paper - (suhayl 02) astronomical handbooks and tables from the islamic world (750-1900) - d a king -...

Astronomical Handbooks and Tables from the Islamic World (750-1900):

an Interim Report

David A. King and Julio Sams6. with a contribution by Bernard R. Goldstein

To Ted Kennedy, in appreciation

Contents

1 Introduction 12 1. 1 The scope of the zij li terature 14 1.2 The purpose of a zij . . . . . . 15 1.3 Regional schools of astronomy 15 1.4 The historiography of modem research on zijes 18

2 The contents of zijes 19 2.1 Sexagesimal alphanumerical notation 19 2.2 Chronology and calendar conversion . 19 2.3 Trigonometry ............. 20 2.4 Spherical astronomical functions ... 21 2.5 Planetary mean motions, equations and latitudes . 24 2.6 Planetary stations and visibility ... 25 2.7 Solar and lunar parallax and eclipses 25 2.8 Lunar visibi li ty ... 26 2.9 Geographical tables . .. 27 2. 10 Sturcatalogues ... .... . . . . . 27 2. 11 Tables fo r mathematical astrology . . . . . 28 2. 12 Analysis of tables and parameters . . . . . . . . . . . 30

10 D. A. King & J. Sams6

3 Overview of the vJliterature 31 31 31 32 33

3.1 The Indian-Iranian tradition. 3.1.1 TheZijal-SMh .. . 3.1.2 The Sindhind ... . 3.1.3 The Zfj of al-Khwarizmi

3.2 al-Ma'mun and the earliest Ptolemaic zfjes . 35 3.2.1 The Arabic Almagest . . . . . . . . 35 3.2.2 The Mumla/.lan Zij and the ZIjes of l:Iabash 36

3.3 The major Eastern Islamic zijes. . 40 3.3. 1 Some important lYes lost for posterity . . . 40 3.3.2 The tradition of al-Battani . . . . . . . . . 41 3.3.3 The tables of a l.ij engraved on an astronomical in-

strumen! .... 3.3.4 The tradition of Abu 'I-Waffi'

42 43

3.3.5 3.3.6 3.3.7 3.3.8

3.3.9 3.3.10

3.3.1 1 3.3. 12 3.3.13

3.3. 14

Sundry l.fjes from al- ' Iraq and Iran . 44 al-BirunI .. 44 A lij from Marw (12th century) . . 45 The tradition of al-Fahhad: from Adharbayjan to Constantinople and the Yemen ...... 45 The Maragha productions ... 46 Syrian zyes and the major production of the chief muwllqqit of the Umayyad Mosque in Damascus 48 The tradition of Ibn YUIlUS in Egypt and beyond .. 49 Some Yemeni l ijes ( 10th- 19th century) ..... 5 1 The proouclions of the Samarqand school ( 15th cen-tury). . . . . . . . . . . . . . . . .. ....... 53 The proouctions associated with the Istanbul Obser~ valory and later Turkish lijes displaying European influence . 54

3.3. 15 ZI)cs from India. . . . . . 55 3.4 AndalusT and MaghribT 1I)es .. 56

3.4.1 The earliest AndalusT lijes 56 3.4.2 Ibn al~Zarqalluh, ~ii< id al~A ndalusT. and the To/etlall

Tables . . . . . . . 58 3.4.3 The works of Ibn al~Kammad and Ibn al ~ lia 'im 59

A.~/ronQm;cal Htllldbo(Jks (tllli TitbIt's

3.4.4 The Zfj of Ibn I s~aq and its deri vatives . 3.4.5 Two zfjes from Fez . 3.4.6 Later Maghribi l fjes 3.4.7 The tables of Zacut

3.5 ZTjes in Hebrew [by 8. R. Goldstein]

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60 62 63 64 65

3.6 The IlOy'a tradition and the ' New ZTj' of Ibn al-Sh5!ir 69 3.6.1 Hay'a in the early Islamic East . 70 3.6.2 Hay'a in al-Andalus 3.6.3 The Maragha School ..... . 3.6.4 The planetary models of Ibn al-Sha~ir 3.6.5 Other developments in hay'a after Maragha

3.7 On the nolion of trepidation . 3.8 Other innovations .. ...... . . .

4 Categories of tables not contained in zijes 4.1 Sexagesimal multiplication tables

72 73 75 76 77 79

82 82

4.2 Trigonometric tables . . . . . . . . . 82 4.3 Ephemerides ... . ... 83 4.4 Auxiliary tables for compiling ephemerides 84 4.5 Tables for detennining lunar crescent visibility 84 4.6 Double-argument planetary equation tables . . 85 4.7 Auxiliary tables for solving spherical astronomical prob-

lems for all latitudes . . . . . . . . ..... .. 8S 4.8 Tables for time-keeping by the Sun and stars ... 4.9 Tables for regulating the times of Muslim prayer . 4.10 Tables for finding the qibla . . . . . . . . . . . .

86 89 90

4.11 Tables for constructing astrolabes and astrolabic quadrants 91 4.12 Tables for constructing sundials 4.13 AstrologicallabJes . 4.14 MisceUaneous tables

5 Concluding remarks

Bibliographical abbreviations

5",,",12(1001)

92 94 95

97

98

12 0, A. King & J. Sams6

1 Introduction

The purpose of this papert is to present an overview of the current state of research on the medieval Islamic astronomical handbooks known as zfjes in panicular,2 and astronomical tables in general. It is intended as a supple-ment to E. S. Kennedy's groundbreak ing survey of Islamic zfjes published in 1956,3 incorporating the numerous categories of tables not contained in zfjes,4 and an attempt has been made to mention most of the research that has been done since Ihallime.~ It is also intended as an interim overview

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nle main authors (O.A.K. and J.S.) are grateful to Franr;:ois Charette, Benno van Dalen. Bernard Goldstein and David Pingree for their comments on earlier versions of this paper, and are alone responsible for any remaining errors and misinterpretations. We are particularly pleased that Bernard Goldstein was willing to contribute an important chapter on Hebrew ZljeS. Bibliographical abbreviations for the basic reference works for the history of Islamic astronomy and mathematics and other frequently-cited works are listed at the end of this paper.

T11e term zfj is tradit ionally derived from Pahlevi zrk, originally meaning 'thread' or 'cord' and already used in Pahlevi with the meaning 'astronomical tables'. presumably by extension of the notion of a thread 10 the warp of a fabric and hence to the orthogonal framework of an astronomical table (Kennedy, "n] Survey". p. 123b, ci ting C. A. Nallino). However, recent research suggests that the term was Originally used in Arabic to denote an astronomical text in verse, as in Sanskrit tanlra, without any tables: see further R. Mercier. "From Tantra to Vj"', in Kunil1,.Sch Festschrift, pp. 451-460. Kennedy. "Zij Survey". See also Sams6. "Tablas astron6micas'. A preliminary survey was presented in King. " Islamic Astronomical Tablcs".

The first version of this paper was prepared in answer to a request for an art icle ''Zidj"' for the 12. It turned out to be far longer than the Edi tors could accept, so we de-cided to prepare this version, reformatting the first for this journal, suppressing all of the quirky features of the /2 (notably. the transliterat ion). but retaining most of the cross-references to other articles on specific topics in thnt monumental work (here cap italized, as, for example: ZlQ1). We have. on the other hand, suppressed references to articles on individual astronomers in r2 and DSB. We assume on the part of the reader a certain familiarity with these works, as well as with the standard bio-bibliographical sources. namely (in chronological order): Suter, MAA; Renaud, "Additions 11. Suter"; Krause, "Stambuler Handschriften"; Storey, PL; Sezgin. GAS; Matvievskaya & Rosen-feld, MAMS; Cairo ENL Survey; and i hsano~lu, ed., Of/oman Astronomy and OOoman Mothematics. Several of the studies listed in this article are reprinted in various volumes

Ihilmulllliro/ /Jalll/boot, (1m! T(I"'r.~ 13

antic ipating vari ous l' ignifi cant advancc." in the field in the not-too-distant future.l>

Most of the relevant astronomical and astrological concepts mentioned below are clearly explaincd in al-Biriin"i's Tajhfm.1 Kennedy's numbering 1- 109 for zijes and X200-X220 for related works (see below) is used in thi s article, with each number preceded by a K and the Xs suppressed. An as-terisk is used for those zijcs singled out by Kennedy for treatment in greater detai l than the rest. The notation K0 means the work was not listed by Kennedy.

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such as: Goldstein. SlIIdiThe m~numental reprint series illamic Matllematics and Astronomy recently pub-lished by the indefatigable F. S..:zgin in Frankfun in over 100 volumes contains numer-ous articles and books (texts and studies) relevant 10 this study and generally difficult 10 access. Suffice il to mention here that materials relating to al-KhwirizmT feature in vols. 1-7: al-FarghiinT 9-10, 68: al-BalllinT 11 - 13: Thibit ibn Qurra 21-22: Ibn Yiinus 25; al-~iifi 26; Ibrahim ibn Sinan 27. 101; AbU N~r 2~. 37; alBiliini 2936, 74: Ibn al .Zarqlilluh 39-40; al-Marrlikushi 41-42: Ibn al-Banna' 43-44; 'Umar al-Khayyam 45-46: al-T\1Si ef al. 47-51; Ulugh Beg 52-55; ai-Kishi 56, 84; Ibn al-liaytham 57-58, 75; Abu ' J-Wafa' 60-61: al-Sijzi66; Maimonides 67; Alfonso X 98-99; calendrics 64-65: astronomical instniments 85-96: SaYlh's Observatory in Islam 97: Nallino's Ta'rikh 'Um alfalaJt. 100. In Barcelona research on Andalusi and Maghribi tables (by J. Sams6 and his team) continues apace: in Frankfun research on lijes in general (B . van Dalen) and various categories of other tables (D. A. King and F. Charette) is in progress. Listed as al-Biliini. Tajhfm: see also Kennedy. "ZIj Survey". pp. 139-145. Also rec-ommended to the reader interested in ancient and medieval astronomy is J. Evans, The His/Qryand Praclice of Ancient AS/1vnomy. New York & Oxford 1998.

14 D.A.King&J.Sams6

/./ The scope ofille zij literature In the 13th century the Yemeni astronomer Mu~ammad ibn Abi Bake al-Farisi was able to c ite the names of 28 zfjes, and in the 16th-century Indian encyclopredist Abu ' I -Fa~1 al- 'AlHimi listed in his A'fll-i Akbarf the titles of 86 works of this genre. In 1956 E. S. Kennedy presented infonnation on some 125 zfjes. We now know that over 225 zfjes were com piled in the Is lamic world during the period from the 8th to the 19th century. They constitute a major source for our understanding of the development and ap-plication of mathematical astronomy in the medieval period. Of these works just less than one-half are lost and known only by references to their titles or their authors, but enough survive to convey a very clear impression of the scope and variety of the activities of the Muslim astronomers in this field and to reveal some of their most outstanding contributions.s

Zfjes are intended to serve a s ingle locality, in the sense that a terrestrial longitude underli es the solar, lunar and planetary tables and a terrestrial lat-itude underlies the tables for spherical astronomy. Some of the more impor-tanl zfjes were the results of serious observational programmes.9 However, many zfjes were simply rehashings of earlier ones, with minor variations, such as a change of meridian for the planetary tables, or a new set of spher-ical astronom ical tables for a different latitude. Such modified versions can be of singu lar historical importance if the original works are no longer ex-tant. Not all zfjes contain the extensive explanations of the astronomical and mathematical background typical of, say, Ptolemy's Almagest. Furthennore. there are numerous extensive sets of tables which do not constitute a zfj or which are not found in any zfj.

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The best survey of Islamic astronomy and astrology in general remains the article by CA. Nallino in the J. Hastings' Encyc/o~dia of Religion and Elhics. XII (1921). I)P. 88-101. shortened from the Italian version in Nallioo. Sail/i. Y, pp. 2-87; see also the same author'S articles ASTROLOCY and ASTRONOMY in E/I . Two recent overviews arc G. Saliba. "Astronomy / Astrology. Islamic", in idem, SUldies, no. 2 (first published in the Diclionary oflhe Middle Agu in 1982), and King, " Mathematical Astronomy in Islamic Civilisation", in Astronomy across Cultures, pp. 585613; a third by F. J. Ragep is currently in preparation.

