The Alfonsine Tables of Toledo

Archimedes Volume 8 Archimedes NEW STUDIES IN THE HISTORY AND PHILOSOPHY OF SCIENCE AND TECHNOLOGY VOLUMES EDITOR JED Z. BucHWALD, Dreyfuss Professor of History, California Institute of Technology, Pasadena, CA, USA. ADVISORY BOARD HENK Bos, University of Utrecht MORDECHAI FEINGOLD, Virginia Polytechnic Institute ALLAN D. FRANKLIN, University of Colorado at Boulder National Technical University ofAthens Princeton University FREDERIC L. HOLMES, Yale University PAUL HOYNINGEN-HUENE, University of Hannover EvELYN Fox KELLER, MIT TREVOR LEVERE, University of Toronto JESPER LOTZEN, Copenhagen University WILLIAM NEWMAN, Harvard University JORGEN RENN, Max-Planck-Institutfur Wissenschaftsgeschichte ALEX ROLAND, Duke University ALAN SHAPIRO, University of Minnesota NANCY SIRAISI, Hunter College of the City University of New York NOEL SWERDLOW, University of Chicago KosTAS GAVROGLU, ANTHONY GRAFTON, Archimedes has three fundamental goals; to further the integration of the histories of science and technology with one another: to investigate the technical, social and practical histories of specific developments in science and technology; and finally, where possible and desirable, to bring the histories of science and technology into closer contact with the philosophy of science. To these ends, each volume will have its own theme and title and will be planned by one or more members of the Advisory Board in consultation with the editor. Although the volumes have specific themes, the series itself will not be limited to one or even to a few particular areas. Its subjects include any of the sciences, ranging from biology through physics, all aspects of technology, broadly construed, as well as historically-engaged philosophy of science or technology. Taken as a whole, Archimedes will be of interest to historians, philosophers, and scientists, as well as to those in business and industry who seek to understand how science and industry have come to be so strongly linked. Archimedes VolumeS New Studies in the History and Philosophy of Science and Technology The Alfonsine Tables of Toledo by JOSECHABAS University Pompeu Fabra, Barcelona, Spain and BERNARD R. GOLDSTEIN University of Pittsburgh, U.S.A. • '' SPRINGER-SCIENCE+BUSINESS MEDIA, B.V. A C.I.P. Catalogue record for this book is available from the Library of Congress. ISBN 978-90-481-6404-2 ISBN 978-94-017-0213-3 (eBook) DOI 10.1007/978-94-017-0213-3 Printed on acid-free paper All Rights Reserved © 2003 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2003 Softcover reprint of the hardcover 1st edition 2003 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. To John D. North, a valued colleague and friend CONTENTS List of Figures ix Preface xi 1 Introduction 1 2Th~ 9 2.1 Need for a new edition 2.2 The manuscript 2.3 The text 2.4 Transcription criteria 2.5 A transcription of the Libra de las tablas alfonsies 9 12 15 18 19 3 Glossary of technical terms 95 4 Astronomical commentary 135 5Con~ ll5 6 The legacy of Alfonsine astronomy 243 6.1 Introduction 6.2 The characteristics of Alfonsine astronomy in Paris 6.3 The astronomers in the Alfonsine tradition in Paris 6.4 Beyond Paris 243 248 266 290 Bibliography 307 Notation 321 Manuscripts cited 323 List of parameters 329 Index 333 vii LIST OF FIGURES Fig. 2.1. Madrid, Real Academia de la Historia, MS 9/5707, f. 1r. 16 Fig. 2.2. Madrid, Biblioteca Nacional, MS 3306, f. 49v. 17 Fig. 4.1. The model for solar motion. 154 Fig. 4.2. The model for the motion of an outer planet. 158 Fig. 4.3. The annual variation in the equation of time. 187 Fig. 4.4. Lunar parallax. 191 Fig. 4.5. Trigonometric functions. 201 Fig. 4.6. The celestial sphere. 206 Fig. 4.7. A portion of the celestial sphere represented as a plane. 215 Fig. 6.1. The celestial sphere in cross-section. 265 Fig. 6.2. A graph of John Vimond's periodic term for trepidation (i.e., the equation of access and recess). 277 ix PREFACE This book is the result of a close collaboration between authors living far away from each other-even on different continents, Europe (Barcelona) and North America (Pittsburgh)-who have exchanged e-mail messages on an almost daily basis for more than a decade, with occasional transatlantic journeys for face-to-face encounters. The event which first led us to consider research on the Alfonsine Tables was a visit to the Royal Library of Belgium in Brussels to look at a copy of the Tabulae Resolutae edited by Johann Schoner (2nd ed., 1551), a well known version of the Alfonsine Tables. Although it was not part of our original reason for consulting this published text, we found in it a table for planetary velocities which had never been described in the secondary literature. We soon discovered that this table was preserved in many manuscripts and the explanation for its neglect seems to be that it was not included in the editio princeps of the Alfonsine Tables (1483). Nevertheless, we