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Al-Bitruji Al-Ishbili, Abu Ishaq


also known as Alpetragius (his surname probably derives from Pedroche, Spain, near Cordoba; fi. Seville, ca. 1190)

astronomy, natural philosophy.

The outstanding astronomer among the Spanish Aristotelians, al-Bitrūjī may have been from Los Pedroches (Bitrawsh), Cόrdoba province. In his only known work, Kitāb fī l-hay’a (“Book of Astronomy”), he says that he is a pupil of Ibn Tufayl (d. 1185), who was already dead by the time the book was finished (I , 61: II, 49).1 Since Michael Scot completed the Latin translation of al-Bitrūjī’s work as De motibus celorum circularibus in 1217, the Kitāb must be dated between those two years. According to YahŪda ibn Solomon Kohen of Toledo, al-Bitrūjī died in 1217; the date is doubtful, however, because of the coincidence with the translation by Michael Scot. The Kitāb fī l-hay’a was translated into Hebrew by Moses ibn Tibbon in 1259; in 1247 Yahūda ibn Solomon Kohen had produced an abridged version. The Hebrew text was translated into Latin by Qalonymos ben David.

According to al-Bitrūjī, Ibn Tufayl expounded an astronomical system that differed from Ptolemy’s and did not use eccentrics or epicycles. Although he promised to develop the system in a book, Ibn Tufayl seems not to have done so. In view of the agreements between al-Bitrūjī’s astronomical system and the much less elaborate ideas of Ibn Rushd, F. J. Carmody suggests that both were derived from the work of Ibn Tufayl.

Al-Bitrūjī considered Ptolemy’s system to be mathematical, not physical, with a recognizable exactitude and precision valuable to the astronomical computer (I , 59–60; II , 37–41). Therefore all the parameters in the Kitāb fīʾ l-hayʾa are derived from the Almagest. Al-Bitrūjī was familiar with Jabir ibn Aflah’s criticisms of certain defects in the Ptolemaic system (I , 113; II , 269; I , 122; II , 309) and the problem of the order of the spheres of the inferior plants (I , 53; II , 5; I , 124, 125; II, 315, 321). Jābir’s I slāh al-Majistī is also one of the ways through which the sine theorem was introduced into Spain (I, 98; II, 207).

Nevertheless, the main “defect” that al-Bitrūjī found in the Ptolemaic system was the incompatibility of its basic principles with Aristotle’s physical concepts. If the the source of all motion in the universe is the Prime Mover, situated in the ninth sphere, it would be absurd to suppose that the Prime Mover transmits motions in opposite directions to the different spheres–the diurnal motion from east to west, the movements of longitude from west to east (see I, 53–57; II, 5–29). One must accept that the motion of the ninth sphere– the fastest, strongest, and simplest – is transmitted to the lower spheres, which are slower in proportion to their distance from the Prime Mover. Precession of the sphere of the fixed stars and the movements of longitude of the planetary spheres constitute a sort of slowing down (taqsīr, incurtatio) that affects the diurnal motion, the transmission of which from the ninth sphere is explained by using the theory of impetus (I , 78; II , 137). Thus Saturn would be the fastest moving plants and the moon the slowest (see, I , 63–68; II , 57–91).

These ideas were not original with al-Bitrūjī. Lucretius (De rerum natura,vv. 621 ff.) attributes them to Democritus, and Alexander of Aphrodisias credits them to the Pythagorean. Theon of Alexandria took them up again in his commentary on the Almagest (I, 7), as did Ibn Rushd. The motion transmitted from the ninth sphere rebounds in the sublunar world and is transmitted to the element fire, producing the shooting stars(?) (shihāb or ashbāh al-kawākib); it is then transmitted to the elements air and water, in the latter case producing the tides and waves (I , 64; II , 63–69). Another anti-Ptolemaic argument of Aristotelian origin used by both Ibn Rushd and al-Bitrūjī is the horror vacui necessarily arising from the movements of the eccentric spheres (I , 61; II , 47–49). Al-Bitrūjī also held antiempirical views: he did not trust human senses, given the distance between the observer and the spheres, and put his faith in human reason (I , 66; II , 79–81).

On these bases al-Bitrūjī elaborated a system that sought only to give qualitative explanations, a limitation of’ which he was quite aware (I , 76: II , 127–129; I , 154; II , 427–429). He postulated the existence of a ninth sphere, the Prime Mover, the discovery of which he attributed to the “modern” astronomers. This sphere moves around the poles of the equator, from east to west, completing one revolution in twenty-four hours (I , 66; II 77: I ,76: II , 129). Next is the eighth sphere, that of the fixed stars, which is moved by the motion of the ninth; its poles (those of the ecliptic) describe two small circles around the poles of the universe, since they participate in the diurnal movement of the ninth sphere.

