IBN AL-SH?T?IR, ‘?L?’ AL-D?N ABU’L-H?ASAN ‘AL? IBN IBR?H?M

(b. Damascus. Syria, ca. 1305: d. Damascus, ca. 1375)

astronomy.

Ibn al-Sh?t?ir (Suter, no. 416) was perhaps the most distinguished Muslim astronomer of the fourteenth century. Although he was head muswaqqit at the Umayyad mosque in Damascus, responsible for the regulation of the astronomically defined times of prayer, his works on astronomical time-keeping are considerably less significant than those of his colleague al-Khal?l?. On the other hand, Ibn al-Sh?t?ir, shared the interest of his earlier contemporaries Ibn al-Sarr?j, and al-Ghaz?l? and al-Mizz? (Suter, nos. 508, 412, and 406) in astrolabes and quadrants; and he constructed sundials. Nevertheless, Ibn al-Sh?t?ir’s most significant contribution to astronomy was his planetary theory. In this planetary models he incorporated various ingenious modifications of those of Ptolemy. Also, with the reservation that they are geocentric, his models are the same as those of Copernicus. Ibn al-Sh?t?ir’s planetary theory was investigated for the first time in the 1950’s. and the discovery that his models were mathematically identical to those of Copernicus raised the very interesting question of a possible transmission of his planetary theory to Europe. This question has since been the subject of a number of investigations, but research on the astronomy of Ibn al-Sh?t?ir and his sources, let alone on the alter influence of his planetary theory in the Islamic world or Europe, is still at a preliminary stage.

Only a few details of the life of Ibn al-Sh?t?ir are known. His father died when the boy was six years old: and he was brought up by his grandfather, who taught him the art of inlaying ivory. at the age of about ten he traveled to Cairo and Alexandria to study astronomy, and, presumably, his interest in spherical astronomy was fired by the extensive compendium on spherical astronomy and instruments compiled in Cairo about 1280 by Ab? ‘Al?al-Marr?kush? (Suter, no. 363). In his early work Ibn al-Sh?t?ir revealed something of his debt to al-Mizz?, who also had worked in Egypt. In his treatise on the “perfect” quadrant, he depended on a pair of distinctive parameters also used, but not derived, by al-Mizz?: 33;27° for the latitude of Damascus and 23;33° for the obliquity of the ecliptic. In A.H. 765 (1363/1364) he derived the new pair of values 33;30° and 23;31°, which he employed in his later works.

Planetary Astronomy. Ibn al-Sh?t?ir appears to have begun his work on planetary astronomy by preparing a z?j, an astronomical handbook with tables. Some two hundred z?jes were compiled by the astronomers of medieval Islam, and several had been prepared in Damascus prior to the time of Ibn al-Sh?t?ir (for example, Kennedy, nos. 15/16, 89, 41, and 42). Ibn al-Sh?t?ir’s first z?j, which has not survived, was inappropriately called Nih?yat al-gh?y?t fi ’l-a‘m?l al-falakiyy?t (“The Final Work on Astronomical Operations”) and was based on strictly Ptolemaic planetary theory. In a later treatise entitled Ta‘l?q al-ars??d (“Comments on Observations’). he described the observations and procedures with which he had constracted his new planetary models and derived new parameters. No copy of this treatise is known to exist in the manuscript sources. Later, in Nih?yat al-s?l f? tas?h??h? al-us??l (“A Final Inquiry Concerning the Rectification of Planetary Theory”), Ibn al-Sh?t?ir presented the reasoning behind his new planetary models. This work has survived.¹ Finally, Ibn al-Sh?t?ir’s al-Z?j al-jad?d (“The New Astronimical Handbook”), which survives in a number of manuscript copies, contains a new set of planetary tables based on his new theory and parameters.²

Ibn al-Sh?t?ir introduced this later z?j in the following way:

God granted me success in working on this science [astronomy] and made it easy for me after I had mastered arithmetic, surveying, geometry, instrument making, and had actually invented many kinds of astronomical instruments. I came across the books of certain of my predecessors among the noted scholars in this branch of science, and I found that the most distinguished of the later astronomers, such as al-Majr?t? Abu’l-Wal?d al-Maghrib? [Ibn Rushd?], Ibn al-Haytham, Nas??r al-T??s?, Mu’ayyad al-‘Urd?? [assistant to al-T??s?, fl. Damascus and Persia ca. 1250]. Qutb al-Sh?r?z? and Ibn Shukr al-Maghrib? [Suter, no. 376], and others, had adduced doubts concerning the well-known astronomy of the spheres according to Ptolemy. These doubts were indisputable and [concerned matters] incompatible with the geometrical and physical models that had been established [by Ptolemy]. These scholars took pains to make models that would adequately represent the longitudinal and latitudinal motions of the planets, and not introduce inconsistencies. They were not granted success, however, and they admitted this in their writings.

I therefore asked Almighty God to give me inspiration and help me to invent models that would achieve what was required, and God—may He be praised and exalted, all praise and gratitude to Him—did enable me to devise universal models for the planetary motions in longitude and latitude and other observable features of their motions, models that were free—thank God—from the doubts surrounding previous models. I described these new models and gave the necessary proof of their viability in my book called T a‘liq al-ars??d. “Comments on Observations.” and I gave a short description of the models themselves in my book called Nih?yat al-s?l f? tas?h??h? al-us??l. “A Final Enquiry Concerning the Recitification of Planetary Theory.” Then I asked God—may He be exalted—for guidance in compiling book that would contain [rules for] the precise determination of planetary positions and motions and the secrets of the planetary attributes, according to the mean motions that I found by observation, the distances that in computed, and the tables that I compiled on the basis of the new corrected astronomy. This book should be a fundametal work of people to rely on, in which astronomical operations and problems are precisely formulated....

Of the surviving works by the scholars mentioned by Ibn al-Sh?t?ir, only the Tadhkira of al-T??s? and the Nih?yat al-idr?k nd the Tuhfa sh?h?ya of Qutb al-D?n al-Sh?r?z? described non-Ptolemaic planetary models.³ Qut?b al-D?n remarked several times in his treatises that most contemporary astronomers preferred such-and-such a non-Ptolemaic model, suggesting that he was one of several scholars who tried to modify the Ptolemaic models.

The essence of Ibn-al-Sh?t?ir’s planetary theory is the apparent removal of the eccentric deferent and equant of the Ptolemaic models, with secondary epicycles used instead. The motivation for this was aesthetic rather than scientific; the ultimate object was to produce a planetary theory composed of uniform motions in circular orbits rather than to improve the bases of practical astronomy. In the case of the sun, no apparent advantage was gained by the additional epicycle. In the case of the moon, the new corrected the major defect of the Ptolemaic lunar theory, since it considerably reduced the variation of the lunar distance. In the case of the planets, the relative sizes of the primary and secondary epicycles were chosen so that the models were mathematically equivalent to those of Ptolemy.⁴

Below is a brief outline of Ibn-al-Sh?tir’s new planetary theory. All numbers are expressed sexa-gesimally (see Kennedy, p. 139).

The Solar Theory . The mean sun, S, is situated on the deferent circle, radius r = 60, which rotates from west ot east about the center of the universe O. The apogee moves from west to east about O at a rate of one degree in sixty Persian years of 365 days each. (Ibn al-Sh?t?ir accepted the rate of precession as one degree in seventy Persian years.)

The primary epicycle has center S? and radius r₁ = 4:37 and rotates with the motion of S? relative to the apogee and in the opposite sense. The radius S?E thus remains parallel to the apsidal line. The true sun, S, is situated on the secondary epicycle, center E and radius r₂ = 2:30, which rotates with double the motion of S relative to the apogee and in the same sense.