See Say.h, The Observatory in Islam, and also lhe EP article MAR~AD.

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J.2 11,e p"rpQ!.e oj a zij The pu rpose of a zfj was to provide astronomers wi th all that they needed in the way of theory and tables for such tasks as calculating the positions ( longitudes and latitudes) of the Su n. Moon and five naked-eye planets and , the lime of day or night from solar or stell ar altitudes. In additi on the as-tronomer could use a zl) 10 delennine the possibility of lunar crescent or planetary visibility. Stell ar positions he cou ld simply take from the star-catalogue. Calculations for meridians other than that underlying the tables could be modified for the longitude differences apparent from the geograph-ical tables. The astronomer could calculate the duration of twilight and the altitude of the Sun at midday or at the time of the afternoon prayer. He could apply the mathematical procedures outlined in the l.ij to specific geograph-ical data and compute the qibla of any locality. He could also detennine the ascendant at a given time and the longitudes of the astrological houses, and having calcu lated the positions of the Sun, Moon and p lanets, he could set up a horoscope: it could be argued that this was the main purpose of zijes, but there is precious little historical evidence how these works were used in practice. In any case, there are a host of other useful operations one can learn from any l.fj. But a l.ij was only part of the astronomer's equip-ment Other sets of tables were compiled which were not usually contai ned in zTjes, and which greatly facilitated some of the above tasks. In addition, various instruments were available, notably for solving problems relating to spherical astronomy and timekeeping. 10

1.3 Regional schools of astronomy In any discussion of Islamic astronomy it is important to keep in mind that after the 10th century regional schools of astronomy developed in the Is-lamic world, with different authorities, different interests and specialities. II

10 On Islamic astronomical instrumentat ion see the EP articles ASTURL AB, RUB',.ll!.AK-KAZIYYA, rASA and MIZWA LA; King, "Astronomical Instruments between Easl and West", in Kommunikalion zwischen Orient und Okzidenl, H. KUhne! cd., Vienna 1994, pp. 143-198; and 1. Vernet and J. Sams6, eds., Ellegado cienlijico antlalusi, Madrid 1992. A new overview is to appear as SATMI, VIII.

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D. A. King & J. Sams6

On regional developments in Islamic astronomy see first SaYlh. The Observatory i1l Is/am. The following regional surveys are avai lable: Early Islamic (mainly al.' lraq and Iran): D. Pingree. '1'he Greek Inftuence on Early Islamic Mathematical Astronomy", JAOS93 (1973), pp. 32-43; idem, " 'ndian Influence on Sassanian and Early Islamic Astronomy and Astrology", in Tile Journal of Oriental Rtst!arch (Madras), 3435 (1964-66), pp. 11 8 126. Iraq : aJ-'Azzlwi, To'ri1l.h 'ifm alfa/aifi 'I-'Iriiq ... Baghdad 1958 (to be used with caution). Egypt, Syria and Yemen: D. A. King. "Aspects or Fatimid Astronomy ... ", in Paris 1998 Fatimid Colloquium Procudings. pp. 497-517; idem, 'The Astronomy of the Mamluks", Isis 74 ( 1983). pp. 53 1-555, repro in idem, Sludies, AIII; idem. "L'aslronomie en Syric It repoque islamique", in Syril!!, mimoire ef civilisalion, S. Cluzan er 01. cds., Paris 1993, pp. 386-395, 432-443 and 480; and idem, Mathenl(Jl-ical AstrOilOmy in MedieVlil Yemen - A 8io.8ibfiogropllicaJ SlIrVlry. Malibu, Ca. 1983. a l-Andalus: Milllls Vallicrosa, Eswdios, A-S; Vernet, Estudios, A-B; Vernet , cd., Esw dios, A-B; J. Sams6, Las ciencias de los amig/40s en aJ-AndaJlls, Madrid 1992; numer-ous other publications of the Barce lona school; and L. Richter-Bemburg, "$a'id, the Toit'dlill Tables. and Andalusi Science", in Kelllll!(/y Festschrift, pp. 373-401. See also G. Toomer_ "A Survey of the Toledm/ Tables"_ Osiris 15 (1968), pp. 5-174; and 1. D. North, "Just whose were the Alphonsine Thb1csr .. in Verne' Festschrift, I, pp. 453-476. The Hebrew tradition: B. R. Goldstein, '1 'he Survival of Arabic Astronomy in He-brew", JHAS 3 ( 1979), pp. 3 1-39, repro in idem. Stlldies, XXI; idem, "Astronomy in the Medieval Spanish Jewish Community", in North Feslschrifl, pp. 225-24 1; Y. T. Langermann, "Science in the Jewish Communities of the Iberian Peninsula: an Interi m Repon", in idem, Sf/wit's, I. and idem, " I-Iebrew Astronomy ... ", in Astnmon/y across Cll/fllres, pp. 555-584. The Maghrih : O. A. King, "On the History of Astronomy in the Medieval Maghrib", in f.:tlldes philo.fOplJiqI4t'S et soci%giqlll!!s dbJiies a Jmllail!!d-Dille A/aoui, Fez 1998, pp. 27-61; J . SamsO, "An Outline of the Hi510ry of Maghribi Zijes from the End of the Thirteenth Cemury", Jl-IA 29 (1998), pp. 93102. Iran and Central Asia: E. S. Kennedy. '111C Exact Seienccs in Iran under the Scljuqs and Mongols", in TfteCumbridgt! lfistor),ojlran. vol. V,Cambridge 1968, pp. 659-679, and 'The Exact Sciences in Iran under the TIOlurids", in The Cambridgt! Hisloryoj frail, VI, Cambridge 1986, pp. 568-51!0; H. J. J. Winter, " Persian Science in Safavid TImes", ibid .. pp. 58 1-609; T. Heidarzadeh, " From the Maragha School to the Darolfonun-a Historical Review of Astronomy in Iran from the 13th to the 19th Century", paper presented althc Istanbul 1994 Symposium but not included in the Proceedings; King, \\'orltl-Mu/J.f (cited in n. 43 below), pp. 1211-134; and the Ef2 anicle ~AFAWIDS, IV.l ll. The Uytantine tradition: A. TIhon, "Tables islamiqueslt Byzanee", 8yztJlltioll - Revue IlIterll(/liofJlIle de.l Eludes Hyzalltine.f 55 (1990), pp. 40 1-425, repro in t!adem, Studies, VI. lind numerous studies by D. Pingree mcntioned below.

Suhayll

Astrrmomical Handbooks amJ Tablt!S 17

They also achieved different levels of sophi stication and had different fates, both with regard to their own internal development and to the nature of their encounter with the new Western science from the 16th century onwards. In the past few years some attention has been paid to these regional schools, and the main studies are listed below. In particular, each regional school had its favorite zfj or zfjes.

In the early period, in the central lands of Islam the Mumra~wn tradition was important, together with al-BattanI and Abu ' I-Warn' al-BuzajanI. In Iran and Central Asia numerous early zrjes eventually gave way to the Zfj-i Tikhiinf of Na~ir ai-Din al-TusI. In Egypt the l:Jiikimf Zrj of Ibn Yunus was never surpassed. In Syria the zrj of Ibn al-Sha~ir was particu larly important. In both Egypt and Syria the institution of the muwaqqit, the professional as-tronomer responsible for the regu lation of the calendar and times of prayer, led to new and impressive developments, mainly. but nOI only, in astronom-ical timekeeping. 12 In al-Andalus the zljes of al-Khwarizmi and al-Battani. based respectively on the Indo-Persian and Hellenistic traditions, played a role perhaps greater than either deserved, and fhe contributions of Ibn al-Zarqalluh were high ly significant. In the Maghrib, the zfj of Ibn Is~aq and a min i-version thereof prepared by Ibn al-Banna' dominated the scene. In the late period, the only zrj to achieve any kind of supremacy all over the Islamic world was the Zfj-i Sul.tiinf of Ulugh Beg.

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Ottoman Turkey: E. Ihsano!lu, " lntroductiOll of Western Science to tbe Ottoman World: a Case Study of Modem Astronomy (1660-1860)", in islanbul1987 Symposiwn Proceedings, pp. 67-120; and idem. ed., Ot/oman ASlronomy and Ol/oman Malhe-mal ics. India: S. A. Khan Ghon, "Development of Zij Literature in India", 11HS 20 (1985), pp. 21-48, 438-441 (notes) and 480-48 1 (bibl.); S. M. R. Ansari, ' 'On the Transmission of Arabic-Islamic Astronomy to Medieval India",A1f1S 45 ( 1995), pp. 273-297; D. Pin-gree, " Islamic Astronomy in Sanskrit", JHAS 2 (1978), pp. 3 15-330, and idem, " Indian Reception of Muslim Versions of Ptolemaic Astronomy", in Nonnall 1995 COllference Proceedings, pp. 471 485.

King, "On the Role of the Muezzin and the Muwaqqit in Medieval Islamic Society", in Nonnan 1995 Conferenct! Proceedings, pp. 285-346, repro as SATMI, V.

18 D. A. King & J. SlImso

1.4 The historiography of moderll research 011 zijes Already in the 19th century, extracts dealing with observation accou nts from the zij of Ibn Y\inus had been published by Caussin de Perceval, and the in-troduction to the zrj of Ulugh Beg had been published by L.-A. Sedill ot (fils) . Before 1950 only two zijes had been published in their entirety. namely, those of al-Battani by C. A. Nallino and of al-Khwari zmf by H. Suter el al. (the latter is extant only in a fo rm substantially different from the orig-inal). In 1952 J. Vernet published the canons of the zij of Ibn al-Banna'. The zij of al-Biriini was publi shed in 1954-56, in an edition originally pre-pared by M. Krause. In 1956 E. S. Kennedy publi shed his survey of some 125 zfjes, and laid the foundation for serious study of this genre of litera-ture. In 1962 O. Neugebauer published an English translation of the text of the ZIj of al-Khwarizmf in the fonn in which it survives for us, together with a commentary and an analysis of the tables. The year 1985 saw the publication of a Byzantine recension of the zij of al-Fahhad by D. Pingree. Many studies of parts of other zfjes, of specific topics in several zijes, or of individual tables of particular interest have been publi shed during the past 50 years. Also certain medieval treatises on the concepts underlying zfjes, the kutub

Aslrt;momica/ Handbooks alld Tables 19

2 The contents of zljes

2.1 Sexagesimal alphanumericaillotation

The entries in the tables in zijes and other corpora of tables are expressed sexagesimally, that is, to base 60, although integers are invariably ex-pressed decimally. (In the modem notation standard in the history of the exact sciences a number expressed in the fonn a,b;c,d stands for a x 60+b+ c/60 + d/3600.) The entries are written in Arabic alphanumer-ical notation,1 7 with the attendant traps for the careless copyist and the trust-ing reader. One of the challenges to modem investigators, indeed, for some, the spice of Uleir lives, is the restoration of original values from carelessly-copied entries. The standard errors are inevitable or careless or compound. 'Inev itable' refers to those cases where the omission of a diacritical point or two in one copy of a table invites an ambiguous interpretation in the next copy (thus, 14 +-+ 54 or 59 +-+ 19 or 80 +-+ 100). 'Careless ' refers to situations where the sloppy rendition of one letter or ligature leads to its misinterpre-tation as another (thus, 0 +-t 5,14 +-+ 15,40 +-t 47, 50 +-+ 7, 20 or 21 +-+ 9, 38 +-+ 18, 44 H 47, or 18 +-t 70). 'Compound' refers to a combination of the previous two (thus 14 +-t 15 +-t 55 or 58 +-t 18 +-+ 13 or 150 +-+ 87).