With this scheme al-Bitrūjī constructed a model of variable precession. B. R. Goldstein has calculated that in it, if k is the mean value of precession, the maximum value is 1. 1 k and the minimum is 0.9 k. This indicates that al-Bitrūjī did not accept the theory of trepidation, although he spoke of “accession” (idbār) and “recession” (idbār): but here the sense is that “accession” refers to precession at an amount greater than the mean value, and “recession” refers to precession at an amount less than the mean value.

Like a1-Zarqālī,2 al-Bitrūjī, when presenting a brief history of the theories of precession and trepidation, attributed to Theon of Alexandria the belief in a combination of the trepidation of the equinoxes along an arc of eight degrees with the Ptolemaic precession of one degree in one hundred years. This may have been a forerunner of the models of variable precession that were used in Spain by the

Alfonsine astronomers and in the Arab world by Nasīr al-Din al-Tūsī and Qutb al-Dīn al-Shīrāzī, and whose echo reaches Copernicus.

On the other hand, the fixed stars were subject to diurnal motion and to precession that moved them, so that they did not describe a perfect circle but a curve called lawlab halazūnī by-Bitruji and, traditionally, interpreted as a spiral. Plato s(Timaeus 39A) had spoken of the spiral motion of the heavenly bodies, but the source used by al-Bitrūjī probably was Aristotle. The first mentions in Kitāb fīʾ l-hayʾa (I , 61; II , 49; I , 62: II , 51, 53) of the lawlabī motion are citations of, or references to De caeloII , 8, in which Aristotle states that the heavenly bodies have two types of motion – δίνησις and κύλισις–the first of which suggests the concept of a vortex and could he interpreted by the commentators as a spiral. Theon of Alexandria (commentary on the Almagest, I, 2) also spoke of spiral motion of the heavenly bodies, as did lbn Rushd and Alhertus Magnus, both of whom attributed the concept to Aristotle.

The lawlabī motion also affected the planets (I . 101; II , 219–221). The planetary models were based on the following schema (see Figure 1 ): Planet A according to al-Bitrūjī, always was ninety degrees from its pole K, moving with the motion of K. The movement in longitude occurred in a circle parallel to the equator, the polar deferent HT, which is the circle traced by the poles of the ecliptic around the poles of the universe. The motion in anomaly takes place on the polar epicycle KSL, which has a radius equal to the maximum latitude of the planet and a center T that moves on circle HT. Al-Bitrūjī stated that the motions of T on HT and of the planetary pole on KSI are in the same direction (I, 110, II, 257) and, speaking of Jupiter (1. 11 7: 11. 289), added that T moves in the direction of signs, thus abandoning the basic principle of only one movement, the diurnal, from east to west.

With this model al-Bitrūjī could justify the variations in the velocity of the planet, which-in the case of Saturn, for example-would be average when its pole was at K and L; maximum when the pole was approximately at S: decreasing when the pole was between S and L; and at its stationary point, beginning afterwards to retrograde, when the pole was between L, and K, The lunar model was very similar to the planetary one, although al-Bitrūjī added some modifications in order to account for its variable motion and lack of stationary points and retrogradation.

An important aspect of al-Bitrūjī’s planetary theory is his discussion of the order of the inferior planets. After presenting the history of the question, he gave the order as moon. Mercury, sun, Venus Mars, and so on: Mercury was slower than the sun, which was slower than Venus. He rejected the objections made to the traditional order (moon Mercury, Venus, sun) based on the fact that the transits of Mercury and Venus across the sun are not visible. He pretended that Mercury and Venus have their own light and do not receive it from the sun, as the moon does (I , 123- 125; II , 313–323). Therefore their transits cannot be perceptible.

As for the solar model, al-Bitrūjī began by considering an epicyclic model similar to the planetary ones; but he rejected it because the radius of the epicycle would have to be extraordinarily small in order not to produce a perceptible latitude. He solved the problem by moving Ptolemy’s eccentric to the north pole of the equator. Then the pole of the solar sphere would describe a circle around the pole of the universe, and the sun would always remain (in theory) ninety degrees from its pole, which would be moving twice as fast as the sun.

E. S. Kennedy states: “AI-Bitrūjī’s system is a clever adaptation, with Ptolemaic parameters, of a device invented by Eudoxus (fl. ca. 360 B.C.) and incorporated into Aristotelian cosmology.”3 He thus demonstrates that the Eudoxian model for Saturn is equivalent to al-Bitrūjī’s. B. R. Goldstein, on the other hand, rejects any Eudoxian influence and favors that of al-Zarqālī: al-Bitrūjī cites a work by the latter, Fī harakat al-iqbāl wa’l-idbār (“On Accession and Recession”), that can be identified with the Treatise on the Movement of the Fixed Stars. In the Treatise al-Zarqālī justifies the positions of the equinoxes with a polar deferent and an epicycle. Goldstein considers this the inspiration for al-Bitrūjī, who substituted a planet for the equinox.