The resultant maximum equation in this model is 2;2,6° and occurs when S? is about 97° from the apogee, the position of which is given as Gemini 29;12° in December 1331. Ibn al-Sh?t?ir retained the Ptolemaic eccentricity 2;30 in his value of r₂; and his maximum equation corresponds to a resultant eccentricity of about 2;8, which is close to his value for r₁?r₂. The solar distances at apogee and perigee are now 52;53 and 1,7;7, as against Ptolemy’s 57;30 and 1,2;30. Ibn al-Sh?t?ir’s new solar model appears to be the result of an attempt to make the variation of the solar distance correspond closely to the variation of the lunar distance in his new lunar model.

The Lunar Theory . The orbit of the moon is inclined at an angle of 5° to the plane od the ecliptic, and the nodes move from east to west with a constant motion. The mean moon, M?, is situated on the deferent, radius r = 60, which rotates about O from west to east in such a way that the resultant motion of M? is the mean sidereal motion. The primary epicycle, center M? and radius r₁ = 6;35, rotates with the mean anomaly in te opposite direction. The true moon, M, is situated on a secondary epicycle, centered at E on the first epicycle and having radius r₂ = 1; 25, which rotates from west to east at twice the difference between the lunar and solar mean motions.

As a consequence of the resultant motion the resultant motion, the moon will always be at the perigee of the secondary epicycle at mean syzygies and at its apogee at quadrature. The apparent epicycle of radius r₁?r₂ = 5;10 at syzygies accounts for the equation of center, and the gradual increase in its apparent radius to r₁+r₂ = 8;0 as it apporaches quadrature accounts for the evection. The maximum equation of the resultant eqicycle is 7;40°, which is Ptolemy’s value. Also the lunar distance now varies between r?(r₁?r₂) = 54;50 and r+ (r₁?r₂) = 11,5;10 at the syzygies and between r– (r₁ + r₂) = 52;0and r+(r₁ + r₂) = 1,8;0

at the quadratures. Thus the major objection to the Ptolemaic model–in which the moon could come as close as 34;7 to the earth at quadratures, so that its apparent diameter whould be almost twice its mean value–was eliminated.

Planetar Theory. The mean planet. P?. here considered in the plane of the ecliptic, is situated on the deferent, radius r=6, which rotates about the center of the universe from west to east with he mean longitudinal motion. The primary epicycle. radius r₁ rotates in the opposite direction at the same rate corrected for the motion of the apogees. again one degree in sixty Persian years. Thus the radius P?E remains parallel tot he apsidal line. The secondary epicycle, radius r₂, rotates about E from west to east at twice this rate. The tru planet, P, is situated on the tertiary epicycle, radius r₃, which rotates with the mean anomaly about point F on the secondary epicycle. The anomaly is reckoned from the true epicyclic apogee, which is point G such that FG is parallel to OP?. In the case of the outer planets, FP remains parallel to the line joining O to S?. In the case of the inner planets. the direction OP? defines S?.

In order to preserve the Ptolemaic distances in the apsidal line and at quadrature, the geometry of the models requires that

r₁?r₁=e and r₁ + r₁+r₂ = 2e,

where e is the Ptolemaic eccentricity, so that r₁ = 3e/2 and r₂ = e/2. At least in the case of the three outer planets, Ibn al-Sh?t?ir values of r₁ and r₂ are precisely these. For Venus he takes

r₁?r₂ =e and r₁+r₂=2 e?.

Where e = 1; 15 is Ptolemy’s eccentricity for Venus and 2 e? = 2;7 is the resultant double eccentricity of Ibn al-Sh?t?ir’s own solar model.

Because of the large eccentricity of the orbit of Mercury, Ibn al-Sh?t?ir’s model was more elaborate than those for the other planets. Two additional epicycles placed at the end of r₃ have the effect of expanding and contracting its length in simple harmonic motion, with a period twice that of the mean longitudinal motion corrected for the motion of the apogee. Also, the sense of rotation of the apogee. Also, the sense of rotation of the epicycle with radius r₂ is the reverse of the for the other planets.

