Table Of ContentArchimedes
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
KosTAS GAVROGLU, National Technical University ofA thens
ANTHONY GRAFTON, 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 ofN ew York
NOEL SWERDLOW, University of Chicago
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 prac
tical histories of specific developments in science and technology; and finally, where
possible and desirable, to bring the histories of science and technology into closer con
tact 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 it
self 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, bro
adly construed, as well as historically-engaged philosophy of science or technology.
Taken as a whole, Archimedes will be of interest to historians, philosophers, and scien
tists, 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 (e Book)
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 9
2.2 The manuscript 12
2.3 The text 15
2.4 Transcription criteria 18
2.5 A transcription of the Libra de las tablas alfonsies 19
3 Glossary of technical terms 95
4 Astronomical commentary 135
5Con~~ ll5
6 The legacy of Alfonsine astronomy 243
6.1 Introduction 243
6.2 The characteristics of Alfonsine astronomy in Paris 248
6.3 The astronomers in the Alfonsine tradition in Paris 266
6.4 Beyond Paris 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 inter
est 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 unprece
dented) 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 litera
ture 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 enor
mous, 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 associ
ated 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 con
tended 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 scien
tific 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 pro
ducing 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 re
produce 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