2.2 Chrollology alld calendar conversion

All zijes begin with one or more chapters and sets of tables devoted to the defin ition of the various eras and calendars in use at the ti me and place of writing, to methods of convening dates from one calendar to another, and to the problem of detenni ning the madkhal, that is, the day of the week cor-responding to the firs t day of a given year and month in a given calendar. The most common are the lunar Hijra calendar and various solar calendars,

!1 See the /2 article ABDJAD; R. A. K. Irani. "Arabic Numeral Fonns", Cellla!lmS 4 (1955), pp. t-12. repro in Kennedy el al., Sl!Idie.~, pp. 710-721; also the comments. based on experience, often biller. with medieval tables or one kind or another, in Kennedy & Kennedy. Islamic Geographical Tables, p. x; Kunitl.Sch, Siernka/n/og des Almagest (cited in n. 44 below), I, pp. 19-21; and King. World-Mal'S (n. 43), pp. 161-163.

Subayll (21~Ul


including the Seleucid (A lexander), the Coptic (Dioclelian), and the Persian (Yazdijird), and, in the West, the Julian (A.D. and Spani sh Era). The Per-sian calendar, using the Egyptian year of 365 days and no intercalation, is particularly convenient for astronomical purposes. Less commonly treated calendars are the Jewish, Syrian, MalikI, Saka and Chinese-Uighur. 18 A few zijes treat the lunar mansions and the Arab system of dividing the year according to the mansions. 19

2.3 Trigonometry

A ll zfjes contain tri gonometric tables, usually of at least the sine (al-jayb) and the cotangent (a/-?ill) functions. The sine, first used by Indian as-tronomers, replaced the Ptolemaic chord functi on (al-lVa/ar) amongst the Muslims. The argument o f the sine was an arc (mther than an angle) 8 of a c ircle of mdi us R units, where R is a base, usually 60, occasionally I. In the Indian tmdition R was taken as 120, I SO, 1000, 3270, 3438, etc.; in the Hel lenistic tradition it was taken as 60. The medieval sine function is denoted by Sin e and is related to Ptolemy'S chord function and the modem function by: Sine = !Ch(26) = Rsine. In timekeepi ng the versed sine (aL-sahm) was also used (Vers e = R - cose = R ( I - cos 8 ), and occasionally also the cosecant function (Wtr ai-?Ul) (Csc e = R2jCos e = Rcsc e). The earli

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See F. K. Ginzel, Handbuch det mathellUltischen Imd tec1l11ischell Chronologie, 3 vols., Leipzig 1906. especially vol. t; Kennedy. "Zfj Survey", p. 139; various anicles in Kennedy et al., Studies, pp. 652-709; B. van Dalen, E. S. Kennedy and M. K. Saiyid, "1be Chinese-Uighur Calendar in T usi's Zij-i TtkMni', ZGA II II (1997), pp. 111-152, and also the E12 an icle TA ' RTK Ii (2: Era chronology in astronomical handbooks) by B, van Dalen.

See the er2 anicles ANW,\' and MANAZIL; and also Sams6, "Cnlendarios populares y lablas astron6micas"; M. Foreada, "Books of Anwa' in al-Audalus", in Th e FormatiOn oj al-Andaills, Pari 2: Langlll/ge, Religion, Cllltu~ anti the Scitnct:f, M. Fierro and J. Sams6 cds., Aldcrshol (Ashgale-Variorum) 1998, pp, 305-328; 0 , M. Varisco, Mediel'al Folk Astronomy and Agricll/wrr in Arabia and Ihe Ytmtn, Aldershot & Brookfield, VI. (Variorum) 1997: idtm, Mtdkl'al Agriculturt: and Islamic Scitnet: - Tht Alman(lC oj a Yemtni Sultan, Seattle, Wa. 1993: and idem. " Islamic Folk Astronomy", in ASlnmomy (lcross C1I111I1'I!S. pp. 615-650.

ASlronomical Handbooks u/ld Tables 21

est sine tables, from the 9th century, gave values to three sexagesimal places for each 10 of argument. By the 15th century accurate tables were available displaying the function to five places for each minute of argument. This was achieved by first deriving a very precise value of Sin 10 and uti li zing a clever method of second-order interpolation.20 The cotangent function invari ably had the solar altitude as argument, and used a base equal to the length of a gnomon, so that the function measures the length of the horizontal shadow cast by the gnomon. The un its fo r the gnomon length used were 12 digits

(i~ba ', a~abj) , or 7 feet (qadam, aqdlim), although other values were also used. AI-Biriini has a detailed discussion in hi s treatise On Shadows (lfrlid al-maqiif fi amr (I/-zila/). The cotangent function was also firs t tabulated in the 9th century.21 Trigonometric fuctions were occasionally tabulated inde-pendently, that is, not in zfjes - see 4.2. Various procedures were used for imerpolation in tables.22

2.4 Spherical astronomical f unctions The study of spherical astronomy - the mathematics of the celestial sphere and of the apparent dai ly rotation of the sphere - was of prime concern to Muslim astronomers, not least because of the importance of astronomical time-keeping.23 The form ulre for deriving time from solar or stellar altitude

20

"

22

A. Anboe, "at-K~shrs Iteration Method for the Determination or Sin 10 ." Scripta Math-ematic(l 29 (1954). pp. 24-29. See funher Kcnnedy,"Zij Survey", pp. 139-140; Schoy, "Bcitragc zur arabischen Tri-gonometric (Originnlstudien nach uncdierten arabisch-astronomischen Manuscripten)", Isis 5 (1923), pp. 364-399, and Die G'IOlllonik der Amber, Bd. I:F of Die Geschicillt du Zeillllessrmg rmd der Uhrtn, E. von Bassennann-Jordan cd .. Berlin & Leipzig 1923, both repro in idem, Beilrage, II , pp. 448-483 and 35 1-447: al-Biriini, 011 ShadolVs, pp. 71-80; and also J. L. Berggren, t,,;sodes illlhe Mathematics ojMetliellallslalll, New York. elc. 1986, pp. 127- 156.

See J. Hamadanizadeh, "A Survey of Medieval Islamic Interpolation Schemes", in Ke/l/ledy FeslSchrifl, pp. 143- 152. and [he /2 article TA'DtL 8AYN AL-SATRAYN. See now King, SATMI. especially I-II on tables for timekeeping and the regutation of the times of Muslim prayer. A summary is already in the Etl survey article Mh,::AT.

22 D. A. King. & J. SamsU

were known from the 8th century onwards and are discussed in every zfj. We can distinguish between several groups of functions that were regularly tabulated in zijes:24

"

- The solar declination (mayl ai-shams or ai-may/) as a function of solar longitude (damjat ai-shams). Underlying such tables was a value for the obliquity of the ecl iptic (almayl al-a'?am), a parameter which changes slowly with time. The second declination (al-mayl al-thtlnf) was used in celestial coordinate transformations.25

- The half length of daylight (ni~f qaws al-,wlulr) for different latitudes, as a funct ion of solar longitude. in equatorial degrees and minutes, or in hours and minutes. Sometimes the latitude-dependent tables would be presented for the seven climates (iqlfm) of Antiquity.26 The tangent of the declination was often tabulated; it is an auxi liary func tion useful in the determination of the length of daylight for any latitude (see below).

- The right ascensions (al-ma!iili'fi 'I-falak al-/7/lIstaqfm) as a function of ecliptic longitude (ai-!u/), defining the rising time of a given arc of the ecliptic (measured from the vernal point) over the horizon at the equator, and the oblique ascensions (al-ma.tiili'al-ba/adiyya), defining the correspond ing times for the horizons of differenllocalities. Often the latter would be tabulated for a series of latitudes.27

On basic tables for spherical astronomy see Kennedy. "lIj Survey", pp. 140-141; D. A. King. Aslronomical Works 0/ Ibn YUnU$ (cited in n. 115 below); alMarrakushT. MabtIdi' wogJuJy41: J. L Berggren. "Spherical Astronomy in Kushyiir ibn Labbin's Jam;' LT. in Ktnntdy Fl!llSchrift. pp. 15-33; and E. S. Kennedy. "Spherical Astronomy in ai-Kishi's Klu'lqlJnf ZiF', ZGAlW 2 (t99O), pp. 1-46, repro in idtm, Slutiil!l. VII. See the E/2 articles MAYL. MINTA~A and SHAMS.

26 See the EP article I~LIM. and on the importance of the climates see King, "Astronom-ical lnslruments" (n. 10), pp. 152. 168-169, and ;dl!m, "Bringing Astronomicallnstru-ments Back 10 Earth: The Geographical Data on Medieval Astrolabes (to ca. 1100)", in NOrlll FtSlschri/l. pp. 3-53. esp. pp. 6-9.

27 On ascensions see lhe EI2 article MATAU'.

Astrollomical Hamlbooh and Tables 23

- The solar meridian altitude (irtifo' ai-shams li-ni~f ai-flaMr), and less frequently the rising ampli tude of the Sun (sa'at al-mashriq) and the solar altitude in the prime vertical (al-irtifo' alladhr iii sam' lahu or ai-irlifo' al-'adrm al-samt), all for specific latitudes. Likewise the solar altitude in the azimuth of the qibla (irtija' ai-shams idhii marrat bi-sanlt al-qib/a) for specific localities, also tabulated for each degree of solar longitude.

Certain functions with no immediate astronomical significance were also tabulated on account of their utility in the computation of other functions. We may mention as examples such 'auxil iary' functions as the tangent of the declination (labelled fil~ii/ al-maliili' Ji- 'l-ar~ kul-lilla), the sine of the right ascension (jayb al-ma.lilli'), and the product of the cosines of the declination and the terrestrial latitude (al-a~'l al-nlttflaq).28

Numerous other minor tables are found in corpora of tables relating to astro-nomical time-keeping, independent of zfjes - see 4.8-9. These collections also contain some more extensive tables for time-keeping. The only variety of these occasionally found in zrjes is a table displayi ng the time (T) since

ri ~ing of the Sun or any star as a function of the meridian altitude (H) and the instanraneous altitude (h), for a specific latitude: these tables are trape-zoidal in shape since II < H and are called zfj af-.tayiasan, after the name of a shawl. A .taylasall table for Maragha is contai ned in the ilkhtinf Zfj.29 We should also mention the extensive tables for spherical astronomy in the compendium on astronom ical instrumentation by al-MarriikushI (Cairo ca. 1280).30

See King. SATMI, \6.7,8.

1') Kennedy. "2i] Survey". p. 161 b .

. m ,Ll-M'lniikushl. Mabiitli' waII'u1)'(II. A. Sec also King, SATMI. 1-4.3.2. and 11-6.7.


2.5 Planetary meatr mOlions, equations and laliludes

These constitute the hard core of all zi]es.~1 Extensive tables display the epoch posi tions and the mean motions (wasa.l, pl. awsii!) of the ' planets' (al-kawiikih al-sayyiim or al-mutattayyam), that is, the Sun, Moon and five naked-eye planets. The tables are intended for a specifi c terrestrial longi-tude, usuall y that of the locali ty where the zfj was compi led. They can eas-ily be modified to the meridian of another locali ty, if required: sometimes subtables of longi tude corrections are provided. The motions for a given number of completed years, months, days and hours are to be added to the epoch positions (Arabic a~l, Latin radix) to derive the actual mean positions. These then needed to be modified by equations (ta'd/I, pI. ta'adfl) to derive the true ec liptic positions (sometimes called al-muttkam or al-mu'addal) . The operation of find ing the true positions is called taqwfm or ta'dfi, the fo nner expression also used for ephemerides (see 4.3), and the positions muqawwam or mll'addal. The professional astronomer who did this could be called muqawwim, but only one example of this usage is known, namely. in a s ignature on an astrolabe made in Damascus in 1222123.32 In the Ptole-maic tradition the equations are calculated by successive applications of a series of auxi liary trigonometric fu ncti ons fo r each planet.33 The more ex-tensive double-argu ment tables for the equations someti mes found in zfjes are di scussed in 3.8 and 4.6. The apogees (awj, pI. awjiit) of the planets

"

32

Kennedy. "Zij Survey", pp. 141-142; idem and H. Salam, "Solar and Lunar Tables in Early Islamic Astronomy". lAOS 87 ( 1967). pp. 492-497, repro in Kennedy et al.. Studies, pp. 108-1 13; idem, "Two Medieval Approaches to the Equalion of Time", Cen-taurus 31 (1988), pp. 1,8, repro in idem, Studies. VIII; B. van Dalen, "al-Khwiirizmi's Tables Revisited: Analysis of the Equation of Time", in Verner Festschrift, I, pp. 195-252, idem, "A Table for the True Solar Longitude in the Him;' Zi.l', in Frankfurt IGN Festband. pp. 171-190; and G. Van Brummelen, "Mathematical Methods in the Tables ofPlanctary Motion in Kushyiir ibn Labbiin's Jami' Zi/', HistMath 25 (1998), pp. 265-280. On practical solulions of the various operations involving Sun, Moon and planets. down to eclipses, see various studies based on al-Kiishi's treatise on the equatorium reprinted in Kennedy et al., Studies, pp. 448-491.