The solar, lunar, and planetary equation tables in al-Z?j al-jad?d were based on these new models. The accompanying mean motion tables, however, were based on parameters different from those stated in the Nih?yat al-s?l. Also, although in this treatise Ibn al-Sh?t?ir presented a new theory of planetary latitudes to accompany his new longitude theory, the latitude tables in al-Z?j al-jad?dwere, with the exception of those for Venus, ultimately derived from Ptolemy’s Almagest.⁵

Astronomical Timekeeping. Ibn al-Sh?t?ir compiled prayer tables, that is, a set of tables displaying the values of certain sphericl astronomical functions relating the the times of prayer. The latitude used for these tables was 34°, corresponding to an unspecified locality just north of Damascus. These tables, not discovered until 1974, display such functions as the duration of morning and evening twilight and the time of the afternoon prayer, as well as such standard spherical astronomical functions as the solar meridian altitude, the lengths of daytime and nighttime, and right and oblique ascensions. Values are given in degrees and minutes for each degree of solar longitude, corresponding roughly to each day of the year.

A more extensive set of tables for timekeeping at Damascus was compiled by al-Mizz?; but it was replaced by the corpus of tables compiled by al-Khal?l?, which were based on slightly different parameters.

Sundials . In A. H. 773 (1371/1372) Ibn al-Sh?t?ir designed and constructed a magnificent horizontal sundial that was erected on the northern minaret of the Umayyad mosque. The instrument now on the minaret is an exact copy made in the late nineteenth century by the astronomer al-T?ant??w?, the last of a long line of Syrian muwaqqits working in the medieval astronomical tradition. Fragments of the original instrument are preserved in the garden of the National Museum, Damascus. Ibn al-Sh?t?ir’s sundial, described for the first time in 1971 by L. Janin, consisted of a slab of marble measuring approximately one meter by two meters. A complex system of curves engraved on the marble enabled the muwaqqit to read the time of day in equinoctial hours since sunrise or before sunset and to reckon time with respect to daybreak and nightfall and with respect to the beginning of the interval during which the afternoon prayer should be performed, this being defined in terms of shadow lengths. The curves on this sundial probably were drawn according to a set of tables, compiled especially for the purpose, that displayed the coordinates of the points corresponding to the hours on the solstitial and equinoctical shadow traces. Tables of such coordinates for horizontal sundials to be used in Mecca, Medina, Cairo, Baghdad, and Damascus had been compiled early in the ninth century by al-Khw?rizm? and less than a century before Ibn al-Sh?t?ir’s time, new sets of sundial tables for various latituded had been compiled in Cairo by al-Marr?kush? (Suter, no.363) and al-Maqs? (Suter, no. 383). None of the several later sets of Islamic sundial tables that are still extant is attributed to Ibn al-Sh?t?ir. One such set based on his parameters survives, however, in MS Damascus Z??hir?ya 9353, where it is attributed to al-T?ant??w?.

A considerably less sophisticated sundial made by Ibn al-Sh?t?ir in A. H. 767 (1365/1366) is preserved in the Ah?madiyya madrasa in Aleppo. It is contained in a box called s?and?q al-yaw?q?t (“jewel box”), measuring twelve centimeters by twelve centimeters by three centimeters. It could be used to find the times (al-maw?q?t) of the midday and afternoon prayers, as well as to establish the local meridian and, hence, the direction of Mecca⁶.

Astrolabes and Quadrants . Among the astronomers of Damascus and Cairo in the thirteenth, fourteenth, and fifteenth centuries , many varieties of quadrants rivaled the astrolabe as a handy analog computer. Certain instruments devised for solving the standard problems of spherical astronomy for any latitude were more of theoretical interest than of practical value. It should also be remembered that tables were available to Ibn al-Sh?t?ir for solving all such problems with greater accuracy than was possible using any of the several available varieties of quadrant.

