Survey of European Astronomical Tables in the Late Middle Ages

270 Pages·2012·1.887 MB·English

by  Jose Chabas, Bernard R. Goldstein

A Survey of European Astronomical Tables
in the Late Middle Ages
Time, Astronomy, and Calendars
Texts and Studies
Editors
Charles Burnett
Sacha Stern
Editorial Board
Dáibhí Ó Cróinín
Benno van Dalen
Gad Freudenthal
Tony Grafton
Leofranc Holford-Strevens
Bernard R. Goldstein
Alexander Jones
Daryn Lehoux
Jörg Rüpke
Julio Samsó
Shlomo Sela
John Steele
VOLUME 2
The titles published in this series are listed at brill.nl/tac
A Survey of European Astronomical
Tables in the Late Middle Ages
By
José Chabás and Bernard R. Goldstein
LEiDEn • BOSTOn
2012
Library of Congress Cataloging-in-Publication Data
Chabás, José, 1948–
A survey of European astronomical tables in the late Middle Ages / by José Chabás and
Bernard R. Goldstein.
p. cm. — (Time, astronomy, and calendars, iSSn 2211-632X ; v. 2)
includes bibliographical references and index.
iSBn 978-90-04-23058-3 (hardback : alk. paper) 1. Astronomy, Medieval—Europe.
2. Astronomy—Tables—History—To 1500. 3. Ephemerides—Europe—History—To 1500.
i. Goldstein, Bernard R. ii. Title.
QB23.C484 2012
528.094’09024—dc23
2012009594
iSSn 2211-632X
iSBn 978 90 04 23058 3 (hardback)
iSBn 978 90 04 23059 0 (e-book)
Copyright 2012 by Koninklijke Brill nV, Leiden, The netherlands.
Koninklijke Brill nV incorporates the imprints Brill, Global Oriental, Hotei Publishing,
iDC Publishers and Martinus nijhoff Publishers.
All rights reserved. no part of this publication may be reproduced, translated, stored in
a retrieval system, or transmitted in any form or by any means, electronic, mechanical,
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Fees are subject to change.
This book is printed on acid-free paper.
COnTEnTS
List of Tables ...................................................................................... ix
List of Figures ..................................................................................... xv
Preface ................................................................................................. xvii
introduction ........................................................................................ 1
Chapter One Chronology .............................................................. 13
1. Epochs and intervals .............................................................. 14
2. number of Days from the Beginning of an Era ................ 16
3. Conversion of Dates ............................................................... 17
Chapter Two Trigonometry and Spherical Astronomy ........... 19
1. Sines and Chords .................................................................... 19
2. Solar Declination ..................................................................... 22
3. Shadow Table .......................................................................... 24
4. Right Ascension ...................................................................... 24
5. Oblique Ascension .................................................................. 28
6. Ascensional Difference ........................................................... 30
7. Length of Daylight .................................................................. 31
8. Meridian Altitude of the Sun ................................................ 33
9. Time of Day from the Altitude of the Sun ........................ 34
Chapter Three Equation of Time ................................................. 37
Chapter Four Precession and Apogees ....................................... 43
1. Trepidation (Access and Recess) .......................................... 44
2. Apogees ..................................................................................... 47
3. Parisian Alfonsine Tables ...................................................... 48
Chapter Five Mean Motions and Radices .................................. 53
1. Mean Motions ......................................................................... 54
2. Radices ...................................................................................... 59
vi contents
Chapter Six Equations ................................................................... 63
1. Sun ............................................................................................. 63
2. Moon ......................................................................................... 67
3. Planets ....................................................................................... 73
Chapter Seven True Positions ...................................................... 83
1. Sun ............................................................................................. 83
2. Moon ......................................................................................... 86
3. Planets ....................................................................................... 88
Chapter Eight Velocity .................................................................. 95
1. Sun and Moon ......................................................................... 95
2. Planets ....................................................................................... 99
Chapter nine Latitude ................................................................... 103
1. Moon ......................................................................................... 103
1.1 Ptolemaic tradition ....................................................... 103
1.2 indian tradition ............................................................. 104
2. Planets ....................................................................................... 106
2.1 Ptolemaic tradition ....................................................... 106
2.2 indian tradition ............................................................. 110
2.3 Further developments ................................................... 112
Chapter Ten Stations and Retrogradations ................................ 117
Chapter Eleven Visibility of the Moon and the Planets .......... 123
1. Moon ......................................................................................... 123
2. Planets ....................................................................................... 124
Chapter Twelve Parallax ................................................................ 127
1. Ptolemaic Tradition ................................................................ 128
2. indian Tradition ...................................................................... 135
Chapter Thirteen Syzygies ............................................................. 139
1. Mean Syzygies ......................................................................... 140
2. Time from Mean to True Syzygy ......................................... 144
3. True Syzygies ........................................................................... 151
Chapter Fourteen Planetary Conjunctions ................................ 155
1. Sun–Planets .............................................................................. 155
2. Superior Planets ...................................................................... 156
contents vii
Chapter Fifteen Eclipses ................................................................ 163
1. Diameters of the Luminaries and the Earth’s Shadow ....... 164
2. Digits of Eclipse ...................................................................... 165
2.1 Lunar eclipses ................................................................. 165
2.2 Solar eclipses .................................................................. 168
3. interpolation Schemes ............................................................ 172
4. Eclipsed Part of the Solar and Lunar Disks ....................... 174
5. Reflexio Tenebrarum ............................................................... 175
6. Colors ........................................................................................ 176
7. Table of the Samt for Solar Eclipses .................................... 178
8. Lists of Eclipses ....................................................................... 180
Chapter Sixteen Fixed Stars .......................................................... 185
Chapter Seventeen Geographical Lists ........................................ 201
Chapter Eighteen Astrology .......................................................... 205
1. Horoscopes and Astrological Houses .................................. 205
2. Projection of the Rays ............................................................ 212
3. Planetary Dignities .................................................................. 215
4. Excess of Revolution .............................................................. 218
5. Revolution of the Months ..................................................... 221
6. Duration of Pregnancy .......................................................... 223
Chapter nineteen Miscellaneous Tables .................................... 227
List of Manuscripts ............................................................................ 231
Bibliography ........................................................................................ 235
index .................................................................................................... 245