Sapir Memorial Volumes, II, pp. 730-731.

See the 12 anicle SHAMS, ~AMAR and TA'oIL.

S.hayll (20Un

AstrolWmical Handbooks and Tablu 25

need to be considered in such calculations, and their positions, which vary with time, were also tabu lated. 0ccasionally, especial ly, but not only, in Andalusi and Maghribi ziJes, we find tables relating to trepidation (al- iqbtil wa-'l-idblir), the presumed oscillation of the equinoxes - see further 3.7. Additional auxiliary tables enabled the computation of the planetary lati-tudes (aJ- 'arf/).J4 In the case of the Moon, a single table would suffice, the argument being the nodal distance, derived from the lunar longitude and the position of the ascending node, which was tabul ated along with the mean motions. In the calculation of solar and lunar eclipses (see 2.7) also the equation of time,3S that is, the difference between true and mean solar time, with a maximum of around 30 minutes, had to be considered ; tables fo r thi s funclion were likewise standard in zrjes. All of the necessary instructions for using these various tables are found in the typical zrj. See also 2. 12 on modem methods of analyzing medieval planetary tables.

2.6 Pkznelary slations and visibility

Additional tables enabled the investigation of the direct and retrograde mo-tions of the planets, their stati ons, and their visibi lity (depending on their apparent e longation from the Su n).36

2.7 Solar and lunar parallax alld eclipses

In 1.Ijes we also find tables for calculating the pamllax of the Sun and Moon (ikhtiliiJ al-manwr), preparatory to the prediction of eclipses (klmlf for the Sun and kllUSli/ 'for the Moon)7 ). Thi s would be ach ieved by means of tables

E. S. Kennedy and W. Ukashah. "al-KhwarizmTs PlmICI~ry Latitude Tahlc.~". C",Utlllfll.' 14 ( 1969). pp. 86-96. repro in Kennedy t'l uf., Sllu/ie.~, pp. 12S-135: M. Vilildrkh. '"The Planetary Lati tude Tables in the MllI/lltI!la/! ZIT, JIIA 19 (1988), rll. 257-26X; lIl1d B. van Dalen, " Planetary Latitude Tables in the Hili/III; fi (II )"' ki ted in n. lOX helllw). See the El l article TA'DIL AL-ZAMAN, :md also tlIC ~tudies (If E. S. Kennedy :U10 B. van Dalen cited in n. 31.

E. S. Kennedy and M. Agh:l. " Planetary Visihil ily T:lhles in hlamic A~trnnomy", CCII-laurus 7 ( 1960), pp. 134-140, repr. in Kennedy "I til .. !fwdi".,. pp. 1M-15().

26 D. A. King & 1. Sams6

of the times of syzygies, of true solar and lunar motions in small critical periods of time, of apparent 501ar and lunar radii , and others.38 There is no survey of Islamic procedures for the computation of eclipses,39 but thi s is currently being undertaken by B. van Dalen .

2.8 Lunar visibiIily

Particular aUention was paid by Mus li m astronomers to the prediction of the visibility of the lunar crescent on the fi rst evening after a conjunction of lhe Sun and Moon.40 From the 9th century onwards tables were prepared to facilitate such predictions, underlying which were limiting conditions on various functions based on the apparent positions of the Sun and Moon rela-tive to each other and to the local horizon. Numerous such tables. of varying sophistication and complexity, are found in various zijes.41 See also 4.5.

31

"

"

"

On various not-too-technical aspects of tile determination of eclipses see Inc 12 ilrticle KUSOF.

E. S. Kennedy. "Zij Survey", pp. 143-144: idem. "Para llax 1bcory in Islamic Astron-omy", Isis 47 ( 1956). pp. 33-53, repr, in idem t!l al., Studies, pp. 164-184: also B. R. Goldstein, "Lunar Veloci ty in the Middle Agcs: a Comparative Study", in Vernet Festschrift, I, pp. 181-194. See already E. S. Kennedy and N. Faris, "'The Solar Eclipse Technique of Ya~ya ibn Abi Man~ur", iHA I ( 1970), pp. 20-38. and J. A. As-Saleh, "Solar and Lunar Di~tanccs and Apparent Velocities in the Aslronomielll Tables of J:l abash al-~Hisib", in ai-Abba/ii (Beirut) 23 (1970), pp. 129-177. repro in idem el al., Strldies, pp. IS5-203 and 204-252; and a study by Kennedy on ecl ipse calculations in the ~mjuJinfZIj d ied in n. 109 below.

See the El l article RU' YAT AL-HrLA L.

E. S. Kennedy, '"The Lunar Crescent Visibility Theory or Ya'qub ibn Tariq", iNES 27 (1968), pp. 126- 132, repro in it/em el af" Sl/ltlir:.I'. pp. 157- 163; D. A. King, "Some Early Islamic Tables for Determining Lunar Crescent Visibility", in Kem1l'd,l' f"/,J/Rltrijt. pp. 185-225. repro in idem. SlIulie.r. C-II : E. S. Kennedy and M. Jnnjanian,'"The Cre~cent Visibi lity Table in al-Khwiirizmrs ZIT, Ct'll/tlllrli.f II (1%5). pp. 73-71t repr. in idem et al .. Studies, pp. 15 1- 156 (deals with un Andalusi table induded in Ihe Latin version); Morelon, Thiibil ibll Qrtrm. pp. xciii-Clt,, ;; i. 93-1 12, and 23U-259 (indudcs materials due 10 Thabi t preserved only in tnc S(lIrjari Zij): J. P. lingendijk, '1llrcc I .~ lamie Lunar Crescent Visibili ty 'nlbles", i Ht , 19 (19111:1). pp. 29-44; D. A. King. " Ihn

Astrt1l1omicul Handbonb (md ulhit's 27

2.9 Geographicallables

Tables displaying longitudes and latitudes of numerous localities are stan-dard in zIjes. They have been published in various fonnats, that is, according to locality, source, increasing longitudes and increasing latitudes, by E. S. and M. H. Kennedy. who provided a valuable research tool that is currently being extended by M. Comes of Barcelona.42 These geographical coordi-nates were included in zijes in order to facilitate the use of planetary tables for other meridians, for which the longitude difference has to be taken into consideration. and also for computing the qibla. A minority of tables also display the qibla for each locality. Such tables are often engraved on astro-nomical instruments, especially those from Safavid Iran.43 See also 4.10 on tables displaying the qibla for ranges of longitudes and latitudes.

2.10 Star caJalogues

]n a typical zij we find a table displaying the ecliptic or equatorial coordi-nates of selected stars, sometimes for a few dozen, sometimes for several hundred. Procedures for coordinate conversion are also described. The star catalogue in the Arabic Almagest has been published by P. Kunitzsch,44 and

.,

..

Yilnus on Lunar Crescent Visibility", JHA 19 (1988). pp. 155168. repro in idem, Stud ies, C-IlI; and Kennedy &. Hogendijk, "rwo fibles from . . . TIbet" (cited in n. :09 below), pp. 238-242. Kennedy & Kennedy, Islamic Geographical Coordinatf:S; also E. S. Kennedy. "Math-ematical Geography", in EHAS, I, pp. 185-201. On the AndaJusi tradition represented by Ibn a1-Zayyat see also M. Comes, "Islamic Geographical CoordiTUltes: al-Andalus ' Contribution to the Correct Measurement of the Size of the Mediterranean", in Istan bul 1991 and 1994 Symposia Proceedings, pp. 123-138, and the same author's study mentioned in n. 72 .

King, World-Mops for Finding lhe Direction and Distance 10 Mecca ... , Leiden & London 1999, pp. 71-89,1'1-9.186. and App. B .

P. Kunitzsch, Der Almagest - Die Syntaxis Mathematica des Claudius Plolemiius jn arabi.rchlateinischer OberUe/eTJUlg, Wiesbaden 1974; idem, C/tJudius Pto/~miil4S -Der Stemkatalog du Almagest - Dj~ arabi.schmittel4lttrliche T/-adiliOtl, 3 vols .. Wies-baden 1986-1991; also idem, Studies.

S .... )'Il(lOOl)


some early Islamic tables have been investigated by D. Girke (alas unpub-li shed).4S More research is necessary to establish the relationshi ps between individual star catalogues. not all of which are related in a trivial way to thaL in the Almagest. Thus, for example, the tables in the Kitiib $uwar al knwiikib. "On Constellations", by 'Abd al-RaJ:Iman al -~fifi, and those in the zfj of Ulugh Beg, are essentially Ptolemaic. Independent catalogues are found in the Mumta~an Zfj, the /:fiikimiZij, the Huihui Ii (a Chinese transla-tion of an independent zfj), etc.46

2.11 Tables f or mathematical astrology Zfjes usuall y contai n tables useful fo r astrological purposes,47 notably, for drawing up a horoscope for a certain moment or for a series of slich mo-ments, such as each year in the li fe of an individual. Given the horoscopus or ascendant, that is, the point of the ecliptic instantaneously ri sing over the

D, Girke, "Drei Beilrage zu clen friihesten is lamisehen Stemkatalogen mit besonderer Rlicksicht auf Hilrsfunktionen rUr die Zeitreehnung bei Nache, Frankfurt am Main. Johnnn Wolfgang Goclhe-Univen;iliit, InstitUi flir Gcschiehle der Naturwisscnschaficn, Preprint Series no, ~ (1988),

E, B, Knobel. U/IIKh"e~'s Cm(/I{)~lte of S/(/rs. Wa~hington, D,C. 1917; M, Y. Shcvchenko. "An Analysis of the Errors in lhe Star Catalogues of Ptolemy and Ulugh Beg", JHA 21 ( 11)90), pp, 187-201; K. Krisciunas, "A More Complete Analysis or the Errors in Ulugh Beg's Star Catalogue". JHA 24 (1993), pp. 269280; and P. Kunilzsch, ' 'The Astronomer ~ . I--?iifi ,IS a Suurce for Ulugh Beg's Star C,llalogue (1437),", in Sims "mll"!: 1995 C(}II(}qlliulII PlVceedillfls, pp. 41-47. On the influence of Islamic star cawlogue.~ in medieval Eorope see p, Kunilzseh. T.111e1J 1'11 /1 SII'rtw{'r:eit;/mis.\"e/1 ill (I.flmllllllli,fdJell H(IIul.fChrijll'lJ des ~elJ/Jlell his ljer:e1mll.!l1 .1(liJrlulIJdt'rI.l", Wieshadcn ]9M. and various contributions to Ihe Klwilz.rch FUlschrijl. On star lists in Hebrew that depend on Islamic sources, see B. R. Goldstein, "Stllr Lists in Hehrew", Cl'III(J//fII.~ 21! (191!51, pp. IIIS-20S; K. A. F. Fischer. P. Kunilzseh .uld y , T. Lmgermnnn. "The Hehrew ASlrOl\omic;11 Codex Ms. Snssoon K23"" , il'U'i.l"1t (julIJ"/('l"l,r R,,\I;"U' 711 (l9KK), pp. 2S~-292. repro in l.;lIIgerrnann. SllIdie,I. X; and Goldstein & Chah.is, " Ihn ,1I-K'lIlltniid's Star LiM"' (c ited in n. 156 below). See also B. van Dnlcn. "A NOll-Pl0lemaie Islamic Slar Tahle in Chinese". in KllIlil :scll Ft:.\'I.~dtrift, pp, 147- I 76,

On the concepts see al-BTrCinT. Jitj7lim. /,W',I'illl: Kennedy, '"ZiJ Survey", pp, 144-1 45 ; and the t..,l article NU I>JOM . AI:lK AM A' .-.