Ibn al-Sh?t?ir wrote on the ordinary planispheric astrolabe and designed an astrolabe that he called al-?la al-j?mi‘a (“the universal instrument”)⁷. Ibn al-Sh?t?ir also wrote on the two most commonly used quadrants. al-rub‘ al-muqant?ar?t (the almucantar quadrant) and al-rub‘ al-mujayyab (the sine quadrant). The first bore a stereographic projection of the celestial sphere for a particular latitude, and the second a trigonometric grid for solving the standard problems of spherical astronomy. A given instrument might have markings of each kind on either side.

Two special quadrants designed by Ibn al-Sh?t?ir were called al-rub‘ al-‘Al?‘’? (the ‘Al?‘? quadrant, the appellation being derived from ‘Al?’ al-D?n, part of his name) and al-rub‘ al-t?mm (the “perfect” quadrant). Both quadrants were modifications of the simpler and ultimately more useful sine quadrant. No examples of either are known to survive. The ‘Al?‘? quadrant bore a grid, like the sine quadrant, of orthogonal coordinate line dividing each axis into sixty (or ninety) equal parts and also a family of parallel lines joining corresponding points on both axes. (In modern notation, if we denote the axes by x=0 and y=0, and the radius of the quadrant by R=60, the grid consists of the lines x=n, y=n, x+y=n, for n= 1, 2,...,R.) Ibn al-Sh?t?ir described how to use the instrument for finding products, quotients, and standard trigonometric functions, and for solving such problems as the determination of the first and second declination and right ascension for given ecliptic longitude, the length of daylight and twilight for a given terrestrial latitude and solar longitude, and the time of day for a given terrestrial latitude, solar longitude, and solar altitude. The “perfect” quadrant bore a grid of two sets of equispaced lines drawn parallel to the sides of an equilateral triangle inscribed in the quadrant with one axis as base. (In algebraic notation, the grid consisted of lines y=±x tan 60° + n, for n=1,2,...,60.) The instrument could be used for solving the same problems as the ‘Al?‘? qualdrant. Ibn al-Sh?t?ir treatise on the perfect quadrant concludes with a hundred questions and answers on topics relating to spherical astronomy.

Mechanical Devices. The Arab historian al-S?afad? reported that he visited Ibn al-Sh?t?ir in a.h. 743 (1343) and inspected an “astrolabe” that the latter had constructed. His account is difficult to understand, but it appears that the instrument was shaped like an arch, measured three-quarters of a cubit in length, and was fixed perpendicular to a wall. Part of the instrument rotated once in twenty-four hours and somehow displayed both the equinoctial and the seasonal hours. The driving mechanism was not visible and probably was built into the wall. Apart from this obscure reference we have no contemporary record of any continuation of the sophisticated tradition of mechanical devices that flourished in Syria some two hundred years before the time of Ibn al-Sh?t?ir.

Later Influence. There is no indication in the known sources that any Muslim astronomers after Ibn al-Sh?t?ir concerned themselves with non-Ptolemaic astronomy. The z?jes concerned al-K?sh? and of Ulugh Beg (Kennedy, nos. 20 and 11), compiled in Samarkand in the first half of the fifteenth century were the only astronomical works of major consequence prepared by Muslim astronomers after Ibn al-Sh?t?ir: and they are based on strictly Ptolemaic planetary theory following the tradition of the thirteenth century ?lkh?n? z?j of al-T??s? (Kennedy, no. 6). Nevertheless, later astronomers in Damascus and Cairo prepared commentaries on, and new versions of, Ibn al-Sh?t?ir Z?j al-jad?d. His z?j was used in Damascus for several centuries, but it had to compete with adaptations of other works in which the planetary mean motion tables were modified for Damascus: a recension of al-T??s?’ ?lkh?n? z?j prepared by al-H?alab?; (fl. ca. 1425, Suter, no. 434); a recension of the z?j of Ulugh Beg prepared by al-S??lih?? (fl. ca. 1500, Suter no. 454): and a recension of al-K?sh?’ Kh?q?n? z?j prepared by Ibn al-Kayy?l (fl. ca. 1550, Suter, no. 474).