noticed that this table appears in subsequent editions of the "Alfonsine Tables" printed in the 16th century. We then clearly understood that behind the term Alfonsine Tables there was a much more complex reality than what was revealed between the covers of a single book. By now we have located copies of this table in Arabic and Hebrew manuscripts in addition to a large number. of Latin manuscripts and printed editions. This discovery led us to wonder what else might have been ignored in the manuscript tradition surrounding the Alfonsine Tables, and that pursuit has kept us quite busy for a long time. Our previous research prepared us for this project in many ways, for both of us have devoted much effort to uncovering and elucidating astronomical material produced in the Iberian peninsula in the Middle Ages in Arabic, Castilian, Catalan, Hebrew, Latin, and Portuguese. These traditions are extremely rich and varied in content, but our focus has been on astronomical tables whose analysis requires a certain amount of technical facility as well as familiarity xi xii THE ALFONSINE TABLES OF TOLEDO with similar tabular material going back to antiquity and continuing into the 16th century. The canons to the Alfonsine Tables of Toledo, a 13th-century Castilian text preserved in a unique manuscript in Madrid, is of interest to scholars of medieval Castile and medieval Castilian as well as to historians of astronomy. In fact, the patronage of science by Alfonso X, king of Castile and Leon (reigned: 1252-1284), known as the Learned (el Sabia), was unusual (although not entirely unprecedented) in his time, and his active sponsorship of various scientific disciplines played a significant role in his political strategies both within his realm and in external affairs. Further, the scientific literature written in Castilian or translated into it during his reign is the starting point of a specialized language for astronomy in Castilian. The impact of the Alfonsine Tables on the development of European astronomy from the 13th to the middle of the 16th century was enormous, and it is the reason why Alfonso X is best remembered. Since almost all astronomy written in Latin (other than elementary student texts) until the mid-16th century derives from these tables and associated material, it is not possible to provide a comprehensive study in a single volume. Hence, we have concentrated on the period up to the mid-14th century by which time a large corpus of texts had already been generated, and the displacement of the most widely consulted previous set of tables, the Toledan Tables, was well advanced. An intriguing problem for historians is how to determine the impact of the Alfonsine Tables of Toledo in the absence of the original Castilian version, for only the canons are extant. Some have contended that the Alfonsine Tables which were diffused from Paris beginning in the 1320s had nothing to do with Castile. However, we argue that this position ignores too much of the evidence for continuity and the complexity of the historical data; indeed, we have taken this opportunity to explore the relationship between Castile and France in the relevant time period, from the 1270s to the 1320s as well as to examine the traces of Castilian astronomical traditions in the Parisian setting of the 1320s. The reader will notice that we have not included a complete translation into English of these canons; in fact, only the introduction and chapter 27 have previously been translated. The text is written in a difficult style, and our view is that a proper translation is a job for a trained philologist who has the necessary linguistic as well as scientific background to do it justice. We have approached this text as historians of science, not as philologists, attempting to make both the text and its contents accessible to a wider public than has previously been the case. All chapters are the result of the collaboration of the two authors, each with his particular skills and background, bringing PREFACE xiii to the project his specific approach, and both with the goal of producing a serious and comprehensive scholarly work. Many libraries in different countries have cooperated in assisting us to locate and consult manuscripts and printed editions. In particular, we would like to thank the Biblioteca Nacional and the Real Academia de la Historia, both in Madrid, for permission to reproduce pages from manuscripts in their collections. We are most grateful to a number of scholars: Alan C. Bowen, Jose Luis Mancha, Fritz S. Pedersen, Beatriz Porres, and Christopher Schabel for their suggestions concerning Latin texts; Paul Kunitzsch for a discussion of references to star lists; and Ruth Glasner for advice on Hebrew texts. But our principal intellectual debt is to John D. North who helped us in many ways over the years, and whose works have served as an inspiration and a model. Barcelona, Pittsburgh February 2003