pythagoras in Paris: Petrus Ramus Imagines the Prehistory of Mathematics », Configurations, 17/1 (2009), p. 51–86.
— Defending Hypatia: Ramus, Savile, and the Renaissance Rediscovery of Mathematical History, Springer, Dordrecht 2010 (Archimedes, New Studies in the History and Philosophy of Science and Technology, 25).
Guarna, Valeria, L’Accademia veneziana della Fama (1557–1561). Storia, cultura e editoria, Con l’edizione della Summa delle Opere (1558) e altri documenti inediti, Vecchiarelli, Roma 2018 (Cinquecento, testi e studi letter. Ital).
Guicciardini, Niccolò, Isaac Newton on Mathematical Certainty and Method, MIT Press Ltd, Cambridge, MA 2011.
Helbing, Mario Otto, « La fortune des commentaires de Proclus sur le premier livre des Eléments d’Euclide à l’époque Galilée », in Gerald Bechtle, Dominic J. O’Meara (eds.), La philosophie des mathématiques de l’Antiquité tardive, Actes du colloque international Fribourg, Suisse 1998, p. 173–193.
Higashi, Shin, Penser les mathématiques au XVIe siècle, Editions Classiques Garnier, Paris 2018 (Histoire et philosophie des sciences, 17).
Hintikka, Jaakko, « Method of Analysis: A Paradigm of Mathematical Reasoning? », History and Philosophy of Logic, 33/1 (2012), p. 49–67.
Hintikka, Jaakko & Unto Remes, The Method of Analysis: Its Geometrical Origin and Its General Significance, Springer, Dordrecht 1974 (Boston Studies in the Philosophy of Science, 25).
Jardine, Nicholas, « Problems of Knowledge and Action: Epistemology of the Sciences », in Charles B. Schmitt, Quentin Skinner, Eckhard Kessler, Jill Kraye (eds.), The Cambridge History of Renaissance Philosophy, Cambridge University Press, Cambridge 1988, p. 685–711.
— « The Forging of Modern Realism: Clavius and Kepler against the Skeptics », Studies in History and Philosophy of Science, 10/2 (1979), p. 141–173.
Kessler, Eckhard, « Clavius entre Proclus et Descartes », in Luce Giard (ed.), Les jésuites à la Renaissance, Système éducatif et production du savoir, PUF, Paris 1988 (Bibliothèque d’histoire des sciences).
Kibre, Pearl, The Library of Pico della Mirandola, Columbia University Press, New York 1936.
Koyré, Alexandre, Metaphysics and Measurement: Essays in Scientific Revolution, Harvard University Press, Cambridge, MA 1968.
— « Galileo and Plato », Journal of the History of Ideas, 5 (1943), p. 400–428.
Levitin, Dimitri, Ancient Wisdom in the Age of the New Science, Cambridge University Press, Cambridge 2015 (Ideas in Context, 113).
— The Kingdom of Darkness: Bayle, Newton, and the Emancipation of the European Mind from Philosophy, Cambridge University Press, Cambridge – New York 2022.
Longeway, John, « The Place of Demonstratio Potissima in some 16th–Century Accounts of Mathematics », in Joël Biard (ed.), Raison et démonstration, Brepols, Turnhout 2015 (Studia Artistarum, 40), p. 223–251.
Mahoney, Michael S. « Barrow’s Mathematics: between Ancients and Moderns », in Mordechai Feingold (ed.), Before Newton: The Life and Times of Isaac Barrow, Cambridge University Press, Cambridge – New York 2021 (Transformations: Studies in the History of Science and Technology), p. 179–249.
Maierù, Luigi, « La diffusione di Proclo, commentatore di Euclide, nel Cinquecento », in 11° Annuario del Liceo Scientifico ‘B.G. Scorza’, Calabria Letteraria Editrice, Soveria Mannelli 1999, p. 49–68.
— « Metafìsica ed enti geometrici: Benito Pereyra, Pedro Fonseca, Francisco Suárez », in Sciences et religions. De Copernic à Galilée (1540–1610) Actes du colloque international, Rome 1996. Rome (Publications de l’École française de Rome, 260), p. 47–67.
Mancosu, Paolo, Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century, Oxford University Press, Oxford 1999.
Martens, Rhonda, Kepler’s Philosophy and the New Astronomy, Princeton University Press, Princeton, NJ 2000.
Martini, Emidio, Domenico Bassi, Catalogus codicum Graecorum Bibliothecae Ambrosianae, t. I–II, Hildesheim–New–York, Milano 1906.
Mioni, Elpidio, Bibliothecae Diui Marci Venetiarum codices graeci manuscripti. Volumen ΙΙ: Thesaurus Antiquus. Codices 300–625, Ministero per i beni culturali e ambientali, Roma 1985 (Indici e Cataloghi, Nuova Serie VI).