Another Damascus astronomer, Ibn Zurayq (fl. ca. 1400, Suter, no. 426), prepared an abridgment of Ibn al-Sh?t?ir’s z?j, called al-Rawd? al-‘?t?ir, that was very popular. Al-H?alab?, in one source (see Kennedy, no. 34) reported to have been a muwaqqitat the Hagia Sofia mosque in Istanbul but more probably to be identified with the Damascus astronomer mentioned above, compiled a z?j called Nuzhat al-n?z?ir;, based on that of Ibn al-Sh?t?ir. An astronomer named al-Nabulush? (fl. ca. 1590), who may have worked in Damascus or Cairo, compiled a z?j called al-Misk al-‘?t?ir based on al-Z?j al-jad?d.

In Cairo, al-Kawm al-R?sh? (fl. ca. 1400, Suter, no. 428) adapted Ibn al-Sh?t?ir planetary tables to the longitude of Cairo in his z?j entitled al-Lum‘a. The contemporary Egyptian astronomer Ibn al-Majd? (Suter, no. 432; Kennedy, no. 36) compiled another set of planetary tables entitled al-Durr al-yat?m, from which planetary positions could be found with relative facility from a given date in the Muslim lunar calendar; he stated that the parameters underlying his tables were those of Ibn al-Sh?t?ir. Another Egyptian astronomer, Jam?l al-D?n Y?suf al-Khit??‘?, prepared an extensive set of double-argument planetary equation tables based on those of Ibn al-Sh?t?ir.

Each of these works was used in Cairo for several centuries, alongside solar and lunar tables extracted from the H??kim? z?j of the tenth-century astronomer Ibn Y?nus (Kennedy, no. 14) and recensions of the z?j of Ulugh Beg prepared by Ibn Abi I-Fath? al-S??f? (fl. ca. 1460; Suter, no. 447; Kennedy, no. 37) and Rid?w?n ibn al-Razz?z (fl. ca. 1680; Kennedy, no. X209). The popularity of Ibn al-Sh?t?ir in Egypt is illustrated by the fact that a commentary on al-Kawm al-R?sh?’s z?j al-lum‘a was written in the mid-nineteenth century by Muhammad al-Khud?r?. There is evidence that Ibn al-Sh?t?ir z?j was known in Tunis in the late fourteenth century but was replaced by a Tunisian version of Ulugh Beg’s z?j. None of the numerous works purporting to be based on Ibn al-Sh?t?ir z?j has been studied in modern times.

Ibn al-Sh?t?ir principal treatises on instruments remained popular for several centuries in Syria, Egypt, and Turkey, the three centers of astronomical timekeeping in the Islamic world. Thus his influence in later Islamic astronomy was widespread but, as far as we can tell, unfruitful. On the other hand, the reappearance of his planetary models in the writings of Copernicus strongly suggests the possibility of the transmission of some details of these models beyond the frontiers of Islam.

NOTES

1. A critical edition of the Arabic text and an English translation have been prepared by V. Roberts but both are unpublished.

2. A brief summary of the contents of this z?j has been published by E. S. Kennedy.

3. These have been discussed in the secondary literature by E. S. Kennedy and W. Hartner, but more research is necessary before the extent of Ibn al-Sh?t?ir debt to them and to other sources can be ascertained.

4. Ibn al-Sh?t?ir’s plantetary theory has been described in series of four articles by E.S. Kennedy, V. Roberts, and F. Abbud Before the theory may be more fully understood, however, the complete text of the Nih?yat al-s?l must be published with translation and commentary, and also the relevant parts of the Z?j al-jad?d, including the planetary tables It is also necessary to continue the search for his other works amidst the vast numbers of Arabic astronomical manuscripts which survive in libraries around the world untouched by modern scholoarship.The manuscript (no. 66/5) in the Kh?lidiyaa Libray, Jerusalem, of a work attributed to Ibn al-Sh?t?ir that is entitled Ris?la fi ’l-hay‘a al-jad?da (“Treatise on the New Astronomy”) is unfortunately only a copy of his Nih?yat al-s’l

5. For the other contents of al-Z?j al-Jad?d. see the summary by E.S. Kennedy. The topics treated are the standard subjects matter of z?jes, although some of Ibn al-Sh?t?ir’s tables for parallax and lunar visibility are of a kind not attested in earlier works.