29

hori zon,4H one needs to determine the positions of the astro logical houses and to assign the Sun. Moon and five nak~-eye planets to the appropriate house, and then to investigate the supposed significance of their positions relative to each other. Some zfjes contain tables displaying the eclipt ic lon-gitudes of the cusps of the houses as a function of the longitude of the horo-scopus, for a fixed latitude. Occasiona ll y we fi nd tables displaying the lon-gitude of the horoscopus as a function of the altitude of the Sun throughout the year or of various fixed stars, also for a fi xed latitude. We may also fi nd tables of the positions of the e lusive, not least because fictitious, astrological body al_Kayd,49 Other tables in zijes serve the astrological notions of the ' projections of the rays' (lIIa.tliri!' al-sllll'ii'iit), the 'year transfers' (ta~liwil ai-sinin), the 'excess of revolution' ifafll al-dawr), and (he duration of ges-tation (maklh ai-maw/ad Ii ba.tll wnmih).50 See also 4.13 on some other

"

"

See the E/2 article TAU'.

E. S. Kennedy, '"Comets in Islamic Astronomy and Astrology", JNES 16 (1956), pp. 44-5 1; O. Neugebauer, "Notes on al-Koid", JAOS 17 (1957), pp. 211 -2 1!i: W. Hartner, "Le probleme de la pla~te Kaid" (published 1955), repro in idem. Swdies, A, pp. 268-286; Kennedy, "Zij Survey", pp. 145; and also Al-KAYO in EP. On various categories of tables see E. S. Kennedy and H. Krikorian-Preisler, "The As-trological Doctrine of Proj ting the Rays", al-AbhtJlh 25 (1972), pp. 3-15, repro in Kennedy el al., Slutiics, pp. 372-384; several papers in Kennedy el al., Slutiies, pp. 3 11 -384, and idem, Slutiies, XVXVIII ; idem, "The Astrological Houses as Defined by Me-dievallslamic Astronomers", in Verner Fesrschrift, II, pp. 535-578, repro in Kennedy, Swdies, XIX; and J. p, Hogendijk, ',-00 Mathematical Structure of Two Islamic As-trological Tables for Casting the Rays", Cenlaurus 32 (1989), pp. 171-202), and idem, " Mathematical Astrology in the Islamic Tradition" (dealing with houses, rays and pr0-gressions), in Cambridge Dibner Inslilule /998 COfIjerence Proceedings, to appear: J. D. North, Horoscopes and HisiOry, London 1986 (includes an analysis of the various ways to establish the cusps of the astrological houses, called by North 'domification'); and M. Vano and M. Viladrich, "Tasyfr Computation of Klishyilr ibn Labban", HislSci 41 ( 199 1), pp. 1-16. On tables for finding the time rrom conception to birth, see J. Vernet, "Un traCiat d 'obstetrfcia astrologica", Bolelin de la Real Academia de Buenas Lelras de Barcelona 22 ( 1949). pp. 69-96, repro in idem, Eslutiios, A, pp. 273-300; ChaMs & Goldstein, "Andalusian Astronomy" (cited in n. 156 below), p. 37; and eidem, Astronomy in lire Iben'an Peninsula (cited in n. 177 below), pp. 86-87 and 150-153. See also Sams6, " Horoscopes and History" (cited in n. 163 below): idem & Berrnni. "World Astrology in the 11th Century" (ci ted in II. 153 below); E. S. Kennedy,

30 D. A. King & J. SamsO

astrological tables not found in zfjes. Of all the aspects of medieval Islamic astronomy, mathematical astrology is the least researched. New insights are to be anticipated from the current investigations of B. van Dalen.

2.12 Analysis of tables and parameters

Already in the early 1960s Kennedy applied the electron ic computer to fa-ci litate the analysis of medieval tables, an activity that was continued by his students. notably. D. A. King, G. Saliba and J. Sams6, and independently by R. Mercier.~l A third generation of younger researchers is currently active: statistical techniques have been applied to individual tables and groups of tables, notably by B. van Dalen and G. Van Brummelen.!i2 The former has reactivated a file of over 2000 parameters found in zijes which was started by Kennedy: more infonnation is available on the Internet at the address http://www.rz. unifrankfurt.der'' dalen.

"A~tronomical Evcnts from a Pcrsian Astrological Manuscript" (wi th an appendix by O . J. Gingerich), C~lIIatmls 24 (1980), PI'. 162-180: and L. P. Elwell-Sulton, Thl!! Haro-.,'C/J/'" /JJ Asudulltill MirJi -" SI'licill1rll of NiIIIlII'CIIIII,CcI/I/lf)' .... slrolog.\', Leiden 1977.

On modem methods of investigating mediev.1I tables with l'Omputers and the way in which our control over such tables has been enhanced see E. S. Kennedy, "The Digital Computer and the History (lfthe Exact Sciences". CI.''''lmnls 12 (1968), PI'. 107-113, repro in idt'III,., III., Studil'!. pp. ]KS-391.

B. van Dalen ..... "cirlll 0/1(/ Mt'IIiIf;:1'tl1 Astronomical 7i,bles: Mallu!/IlO,ficol Stnlctllf'e ami Pa,."mett!f \1,IIIt''', Utrecht 1992: itlt'lII, "A Statistical Method for Recovering Un-known Pan/meters from Medieval Astronomical Tables", Cefllmlfll! 32 (1989), pp. KS 14S: idt!lII. "A Table for the True Solar Longitude in the Jallli ' Zij' (n. 31): idem, "nl-Khwarizmi's Astronomical T'olbles Revisited ..... (also n. 31): G. Van 8rumme-len, 'The Numerical Structure of al-KhalTIi's Auxiliary Tables". in Ph),"i! 28 ( 1991), 1'1' .667-697; iuem, "A Survey of the Mathematical Tables in Ptolemy's Alma/:e.ft", in FrrmkfllrllGN FI!!.ffixmd, pp. 15S 17(); and H. Mielgo. "A Method of Analysis ror Mean Motion Astronomical Tahles", in Vt'mel FI'J/.fcllrifl, I, PI'. 159- 11K>.

AJtlTllIlJlllicul H,,,,dhoflu ami T"bles 31

3 Overview of the l.fj literature

3.1 Ti,e Indian-Iranian tradition

3. /. J The Z1j aJ-Shiih The first Islamic zfjes were part of an Indian-Iranian tradition which has a pre-Ptolemaic Greek origin. This is the case of the Zij al-Arkalld (K214), written in Arabic in 735 probably in the Sind region, which is related to the Kha!14akhiidyaka, composed in Sanskrit by Brahmagupta in 665. The same main influence appears in the Zfj-i Shahriyiir, translated into Arabic as the Zfj ai-Shdh (K30) ca. 790 probably by a certain Abu '1-l;Iasan


ters of the mean motions of Saturn, Jupiter and the lunar nodes using the collection of historical horoscopes written by the Jewish astrologer of Basra Mashii'aJUih (d. ca. SISt' who computed them with this 1.fj. Both the Zij at Shah and the ZIj al-Arkand. as well as, probably. other early tJjes. were the channel through which the astrology of great conjunctions was introduced in Islam.S5 These concepts were first expounded in Arabic in the KiUib al Qirtintit wa'/-duwal of Zariidusht, translated from the Pahlevi by Sa'id ibn Khurasankhurrah co. 750.56 An important source for the early history of Islamic ,Tjes is 'Ali ibn Sulayman al-Hashimi's Kittib fi '[Jal al_zfjdJ.S7

3.1.2 The Sindhind

The third great zfj within the Indian-Iranian tradition was the Sindhind (K28).58 This text seems to derive, indirectly. from the Sanskrit Brahmii-sphu!asiddhiinta composed in 629 by Brahmagupta, through a work the title of which was probably Mahiisiddhiinta. According to tradition, this Mahiisiddhiinta was introduced in Baghdad in 771 or 773 by an Indian em-bassy sent to the court of the Caliph al-Man~ur. One of the members of this embassy was an astronomer Kanaka who is not necessari ly to be identified with the Indian astrologer Kanka or Kanaka, who worked in Baghdad ca. 775_820.59 With his help, the astronomers Ya

Astronomical Handboolf and Tables 33

Imnslated the Sanskrit text of the Sindhind into Arabic. Both YaCqub and al-Fazari compiled severalzfjes based on the Sindhi"d system, which was used by them to compute the tables of the mean motions of the planets. although the planetary equations were taken from the ZTj a/-Shiih. At the same time, the extant scattered indirect quotations from these zfjes bear witness to the first limited appearance of Ptolemaic elements in Islamic astronomy.60

3./.3 The ZTj of al-Khwlirizmf This tendency was strengthened in the revision of the Sindhind prepared by al-Khwarizmi (ca. 825) (K21 *),61 the first Islamic zrj which is extant, and which has been published and translated, albeit in a fonn substantially different from the original. Most of al-Khwarizmi's original text has not been preserved, but we do possess one complete Latin translation, made by Adelard of Bath (jl. 1116-1142) of a revision of the zrj by the An-dalusi astronomers Maslama al-Majri~i (d. ca. 1010) and Ibn al-~afrar (d. 1034/35).62 A second Latin translation, probably by the Spanish Jew

10 Astrology (n. 56), pp. 51-62. 60 See D. Pingree, ''The Fragments of the Works of Ya'qub ibn Tariq", JNES 27 (1968),

pp. 97-125; and idem, "The Fragments of the Works of al-Fazan""", ibid. 29 (1970), pp. 103-123; as well as the papers by Kennedy and Hogendijk on the lunar visibility table of Ya'qub ibn Tariq (n. 41). On this topic see also Pingree, ''Greek Influence on Early Islamic Mathematical Astronomy" (n. II).

" The relation of al-Khwarizmi's Sindflind tradition to Brahmagupta's Brlihmasphu!a-siddhiinta is shown in detail in D. Pingree, 'The Indian and Pseudo-Indian Passages in Greek and Latin Astronomical and Astrological Texts", in Viator 7 (1976), pp. 141195, esp. 151-169.

62 See the edition of H. Suter and the translation and commentary of O. Neugebauer listed under al-Khwarizmi, Zij, as well as B. R. Goldstein's edition of the Hebrew t~t of Ibn al-Muthanna's commentary listed as Ibn al-Muthanna, Commentary on al-Khwlirill1lf. More recent studies include B. van Dalen, "al-Khwarizmi's Tables Revisited ... " (n. 31), of singular importance for differenliating between original material and later addi-tions; M. Castells and J. Sams6, "Seven Chapters of Ibn a1-~affiir's Lost Zil' (cited in n. 149 below); and also D. Pingree, "Indian Astronomy in Medieval Spain", in Vernel Festschrift, I , pp. 39-48.