LiST OF TABLES
1.1A: Epochs ...................................................................................... 15
1.1B: Weekdays of epochs .............................................................. 15
1.2A: number of days in the Hijra calendar ............................... 16
1.2B: Weekdays in the Hijra calendar .......................................... 17
1.3: Conversion of Hijra dates to Julian dates .......................... 18
2.1A: Sines .......................................................................................... 20
2.1B: Trigonometric functions ....................................................... 21
2.2A: Some historical values of the obliquity .............................. 23
2.2B: Solar declination in the Toledan Tables ............................ 24
2.2C: Solar declination in the Tabule Anglicane ......................... 24
2.2D: Solar declination in the Tabule directionum ..................... 24
2.3: Shadows ................................................................................... 25
2.4A: Right ascension in the tradition of al-Khwārizmī ............ 27
2.4B: Right ascension in the tradition of al-Battānī ................... 28
2.5: ibn al-Kammād’s table for the oblique ascension for
Córdoba ................................................................................... 29
2.6A: Ascensional difference in the tradition of al-Khwārizmī ... 30
2.6B: Ascensional difference for ε = 23;33° ................................. 30
2.7A: Length of daylight in hours and minutes .......................... 32
2.7B: Length of longest daylight and geographical latitude ...... 32
2.8: Meridian solar altitude for Liège ......................................... 34
2.9A: Solar altitude from the time of day according to the
Toledan Tables ....................................................................... 35
2.9B: Time of day from the solar altitude according to the
Toledan Tables ....................................................................... 36
3A: Equation of time, in time-degrees and minutes ............... 39
3B: Some historical examples of the equation of time ........... 40
3C: Equation of time, in minutes and seconds of an hour .... 41
4.1A: Mean motion of access and recess of the 8th sphere ...... 46
4.1B: Equation of access and recess of the 8th sphere ............... 46
4.1C: Variable obliquity ................................................................... 47
4.2: Apogees for 1320 .................................................................... 48
4.3A: The linear term for precession/trepidation in the Parisian
Alfonsine Tables ..................................................................... 49
x list of tables
4.3B: The mean motion of access and recess in the Parisian
Alfonsine Tables ..................................................................... 50
4.3C: The Alfonsine equation of the 8th sphere ......................... 50
4.3D: Alfonsine apogees ................................................................... 52
5.1A: Mean motion of the Sun in the Tables of Toulouse ........ 55
5.1B: Mean motion of the Sun in the Tabule magne ................. 56
5.1C: Daily mean motion of the Sun in the editio princeps
of the Alfonsine Tables ......................................................... 57
5.1D: Some historical values of the mean motions of the
Sun and the length of the year ............................................ 57
5.1E: Some historical values of the mean motions of the Moon
and the lunar node ................................................................. 58
5.1F: Some historical values of the mean motions of the
superior planets ...................................................................... 59
5.1G: Some historical values of the mean motions of the
inferior planets ........................................................................ 59
5.2A: Radices for Prague for 1400 ................................................. 60
5.2B: Alfonsine radices related to the Moon ............................... 61
6.1A: Alfonsine solar equation ....................................................... 65
6.1B: Some historical values of the maximum solar equation ... 66
6.2A: Alfonsine lunar equations ..................................................... 71
6.2B: Some historical values for the maximum values of the
lunar equations ....................................................................... 72
6.2C: Displaced lunar equations .................................................... 73
6.3A: Some historical values of the planetary equations ........... 77
6.3B: Equations for Jupiter in the Toledan Tables ..................... 78
6.3C: Equation of center for Jupiter according to
John Vimond .......................................................................... 79
6.3D: Equation of anomaly for Jupiter according to
John Vimond .......................................................................... 79
6.3E: Double argument table for the equation of Jupiter ......... 81
7.1A: True positions of the Sun at Toledo for 1321 ................... 83
7.1B: Solar correction ...................................................................... 84
7.1C: Entry of the Sun into zodiacal signs at
Salamanca for 1461 ................................................................ 85
7.1D: True position of the Sun at the beginning of each
month for 1252 ....................................................................... 85
7.2A: True positions of the Moon at Salamanca for 1473 ........ 86
7.2B: Zodiacal sign of the Moon ................................................... 87
7.2C: Table of the zodiacal signs ................................................... 88