6. A treatise on the use of Ibn al-Sh?t?ir’s “jewel box” was written by the Egyptian astronomer Ibn Abi ’l-fath? al-S??fi (fl, ca. 1475: Suter, no 447/7).

7. Two examples of this instrument, both made by Ibn al-Sh?t?ir in a.h. 738 (1337/1338) are preserved at the Museum of Islamic Art, Cairo, and the Bibliothèque Nationale. Paris. but have not been properly studies. Another astrobe made by him in 1326 is preserved at the Observatoire National, Paris.

BIBLIOGRAPHY

I. Oringinal Works. For list of Ibn al-Sh?t?ir’s works and MSS there of, consult H. Suter, no 416; C.Brockelmann, Geschichte der arabischen Literatur 2nd ed., II (Leiden, 1943–1949), 156, and supp., II (Leden, 1937–1942), 157; and the much less reliable A. Azzawi, History of Astronomy in Iraq (Baghdad, 1958), 162–171, in Arabic.

The following titles are attributed to Ibn al-Sh?t?ir: N Planetary astronomy, Nih?yat al-gh?y?t fi ’l-a‘m?l al-falakiyy?t, and astronomical handbook with tables (not extant but mentioned in Z?j Ibn al-Sh?t?ir); Nih?yat al-s?l f ‘? tas?h??h? al-us?l, on planetary theory (extant); Ta ‘l?q al-ars??d, on observations (not extant but mentioned in Z?j Ibn al-Sh?t?ir); and Z?j al-jad?d Ibn al-Sh?t?ir or al-Z?j al-jad?d, astronomical handbook with table (extant).

His sole work on astronomical timekeeping is a set of prayher tables of latitude 34° (extant in MS Cairo D?r al-Kutub m?q?t 1170, fols. 11r–22v; intro in Ms Leiden Universitesbiblionthek or. 1001, fols. 108r–113r).

works on instruments are al-Naf‘ al-‘?mm fi ’l-‘amal bi-l-rub‘ al t?mm li-maw?q?t al-Isl?m, on the “perfect” qudrant (extant); Id??h al Mughayyab fi ’l-‘amal bi-l-rub‘ al-mujayyab, on the since quardrant (extant); Tuh?fat al-s?mi‘ ’l-‘amal bi-l-rub‘ al-j?mi‘, on the “universal” quadrant (not extant, but see Nuzhat al-s?mi‘ ’l-‘amal bi-l-rub‘); Nuzhat al-s?mi‘ ’l-‘amal bi-l-rub‘, a shorter version of Th?ufat al-s?mi‘ (extant); al-Ashi‘‘a al l?mi‘a fi ’l-‘amal bi-l-?la al j?m?‘a, on the “Universal instrument (extant): al-R?awd??t al-muzhir?t fi ’l-‘amal bi-l-rub‘ al muqant?ar?t, on the use if the almucantar quadrant (extant); Ris?la fi ’l-rub‘ al-‘Al?‘? on the ‘Al?‘? quadrant (extant): Ris?la fi ’l-as?t?url?b, on the astrolabe (extant): Ris?la fi us??l ‘ilm al-as?t?url?b, on the principles of the astrolable (extant); and Mukhtas?ar fi ’l-‘amal bi-l-as?t?url?b wa-rub‘ al-muqant?ar?t wa-l-rub‘ al-mujayyab, on the use of astrolable, almuncantar quadrant, and sinde quadrant (extant).

Miscellaneous writing are Fi ’l-nisba al sitt?niya, probably on sexagesimal arithmetic (extant): Urj?za fi ’l-Kaw?kib, poem on the stars (extant): Ris?la fi istikhar?j al-ta‘r?kh, on calendrical calculations (extant): and Kit?b al-jabr wa-l-muq?bala, on algebra (Azzawi, p. 165, states that there is a work with this title by Ibn al-Sh?t?ir preserved in Cairo).