Petrus Alfonsi (Mesheh Sefardi ), who seems to have been responsible for Ihe introduction of the zij in England towards (he beginning of the 12th cen-tury. is extant in two manuscripts. MS Oxford Corpus Chri sti College 283 was edi ted and commented upon by O. Neugebauer in hi s study of the ta-bles of aJ-Khwarizml. A new manuscript has recently appeared, namely. Lambeth Palace Library 67.63 There exists a third Latin translation which might be closer to al-Khwiirizml's original work than Adelard's version.64 Funher Khwarizmian materials can be recovered from commentaries such as those written by Ibn al-Muthanna, extant in Latin and Hebrew transla-liol15,65 by 'Abdallah ibn MasnJr,66 and by the Spanish Jew of the 12th cen-IU ry Abraham ibn 'Ezra.67 Material rrom al-Knwarizmi's ziJ was also used in an I Ith -centllry Byzantine lext.68

It is sometimes dirficu lt to establish which or the tables in the later trans-lation correspond to al-Khwarizmi's original work or are to be considered interpolations by Maslama or by Ihe subsequent AndaluSi tradition. How-ever, research has been able to establish a few instances in which materials in Ihe zTj are clearly Andalusi as in the case of the table for lunar crescent

"

"

"

..

1. Cnsulleras, "Las Thblas astron6mieas de Pedro Alfonso", in ESllUJios sobre Pedro Alfonso de H'lesca, M. J, Laearra cd., Huescn 1996, pp. 349-366.

R. Mercier. "Astronomical Tables in the lWetfth Century", in Adelard of Bmll: An English Scilmlisf and Arabi!t of the Early Twelfth Cellwry, C. Burnell cd .. London 1987, pp. 87-1 18, esp. 101.

E. Mil1b Vendrel1, 1 COIllentario de Ibn alMllil/llJl(} a las tobias astron6micas de 01 )/iwariZJ//i - Estudio y ellici6n critica deltato {atine en (a version de Hugo &lIIctallen lois, Madrid & Barcelona 1963: and B. R. Goldstein. Ibn alMllthllllniiS Commentary 011 a{.Khwiiriuni(n. 62).

Cairo ENL Survey, no. B37.

J. M. Mil1as ValIicrosa, Ilibro de losfimdomcllfos de las tablas astronOmicas lit R. Abraham ibn 'El ra, Barcelona 1947 .

A. Jones, An leVt lllhCtntury Manual of AmboBywntint Astronomy. Amsterdam \987.

S ..... )'I2(~llll

AS/f(Hlom;cal Handbooks alld Table., 35

visibility ;69 the tables for the astrological houses;7o the very extensive as-trological tables for 'casting the rays' ;7 1 or the introduction of a new prime meridian placed 17;30 to the Wesl of the Canary Is lands producing a sign if-icant reduction in the size of the Mediterranean, which acquires proportions much c loser to the actual ones.72 It seems clear that, apart from the preva-lent Indian-Iranian tradilion which fits well with what we know of al-Fazari and Ya


to Ibn al-Nadim). Neither of these translations is extant. The new translation from the Greek was ach ieved by al-l:Iajjaj ibn Yusuf ibn Ma!ar in 827/28. This survives in one complete manuscri pt and another fragmentary one. A related translation from the Greek is by Isl)uq ibn l;Iusayn, prepared for the wazfr Abu ' I-$aqr ibn Bulbul (d. Cll. 890). Shortly thereafter this was re-worked by Thiibil ibn QUIT'J., whose version survives in ten manuscripts, only two of which are complete, the version of ls~aq being avai lable only in the fonn of quotations (by Ibn a1-$aI5l) . The ls~iiqrrh.5.bit version was edited by Na~Tr aI-DIn al-TusT in 1274, whose version survives in several copies. According to P. Kunilzsch, Jabir ibn AftaJ:t used both of the trans-lations of all~ajjaj and Isl)aq in al-Andalus in the 12th century, and this is confirmed by the Lat in translation of Gerard of Cremona, also from that cenlury.74 But the Muslim astronomers were concemed from the outset to test and to im prove what they found in the astronomical traditions to which they were heirs.

3.2.2 The Mumtal)an Zij and the Zijes of I:fabash It is clear that al-Ma'ml1n's reign marks a turn ing point in the development of Islamic astronomy. Although al-Nihawandi (jf. ca. 790) had made observa-lions of his own in Jundishapur, the first systematic program of astronomical observations took place between 828 and 833 in the Shammasiyya quarter of Baghdad (828, led by Yal)ya ibn Abi' Man~iir) and in the monastery of Dayr Murran in Mou nt Qasiyyii n, near Damascus (833, led by Khiilid ibn 'Abd al-Mali k al-Marwam1dhi), Al-Ma'mun may have sponsored these observations for astrological reasons (like his predecessor al-Man~fir, he seems 10 have been a keen believer in astrology), although it seems probable Ihal the main purpose of the programme was to reach defin ite conclusions aboul the prob-lem of contradictory parameters and geometrical models in use in early Is-

14 This account is based Oil Kuni tzsch, DerSlemkotalog des Almagest (n. 44), I, pp. 2-3. See also the Ell anicles BATLAMIYOS and TAROJAMA, ii.; as well as G. Saliba, ''The Role of Ihe A/magesl Comment~ries in Medieval Arabic Astronomy: a Preliminary Survey of TusT's RedactiQn of Ptolemy'S A/I/U/gest", AlUS 37 (1987), pp. 3-20, repro in idem, SUlllies, no. 7.

A.I'/wllolllinil Hw/(II)(HJb (/lid Tilhlc.~ 37

lamic astronomy, resulting from the simultaneous application of three main known trJ.ditions: Indian, Persian and Greek. The programme seems to have concentrated mainly on solar, lunar and stellar observations but it also deter-mined new parameters for the mean planetary motions. Several zijes were written as a resu lt of these observations: the official one was compiled by Ya~ya ibn Abi Man~ur and bore the title of al-Zfj al-Mlllnra/:1011 (KSI *), of which a later recension from Mosul survives in a unique manuscript in the Escorial. 7S Other astronomers who were directly or indirectly associated with the observatories of Baghdad and Damascus also wrote their own zijes: among these works, the zfj of l:Iabash al-l:Iasib is the most prominent. This is extant in two manuscripts in Istanbul and Berlin. On ly the former (KI6) has been properly investigaled, although it has not been published.7~ The latter (KI5) is a later recension. Whereas J:labash (d. ca. 864-874) does not seem to have taken an active part in the Ma'ml1ni observations, he used their results for the compilation of his zij. Aa analysis of both l:Iabash's and YaJ:lya's zfjes shows that they are Ptolemaic in character and that they improved certain parameters, especially the solar ones.77 The determina-tion (made in 829) of the position of the solar apogee at 82;390 from the vernal equinox, when compared with the value obtained by Hipparchus and Ptolemy (65;30) destroyed the Ptolemaic belief in its immobility. Several more or less successfu l attempts were made to improve Ptolemy's value for the length of the tropical year. The obliquity of the ecliptic was observed as being 23;33 (a parameter used by YaJ:lya) or 23;35 (used by J:labash) while Ptolemy had 23;5 1,20. A new parameter for the precession of equinoxes

Kennedy, "Zij Survey", pp. 145-147; J. Vernet, "Las tabula proba/a", in Homenaje a Millds-Vallicrosa, II , Barcelona 1956, pp. 501-522, repro in idem, Estudios, A, pp. 191-212. The Escorial manuscript has been published (Frankfurt am Main (IGAIW), 1986) in a 'facsimile', in some respects unfaithful to the original.

76 M. Th. Debamot, 'The Zij of J:labash al-l;liisib: a Survey of MS Istanbul Yeni Cami 78412", in Kennedy Festschrift, pp. 35-69. The literature on J:labash is growing fast: see now E.S. Kennedy. P. Kunitzsch and R. P. Lorch, The Melon-Shaped Astrolabe in Arabic Astronomy, Stuttgart 1999 (see also n. 271); King, WorldMaps (n. 43), pp. 345-359; and the paper by Charette and Schmidl in this volume (on which see also n. 283).

77 See also As-Saleh, "Solar and Lunar Distances and Apparent Veloci ties . .. "(n. 39).

S ..... yll(lOO l )

38 D. A. King & J . Sams6

was determined: 1 in 66~ years, which might have an Indian origin,78 in-stead of the Ptolemaic 1 in 100 years. The Moon's maximum latitude was establi shed as 4;460 (Ptolemy: 5) and Ya~ya, whose tables for the com-putation of lunar longi tude derive from those in the Handy Tables, added a supplementary table which introduced a correcti on based on the fac t that lu-nar motion does not take place on the ecliptic but on the lunar orbit inclined to it. Finally, an important improvement was introduced by J:labash in his lunar equation tables for he seems to have been the first Muslim astronomer to use 'displaced ' functions - on wh ich more wi ll be said below - for lunar equations.79

On the other hand both zijes seem to keep a certai n number of e lements from the Indian-Iran ian tradition: the solar model used in both lijes is Ptole-maic with new parameters (a max imum equation of 1;590 , instead of the Ptolemaic 2;230 ) in spite of the fact that severa l sources attribute to both as-tronomers the use of pre-Ptolemaic techniques, wi th an Indian-Iranian ori-gin, for the computation of the solar equation. This is also t:le case for the mode l underly ing the tables for the computation of planetary latitudes in Yal)ya's lij,80 but the most conspicuous Indian-Iranian influence is seen in the model implied, in both lijes, for Venus. J:labash (and probably Y~ya) as well as, later on, al-Battanl (d. 929) fo llow the Zij al-Shlih when they establish that the mean motion of Venus equals that of the Sun, and that the positions of their apogees and the values of their maximum equations o f the centre are the same.81 This means that they use, implicitly. a kinematic

"

.,

"'

D. Pingree, "Precession and Trepidmion in iridian Astronomy before A.D. [200", lllA 3 (1972), pp. 27-35 See E. S. Kennedy and A. Muruwwa. "Biruni on the So[nr Equation", lNES 17 ( 1958). pr. 112- 12 [, repro in Kennedy el al., SlUdies. pp. 6036 [2: H. Salam and E. S. Kennedy, "Solar and Lunar Tab[es in Early Islamic Astronomy". lAOS 87 ([967). pp. 492-496. repro in Ken!1edy el al. , SlUdies, pp. [08-[ 13: E. S. Kennedy, "The Solar Equation in the Zij of Yal.lya ibn Abi Man~iir", in flarlner FeSlschrifl, pp. 183-186. repro in idem el a/.. SlIIdies, pp. 136-139; and B. van Dalen, "A Table for the True Solar Longitude in the itimi' Zij", in FrankfurllGN Feslband. pp. 17 1-190 . Viladrich. "Planetary Latitude Tables in the MllnZla!lan Zij .. (n. 34). B. R. Goldstein, "Remarks on Ptolemy'S Equant Model in Islamic Astronomy", in Hart-

A""mlwlII;C(/IIf(/l1dbook.~ (II1//7iI"k~ 39

model in which the centre of the epi cycle of Venus lies along the directi on of the mean Sun. (The Ind ians also made the centre of Venus' epicycle, and that of Mercury, lie in the di rection of the mean Sun .)

After al-Ma'mun , Islamic astronomy fo llowed along the same lines. Ob-servations continued almost Without interruption either in small pri vate ob-servatories or in more or less organised insti tutions with official support. These resulted in the compil ation of new ziJes in which the old Indian-Iranian tradition seems to be forgotten (except in al-Andalus - see below), and the tradition of the Almagest and the Halldy Tables was followed. The au thors accepted Ptolemy's kinematic models but used new parameters and destroyed some dogmatic beliefs of the Almagest such as the invariability of the obliquity of the ecliptic, the constant character of the precession of equinoxes, the im mobility of the solar apogee, and the impossibility of an-nular solar eclipses.82 Some of the changes introduced are improvements, whilst others are understandable mistakes resulti ng from the fact that Mus-lim astronomers relied excessively on the accuracy of observations made in Antiquity and in their own times. In any case, it is obvious that Ptolemaic astronomy was not always fo llowed unquestioningly. At the same time, these astronomical tables - starting with J:labash - introduced a new spher-ical trigonometry which had remote Indian roots but which was mainly an Islamic creation: while the only trigonometrical tool known to Ptolemy was Menelaos' Theorem, which established the relation between the six arcs generated by a transversal of the three sides of a spherical triangle (that is, a 'complete' spherical triangle), the new spherical trigonometry developed a series of new theorems which related four elements of a simple spherical triangle. SJ

ner Festschrift, pp. 165-181.