Morrow, Glenn R. Proclus: A Commentary on the First Book of Euclid’s Elements, Princeton University Press, Princeton, NJ 1970.
Navarro-Brotons, Victor, Enrique Rodríguez Galdeano, Matemáticas, cosmología y humanismo en la España del siglo XVI: Los Comentarios al segundo libro de la Historia natural de Plinio de Jerónimo Muñoz, Instituto de Estudios Documentales e Históricos sobre la Ciencia, Valencia 1998.
— « The Cultivation of Astronomy in Spanish Universities in the Latter Half of the 16th Century », in Universities and Science in the Early Modern Period, Springer, Dordrecht 2006 (Archimedes, New Studies in the History and Philosophy of Science and Technology, 12), p. 83–98.
— Disciplinas, saberes y prácticas: Filosofía natural, matemáticas y astronomía en la sociedad española de la época moderna, Publicacions de la Universitat de València, Valencia 2014.
— Jerónimo Muñoz: Matemáticas, cosmología y humanismo en la época del Renacimiento, Publicacions de la Universitat de València, Valencia 2019.
Oosterhoff, Richard J. Making Mathematical Culture: University and Print in the Circle of Lefèvre d’Étaples, Oxford University Press, Oxford 2018 (Oxford – Warburg Studies).
Osterhage, Wolfgang, Johannes Kepler: The Order of Things, Springer, Berlin 2020 (Springer Biographies).
Palmieri, Paolo, « On scientia and regressus », in Henrik Legarlund, Benjamin Hill (eds.), Routledge Companion to Sixteenth Century Philosophy, Routledge, New York 2017 (Routledge Philosophy Companions), p. 319–349.
Puntoni, Vittorio, Indice dei codici greci della Biblioteca Estense di Modena, Firenze 1986.
Rabouin, David, « Le rôle de Proclus dans les débats sur la ‘mathématique universelle’ à la Renaissance », in Alain Lernould (ed.), Etudes sur le Commentaire de Proclus au premier livre des Eléments d’Euclide, Presses Universitaires du Septentrion, Villeneuve D’Ascq 2007, p. 217–235.
— Mathesis universalis: L’idée de « mathématique universelle » d’Aristote à Descartes, Presses Universitaires de France (PUF), Paris 2009 (Épiméthé essais philosophique).
Randall, John H., The School of Padua and the Emergence of the Modern Science, Editrice Antenore, Padova 1961.
Raschieri, Amedeo A. « Giorgio Valla Editor and Translator of Ancient Scientific Texts », in Paula Olmos (ed.), Greek Science in the Long Run: Essays on the Greek Scientific Tradition (4th c. BCE–16th c. CE), Cambridge Scholars Publishing, Cambridge 2012, p. 127–149.
Rigaud, Stephen P. On the Arenarius of Archimedes, S. Collingwood, Oxford 1837.
Rommevaux, Sabine, Clavius, une clé pour Euclide au XVIème siècle, Vrin, Paris 2006 (Collection Mathesis).
Rose, Paul L. A Venetian Patron and Mathematician of the Sixteenth Century: Francesco Barozzi: 1537–1604, Giardini Editori, Pisa 1977.
— « Bartolomeo Zamberti’s Funeral Oration for the Humanist Encyclopaedist Giorgio Valla », in Cecil H. Clough (ed.), Cultural Aspects of the Italian Renaissance: Essays in Honor of Paul Oskar Kristeller, Manchester University Press, Manchester 1976, p. 299–310.
— « Certitudo Mathematicarum from Leonardo to Galileo », in Leonardo nella scienza e nella tecnica: Atti del Simposio Internazionale di storia della Scienza, Giunti Barberà, Firenze – Vinci 1969, p. 43–49.
— The Italian Renaissance of Mathematics: Studies on Humanists and Mathematicians from Petrarch to Galileo, Libraire Droz, Genève 1975 (Travaux d’humanisme et renaissance CXLV).
Schöttler, Tobias, « From Causes to Relations: The Emergence of a Non–Aristotelian Concept of Geometrical Proof out of the Quaestio De Certitudine Mathematicarum », Society and Politics, 6/2 (2012), p. 29–47.
Stewart, Ian, « Mathematics as Philosophy: Barrow and Proclus », Dionysius, 18 (2000), p. 151–181.
Velilla-Jiménez, Helbert E. « El debate sobre la certeza de las matemáticas en la filosofía natural de los siglos XVI y XVII (De quaestio [sic] de certitudine mathematicarum) », Estudios de Filosofía, 3 (2018), p. 59–93.
— « Francisco Sánchez and the Quaestio de certitudine mathematicarum: A Sceptical approach », Endeavour, 46/4 (2022), p. 1–10.
Wilson, Nigel, A Descriptive Catalogue of the Greek Manuscripts of Corpus Christi College Oxford, D. S. Brewer, Oxford 2011.