II. Scondary Literature. References to suter and Kennedy are to the basic bibliographical sources: H. Suter, Die Mathematiker und Astronomen der Araber und ihre Wereke (Leipzig, 1900), and E. S. Kennedy, “A Survey of Islamic Astronomical Tables,” in Transactions, of the American Philosophical Society, n.s.46 , no. 2 (1956), 121–177.

The only biographical study thus far is E. Wiedemann, “Ibn al-Shât?ir, ein arabischer Astronom aus dem 14. Jahrhundert,” in Sitzungsberichte der physikalisch medizinischen Sozietät in Erlangen60 (1928), 317–326, repr in his Aufätze arabischen Wissenschaftsgeschichte II(Hildesheim, 1970), 729–738.

On the z?j of Ibn al-Sh?t?ir, consult E. S. Kennedy, “A Survey of Islamic Astronomical Tables,” in Transactions of the American Philosophical Society, n.s. 46 no.2 (1956) no. 11 See also A Sayili, The Observatory in Islam (Ankara, 1960), 245.

On Ibn al-Sh?t?ir’s planetary theory, see the following, listed chronogically: V. Roberts, “The Solar and Lunar Theory of Ibn al-Sh?t?ir: A Pre-Copernican Copernicam Model,” in Isis48 (1957), 428–432: E. S. Kennedy and V. Roberts, “The Planetary Theory of Ibn al-Sh?t?ir,” ibid., 50 (1959), 227–235: F. Abbud, “the Planetary Theory of Ibn al-Sh?t?ir: Reduction of the Geometric Meodels to Numerical Tables, ibid., 53 (1962), 492–499: V. Roberts, “The Planetary Theory of Ibn al-Sh?t?ir: Latitudes of the Planets,” ibid., 57 (1966), 208–219: E. S. Kennedy, “Late Medieval Planetary Theory” ibid., 57 (1966), 363–378: and W. Hartner “Ptolemy, Azarquiel, Ibn al-Sh?t?ir, and Copernicus on Mercury: A Study of Parameters,” in Archives internationales d’ historie des sciences24 (1974), 5–25.

The possible transmission of late Islamic planetary theory to Europe is disccused in W. Hartner, “Nas??r al-D?n’s Lunar Theory,” in Physis: Rivista Internazionale di storia della scienza II (1969), 287–304: E. S. Kennedy, “Planetary Theory in the Medieval Near East and Its Transmission to Europe,” and W. Hartner , “Trepidation and Planetary Theories: Common Features in Late Islami and Early Renaisannce Astronomy,” in Accademia Nazionale dei Lincie, 13° Convegno Volta, (1971), 595–604 and 609–609, respectively; I. N. Veseslovsky, “copernicus and Nas??r al-D?n al-T??s?,” in journal for the History of Astronomy, 4 (1973), 128–130 G. Rosinska, “Nas??r al-D?n al-T??s? and Ibn al-Sh?t?ir in Cracow?” in Isis, 65 (1974), 239–243; and W. Hartner, “The Astronomical Background of Nicolaus Copernicus,” in Studia Copernicana (1975).

On the quadrants designed by Ibn al-Sh?t?ir, see P. Schmalzl, Zur Geschichte des Quadranten bei den Arabern (Munish, 1929). On his sundial, see L. Janin, “Le cadran solaire de la mosquée Umayyade à Damas,” in Centaurus, 16 (1971), 285–298. Ibn al-Sh?t?ir’s “jewel box” is described and illustrated in S. Reich and G. Wiet, “Un astrolabe syrien du XIV^e siècle,” in Bulletin de I’Institut fransçais d’archéologie orientale du Caire, 38 (1939), 195–202. See also L. A. Mayer,Islamic Astrolabists and Their Works (Geneva, 1956), 40–41.

David A. King