82 On an observalion of an annutar solar eclipse by al- lr1inshahri in 873 A.D. , see B.

83

R. Goldstein, "Medieval Observations of Solar and Lunar Eclipses", AIHS 29 ( 1979), pp. 101-156 (repr. in idem, Studies, XVII), esp. p. 101.

See, for example, alBTriini, Maqiilrd.

Suhoyl2(lOO1)


J.J The major Easlern Islamic zijes It is possible to mention here only a limited number of later zrjes from the Eastern Islamic world, arranged more or less according to the geographical location where they were compiled.

3.3. J Some imporlant zijes lost/or posterity Confident that the glass is more full than empty, we begin with a sample of some important zfjes which are not known to have survived:

..

Some four zfjes (K8. 67. 78, 79, also 90 in the Indian tradition) are attributed to the Banti Amajur (Baghdad ca. 900), none extant Some of their observations are recorded by Ibn Yunus (see 3.3.11). These zfjes would surely have been works of supreme interest.

- al-Zij al'A4iidT(K70) by Ibn al-A'iam (Baghdad ca. 960). produced for the Buwayhid ruler ' Ac;iud al-Dawla, influential in later astron-omy in al- ' Iriiq and Iran, notably in the Zfj-i flkhlinf (see 3.3.9) and in Byzantine astronomy, not extant but some details have been recon-structed. S4

A zfj (K I07) by 'Abel a l -Ra~man al-!?ijfT of Shiraz (ca. 975), lost in the original but now known through extracts preserved in medieval llalian tables from Pisa recently investigated for the fi rst time.8s

al-Majis.tf al-Shiihf (K77) of Abu N~r ibn ' Iraq (Khwarazm ca. 1(00), not extant except for a small extract.86

E. S. Kennedy. 'The Astronomical Tables of Ibn al-A'lam", JHAS I (1977). pp. 13-23: A. Tihon. "Sur l'idcntitc de I'astronome Alim". AlHS 39 (1989). pp. 3-2 1. repro in cat/em. Studies, IV; and R. Mercier. 'The Parameters of the Zfj of Ibn al-A' lam", AIHS 39 (1989). pp. 2250. Sec R. Mercier. 'The Lost Zij or al -~iifi in the Twelfth-Century Tables for London and Pisa", in uClurt!s from tilt! Conft!rt!/lct! on al-$il,/r and Ibl! ol-No/is ... , 5-8 OclolH!r. 1987. Amman (University of Jordan). pp. 38-74. Sezgin. GAS. VI. pp. 242245.

Suh:oyl2 (lIIU)

ASlronomical Handbooks ami Tables 41

- alZfj al-Malikshiihl (K22) by 'Umar alKhayyam (Nishapur ca. 1090), alas not extant.

3.3.2 The tradition of al-Battiinf al-Zlj al-$abi' (K55) of al-Battani (Raqqa co. 900) is a respectable and orderly work, if lacking the originality of the lijes of f:labash. This was one of the most important works for the transmission of Ptolemaic astronomy to Europe but it enjoyed far less influence in the Islamic world (not least because there it had more competition).87 The canons were translated into Castilian under the auspices of King Alfonso X of Castile ( 13th century).88 There were two Hebrew ver-sions of the zfj of al-Battini: the first by Abraham Bar l:Iiyya (12th century), and the second by Immanue l ben Jacob Bonfi ls of Tarascon ( 14th century): see further 3.5.

- Two zIjes by Kushyar ibn Labban (ca. 1000), entitled aJ-Zfj al-lamj' and al-Z!j ai-Baligh (K9 and K7). are extant in several copies of vary-ing content. The contents of the two zfjes have yet to be sorted out. It is certain that the expression al-Zlj allami" wa- 'I-bdligh refers to two separate works because Kushyar himself refers to them using the phrase kitlJoon sammaytuhumii. .... 89 Kushyar calculated accurate mean motion parameters from al-Battani's data, but made slight ad-justments for Mars. He applied a different, less accurate type of Ptole-maic interpolation for his planetary equations, which were systemati-cally of the ' di splaced' type.90

81 The edition of the Arabic text with a Latin translation and a commentary, also in Latin, by C. A. Nallino is listed under alBattini', Zij.

88

"

Edited in G. Bossong, Los c6nont:s d~ Albattni, TIlbingen 1978.

M. YallO, ed. and trans!., Ki1.fylir ibn Labban's Introducrion ro Asrrology, Thkyo 1997, pp.6-7.

90 1. L. Berggren, "Spherical Astronomy in Kushyir ibn Labban'$ Jam;' Zij" (n. 24); M. Bagheri, 'ibe Persian Version of ZlJ; Jlimi' by Ku!ylr Gilinf', in SrrasboU18 1995 Cofloquiwn Proc~~dings, pp. 2531; idem, "A Chapter from Kusbyar's Lost ZIT', paper

5 ..... 112 Gill!)


ZJj-i MII/rad (K65) in Pers ian by Mu~ammad ibn AyyGb al-Tabari (N. Iran, ca. 1230), apparently based on al-Battani, is extant in the unique copy MS Cambridge Browne 0.1, merits detai led study. This manuscri pt contains a lunar crescent visiblity table attributed to al-Binini (see below), not known from the work s of the master.91

3.3.3 The lalJles of a i ij ellgra ved 011 (III (Mlml/omical instrument

"

"

- The tables of a zJj were engraved on the mater and plates of an as-tro labe in an instrument labelled Zfj al-$afil 'ifl (K200) by Abu Ja'far al-Khazin (Baghdad ca. 950): together with this was an extensive treatise on all manner of astronomica l subjects, of sufficient meri t to aUrael the attention of scholars of the calibre of Abu N~r ibn

A~/rr)llomico.l Handbooks anti Tables 43

in the Silldhilld tradition also found in the manuscript. The AndaJusi astronomer Ibn al-Sam~ (d. 1035) also engraved mean-motion tables on the plates for each planet in his equatorium.94 A table for lunar visibility atlributed to Abu Ja'far al-Khazin is found in the Dustiir al-mullajjimfll mentioned below.9S

3.3.4 The tradition of Abu 'I-Wafii'

"

- A zij entitled al-Majis!f(K73) by Abu ' I-Wara' al-Biizajani (ca. 970) is partially extant in MS Paris BNF ar. 2494. The tables are indi-cated but are not found in this copy; nevertheless, the sections on trigonometry and spherical astronomy are extensive and systematic and of considerable historical imeresl.96 Abu ' I-Warn' also compi led another work entitled (If-Zij al-W1l4ftl, which is not extant.

- The later, anonymous zij entitled al-Zij ai-Shamji (K29), was based on that of Abu 'I-Warn', and was clearly of some in fluence, with some spherical astronomical tables for the latitude of Mardin. This is extant in several manuscripts,97 of which a preliminary study has been made by J. P. Hogend ijk. The Athfrf Zij (K40 = K56) by Athir ai-Din al-Abhari of Mosul, extant in MS Dublin Chester Beatty 4076, is closely related lO, if not identical wi th, the Shamil Zij.

J. Sams6, "Notas sobre el eeuatorio de Ibn al-Sam~", in Vernet, cd., ~/Udios, B. pp. 105-118, repr, in SamsO, Studies, XVI; and M. Comes, Ecuatorios andalusies -fbll al-Stlln~, al-Zarqiilluh Y Abii-l-.)alt. Barcelona 1991 .

King, "Early Islamic Tables ... "(n, 41), pp. 208-210, and l'logendijk, '"Three Tables ... "(also n. 41), pp. 36-42.

96 B. Carra de Vaux, "L' Almageste d ' AbO'I-WCfa AlbQzdjani", Journal AsiUlique, 8e ~r" 19 (1892), pp. 408-47 1.

" See, for example, Cairo Nt Survey, no. B 100.

SWyIl(20lI)

44 D. A. King & 1. Sums6

3.3.5 Sundry zijesJrom af- 'Iraq and Iran A substantial tIj (K3) by Jamal ai-DIn al-Qasim ibn Ma~fGt al-Baghdadi (Baghdad, 1258) is extant in a unique copy, MS Paris BNF ar. 2486.98 The planetary tables are computed with the parameters of 1:Iabash (see above). However, a set of nine tables for spherical astronomy were taken over from the Majistf of Abu ' I-Wata',99

- The Zlj; Ashraj7(K4) of Sayf-i Munaij im (Shiraz, ca, 13(0) is extant in MS Paris BNF supp. per'S. 1488,100 and merits further investiga-tion. The qibla-table is something of a disaster, and the geographical tables were lifted from the Sanjarf Zij (see betow).'01

3.3.6 a/-Bfriinf

"

"

- al-QlllIIlII al-Mas'adf (K59*) by al-8imni (ca. 1025), dedicated to Su l!an Mas' lid of Ghazna, is much more than an ordinary V}, being a greal astronomical handbook, full of good sense, containing substan-tial infonnation about the author's personal astronomical research as well as about the development of astronomy in Islamic countries until the author's lime. There is an edition by M. Krause. '02 The Qiilliin was not as influential as it should have been (the same is true of al-BirUni's other productions): some of the trigonometric tables were laken over in the ZiJ-i flkhiinf (see below) and the geographical tables,

C. Jensen, 'The Lunar Thrones of aI-BaghdAdi', AHES 8 ( 1971 -72), pp. 321-328. See van Dalen, Ancient and Medill:\l(J1 Astronomic(ll T(lbles (n. 52), ch. 4.

100 Storey, PL. 11 :1, pp. 64-65.

to! See n. 264 below, and King, World-Maps (n. 43). pp. 66 and 71. 102 TIlis was published as al-8imni, al-Qunlin al-Mas'Udf, 3 vols., Ilyderabad 1954--56.

albeit without the editor's critical apparatus. Sec the annotated table of contents in E. S. Kennedy, "al-Binini"s Masudic Callan", alAblla/1I 24 (197 1), pp. 59-81, repro in idem et al., Swdies, pp. 573-595. A valuable study of part of this work is C. Schoy, Die trigonometrischen Lehnn des peT$ischen As/ronomen ... ol-Birimi, Hanover 1927, repro in idml, Beitriige, II. pp. 629-7-Ki.

5.....,..1 (211111)

lulronomicu/ Handbooks a/ld Tabfer 45

albeit in a slightly modified form, as if read from a map, in the Sail' jarT ZTj (see below). No recensions or modified versions have come to light.

3.3.7 A zij/rom Marw (12lh century)

- aJ-ZIj aJ-Sa/ljarf (K27) by 'Abel alRa~man al-Khazini (ft. ca. 1120), dedicated ta the Seljuq sultan Sanjar ibn Malikshah, is an imposing wark on which much more research needs 10 be dane. to] Besides the original Sal/jarf Zfj there exists a shorter version, designated aJ Wajfz, apparently also by alKhiizini. This was translated into Greek by Gregory Chioniades (ca. 1290-1300).104

3.3.8 The traditiOl/ of aJFahhad: from Adharbayjdll to COllstantinople and the Yemen

Several zTjes (K23, 42, 53, 58. 62, 64, 84), including one called at ZTj al 'Alti'l. are associated with al-Fahhad (Shirwiin ca. 1150), none extanl in their original form. The Yemeni astronomer Mu~ammad ibn Abi Bakr al-Farisi (see 3.3.12), as well as variaus Byzantine as tronomers, used al-Fahhad's work and preserve for us substantial por-tions of it. ,05

10) See D. Pingree. "Gregory Chioniades and Palzologan Astronomy". in DumbartOll Oah p(Ifierr 18 (1964). pp. 135-160, esp. 151158; and. on the geographical tables. D. A. King. World-Mallr (n. 43). pp. 7 I -75. and App. D. The tables for lunar crescent visiblity in the Stmjari ZTj arc due to TIlabit ibn Qurm and have been published by R. Morelon (see n. 41).

104 On the relation between the original ziJ. the abridgement. and the translation, see D. Pingree, "A Preliminary Assessment of the Problems of Editing the ZIj al.Sonjarr of al Khazinf. in Editing Islamic Mallll5Cri/lIs on Science. Y. Ibish cd . London 1999, pp. 105-113. The Byzantine text is being published by J. Leichter of Brown University.

I~ For the Byzantine version see D. Pingree. The Astronomical Works a/Gregory ehiOlli-adl!S. vol. I: The Zij al-' Alli'i. Amsterdam 1985-86.

Suh>.yllI2UUJ


3.3.9 Thl!. Maragha productio,IS

The Zij-i Tikhanf, the major production of a group of astronomers working at Maragha under N~lr ai-Din and purportedly based on their observations, is still in the Ptolemaic tradition. The parameters underlying the solar, lunar and planetary tables were, however, taken from Ibn al-A'iam and Ibn Yunus, and the trigonometric tables lifted from Ibn Yunus and al-Blliin!. What is new is the calendrical material. There is no influence of the important modifications of the Ptolemaic planetary models conceived by the Maragha astronomers (see 3.6).

- The 2ij- ; Tikhanf (K6*) is generally attributed to N~ir ai-Din al-Tus! (1201_ 1274).106 This work has not yet received the attention it de-serves. It is, however, already apparent that the authors were indebted to Ibn al-A' lam, Ibn Yunus and al-Birun!. The ZIj-i flkhiinf was later revi sed and corrected by al-Kash! in his Zfj-; Khiiqdnf (see below). Two works are based on the new observations made at Maragha:

- A 1.ij for Maragha (KI08) by Mu~yi ai-Din al-Maghribi (ca. 1280), distinct from his earlier compilation for Damascus, extant in several copies, including MS Meshed 3321103, merits detailed investi gation. We are fortunate to have a kind of notebook in the author's hand. I07

A substantial 1.ij by Shams (ai-Din) al-Munajjim al-Wabiknawl (K35), compiled ca. 1320, survives in a unique copy MS Istanbul Aya Sofya 2694. It seems to be based on flkhiinf parameters, but is currently under investigation in Frankfurt.

106 See J. A. Boyle, 'The Longer Inlroduction to the ZIj-j.flkhllni of Na~ir-ad-Din TUsf'. Journal of Semitic Studies 8 (1963), pp. 244-254. Further, R. Mercier, 'The Greek 'Persian Syntaxis' and the 'lij.j 'Ikhiinf', A/HS 34 ( 1984), pp. 35-60; and. with a dif-fe rent interpretation. D. Pingree, " In Defence of Gregory Chioniades", ibid. 3S (1985), pp. 436-438.

101 G. Saliba, '''The Observational Notebook of II ThirteenthCentury Astronomer". Isis 74 (1983). pp. 388-401, repro in idem, Studies, no. 8.

Astronomical Handbooks and Tables 47

Another Islamic tij (K0) from the Mongol period (ca. 1275) is avai l-able in a Chinese trans lation printed several limes between the late 14th and the 18th century known under the name Hllihui Ii, meaning ' Islam ic astronomical system,.I08 Whereas Yabuuti assumed a rela-lion with the Tlkhiini Zij, Yano and Van Dalen recently showed that the underlying parameters of the fluihui Ii derive From independent ob-servations presumably made by Muslim astronomers in Yuan China in the lale 13th century. Some of the original tables of the work are contained in the zij (K0) by Abu Mu~ammad


3.3.10 Syrian zijes and the major production of the chief muwaqqit of the Umayyad Mosque ill Damascus

An anonymous zJj for N. Syria (7) entitled Dusll7r al~munajjimrn (K0) is extant in the unique MS Paris BNF ar. 5968. 110 The work contains cons ideruble material attributed to earlier astronomers, such as the lunar visibility table of Abu Ja'far al~Khiizin (see above).

A zrj (K89) was prepared by Ibn al~Dahhan (ca. 1170), who worked in Damascus in the service of the Ayyubid ruler $alaJ) al~Din (Saladin), not extant, although the geographical table is preserved in a RasUlid Yemeni compendium. I I I

- The Taj al-azyiij (K4 1) of Muhyi al~Din al-Maghribi was compi led for 'Damascus ClI. 1250 and is extant in three copies: MS Escorial ar. 932, MS Dublin Chesler Seauy 4 129, and a manuscript belonging to the Arabic Department of the University of Barcelona. 112 The author moved on to Marugha where he compi led two other zrjes (see above). It is perhaps worth noting that the sole survi ving copy of a recension of the zJj of Ibn Isryaq al-Tunisi (K0) was copied in l:Iim~ in the year 1317 (see fu rther 3.4). Otherwise Ibn IsJ:laq seems to have been known in the East only in the Yemen.

- lIl-Zrj 1I1-Jadrd (K II *) of Ibn at-Sha~ir (Damascus ca. 1350),113 with equation tables based on hi s new planetary models, which represent the cu lmination of the Islamic activities to replace those of Ptolemy:

110 Sczgin. GAS. VI. pp. 6364: Pingree. The Thousands of Aha Ma 'shar (n. 53). pp. 24-25. I'IC.: ;md F. W. Zimmermann, "The Dllsliiral.Muntljjimfn of ms. Paris, BN ar. no. 5968". in Alel/11O 1976 SYIllIIO.~illm Procttdifl~s. rr. pp. 184- t92.

I I I King. A.wrrlllvml' ill YI'/U('/I (n. It), pp. 37. m See S:lliba. "Observational N(ltebook" (n. 107). esp. p. 167; and SamsO. "Maghribi

Zfjes" (n . 11 ), pp. 96-97. ll~ Various carly studies are reprinted in E. S. Kennedy and I. Ghanem. Tht! Uft! and Work

(If f/JIIlJIShti.tir .. . . Aleppo 1976.

AJllTJfIOIllictll Handboola and Tablu 49

see further 3.6.4 below. This work merits detailed investigation. Sev eral recensions were made for Damascus in later centuries, also one fo r Algiers, and one for Cairo was made ca. 1400 by alKaw m al Rishi (see below). I 14 A copy of Ibn al-S hapr's l.fj in Hebrew charac ters, executed in Aleppo in the mid- 19th century, has been preserved: see further 3.5.

- Around 1500, recensions fo r Damascus were prepared of the flkhiillf Zij (by Shihiib alDin alJ:lalabi) and the SU(liinf Zfj (by 'Abd al Ra1:lmiin a l -~ali ~i).

3.3.11 The lradition of Ibn Yiillw; in Egypt alld beyond A monumental work entit led al-Zfj a/-f:/iikimf 'Ikabfr (KI4), com piled ca. 1000 for the Fa~imid Cali ph al-J:lilim by lbn Yllnus, some four times as large as the zfj of alBattiini Substantial parts of the work survive in manuscri pts in Leiden, Oxford and Paris (with deriva tive tables in MS Istanbul Selim Aga 728/2), Of particular hi storical interest are the accounts of observations by the author and his prede cessors in

50 D. A. King & 1. Sams6

the Yemeni Mukhtiir Zrj and a collection of tables by the Cairo as-tronomer A~mad ibn Timurbay ca. 1475. as well as in a Byzantine source. 117 Towards the end of the 17th century, Cezmi Z3de, qii{lf of Belgrade, wrote that he had come across a copy of the /jakimfZij in a pri vate library in Istanbul , where he had earlier worked sweeping the floor. Perhaps it is this copy that is now preserved as MS Istanbul Se-lim Aga 728/2, which contains tables based on, but not actually taken from, the /fiikim f Zij (although the title indicates that they are origi-nal).118 He can hardly have been referring to the copy now in Leiden, which belonged to Taqi ai-DIn (see 3.3 .1 4) in the late 16th century, I 19 because it was bought by Golius ca. 1600.

- al-Zij a{-Mu~.ralafl (K47) was the most popular zij in medieval Egypt, attributed by J:lajjf Khalffa to one Muryammad ibn Muryammad al-Fariqf, who is not otherwise known to the li terature and whose name has not been found in any medieval sources. The work is extant in two recensions. one Yemeni and the other Egyptian preserved respec-tively in MSS Pari s 8NF ar. 25 13 and 2520. and contains material from < Abbasid zijes and from the ijiikimf Zij but nothing original. 120

- Two zijes were compiled by Ibn al-Lubiidi" (ca. 1250), al-Zij al-Ziihf (K86) and al-Zij al-Muqarrab (K87) (an unlikely title), the latter ap-parently based on the Mlltntatwll observations. are not extant. 121

117 King, Astronomy in Yemen (n. II), p. 3 1; Cairo ENL Su".,ey~ no. B5912. 1.6; and D. Pingree, "Gregory Chioniades and Palreologan Astronomy" (n. 103), pp. 138- 139.

li S First mentioned in i hsano~lu, "Introduction of Western Science to the O!toman World" (n. II), p. 73. A microfilm of this manuscript was kindly shown to us by Dr. Sonja Brentjes.

119 SeeS. Dnver, Istanbul rasathtinesi, Ankara 1969. pp. 101 -104 and figs . 41-42 on some of the manuscri pts from Taqi al-Din's library.

120 See King, "Astronomy of the Mamluks" (n. 11 ), pp. 535-536; idem, "Double-Argument Equation Table" (cited in n. 222 below), pp. 145146; and idem, "Ibn Yiinus on Lunar Crescent Visibi lity" (n. 41), pp. 155-156.

121 See Suter, MM, no. 365. On the problems of the documentation of this interim period

Suhayll (21~)1l

Astronomical Hwulbo(}k.f (Uul Table.l 51

- A zfj for the Sun and Moon (K0) was compi led by the e:u ly-l3th-century Coptic scholar al -As'ad Ibn 'Assai, with text in Arabic and ta-bles in Coptic numerical nolalion. extant in MSS Cairo Dar al-Kutub mfqlit 910, I and Vatican ar. 152, as yet unstudied. 122

- The work entitled al-Lum'aJr ~wlllll-kawli.kib lll-sab 'a (K0) by the Cairene muwaqqit al-Kawm al-RTshT Cll. 1400 is a recem;ion for Cairo of Ibn a l -S ha~ir's lll-Zfj al-Jlldfd (see above) . 12.1

Zfj al-$iljf (K37), an Egyptian recension of the Sul.tllllf Zfj of Ulugh Beg, was compiled by Ibn Abi ' I-Fatl) a l-~ufT (ca. 1460). one of the leading Cairene astronomers of his time. It is extant in several copies. of which the best appears to be MS Tehran Mi lli76S. 124

- aL-Zlj aL-Mujfd 'ala u~ill al-ra~lld al-jadfd (K209), by Ric,1wan Efendi (Cairo ca. 17(0), is based on Ulugh Beg but has expanded equation tables; it is extant in several copies. 125

3.3.12 Some Yemeni zijes (10th-19th century) Altogether some IS zfjes are known from the Yemen. Their hi storical impor-tance derives not only from the fact that they attest to a serious tradition of mathematical astronomy for close to a millennium but also from the fact that they preserve for us 'Abbfuiid and Fa~imid materials which would otherwise have been lost. 126

between Ibn Ylinus in the tale 10th century and the 131h century, when the Mu~!ala~1 Zlj (see n. 116) was compiled, see King. "Astronomy of the Mamluks" (n. I I), pp. 532-534.

122 Cairo ENL Survey, no. CIO.

123 Ibid. , no. C41.

124 Ibid. , no. C98.

125 Ibid. ,oo. D58.

126 See King, Astronomy in Yemen (n. II ).

S .... yl2 (2001)


- The zij (K69) of ai-Hamdan! (Yemen ca. 930), who was familiar with the works of the astronomers of the 8th and 9th cemuries, is not extant. 127 The 13th-century historian of science Ibn a l-Qi f~i Slates that it was used in the Yemen in his time ('a/ayhi 'till/lid ali i al-YanulII), but he was not well infonned on Yemeni astronomy. The recovery of this work would be a major breakthrough; the scope of al-Hamdanl's mastery of astronomy is indicate

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