Al-Bitrūjīs astronomical system spread through much of Europe in the thirteenth century. William the Englishman cited it; and Grosseteste referred to it in several works, even plagiarizing from it in his refutation of the Ptolemaic system. In the second half of the century there were disputes between supporters of Ptolemy and Aristotelian defenders of al-Bitrūjī Albertus Magnus spread al-Bitrūjī’s ideas in simplified form, although he ultimately preferred the Ptolemaic system. His De caelo, or a similar work, may have been the source in which Dante found the ideas of al-Bitrūjī: the same may be true found the ideas of al-Bitrūjī; the same may be true of Vincent of Beauvais in his Speculum naturale. Richard of Middleton also chose the Ptolemaic system, rejecting the views of Ibn Rushd and al-Bitrūjī. Roger Bacon, in his Communia naturalium, expounded al-Bitrūjī’s system in detail and compared it with Ptolemy’s: parts of this work have been brought together in Liber tertius Alpetragii in quo tractal de perspectiva. In his Opus maius Bacon discussed al-Bitrūjī’s theory of the tides. Others who considered the problem and opted for the Ptolemaic system were Bernard of Verdun, Giles of Rome, Pietro d’Abano, and John of Jandun.

The fourteenth century saw the definite return of the Ptolemaic theory, although Henry Bate of Ma-lines toward the end of the previous century and Henry of Hesse sought to construct astronomical systems without eccentrics and epicycles.4 The system of Henry of Hesse, however, seems to be related not to al-Bitrūjī’s but to that of Abū Ja’far al-Khāzin (died between 961 and 971), although the connection is not clear.

Among Hebrew authors, besides the abridgment of the Kitāb by Yahūda ibn Solomon Kohen (1247), Isaac Israeli of Toledo (fl. 1310) seems to refer to al-Bitrūjī in his Liber Jesod Olam when speaking of ha-īsha ha-mar’ʾīsh (“the man [whose theory] shook [the world]”), who lived until 1140 and opposed the Ptolemaic system. Isaac Israeli seems quite skeptical, however, about the reality of the new system, since it cannot be verified. Levi ben Gerson, in his Sefer Tekunah, discusses al-Bitrūjī’s model for Saturn, introducing corrections that lead Goldstein to believe that the discussion is based on memory and that Levi did not have al-Bitrūjī’s text before him. In general, Levi ben Gerson rejects the system for not agreeing with observed reality and indicates that various philosophical arguments of al-Bitrūjī’s are refuted in other chapters of his Mil-hamot Adonai.

The diffusion of al-Bitrūjī’s ideas continued in the fifteenth and sixteenth centuries. At the end of the fifteenth, the astrologer Simon de Phares cited him (but had not read his work) and attributed fantastic ideas to him. Regiomontanus wrote a brief work on al-Bitrūjī’s errors, in which he used both astronomical arguments–parallax, the impossibility of explaining total and annular solar eclipses if the moon is always at the same distance from the earth-and astrological ones. In some instances his criticism reflects misunderstanding of al-Bitrūjī’s system: for instance, he states that the latter placed Mercury and Venus above the sun. In the sixteenth century Copernicus (De revolutionibus, I , 10) cited his system in connection with theories of the order of the inferior planets.


1. The references in parentheses are to Goldstein’s English trans.(I )with Arabic text(II ).

2. J.M.Millás Vallicrosa, Estudios sobre Azarquiel(Madrid Grananda, 1943–1950), 275–276.

3.Speculum,29 (1954), 248.

4. Claudia Kren, “Homocentric Astronomy in the Latin West: The De reprobatione eccentricorum et epiciclorum of Henry of Hesse,” in Isis, 59 (1968), 269–281.


I. Original Works. Bernard R. Goldstein has edited, with English trans.,the Arabic text of Kitāb fīʾ l-hayʾa(facs.of MS Escorial 963 with variants from MS Istanbul Seray 3302) and the Hebrew trans., by Moses ibn Tibbon: Al-Bitrūjī: On the Principles of Astronomy....2 vols.(New Haven-London, 1971). The Latin trans. by Michael Scot has been edited by Francis J. Carmony as Al-Bitrūjī De motibus celorum...(Berkeley-Los Angeles, 1952). The Latin version by Qalonymos ben David was published with Sacrobosco’s Sphere as Alpetragii arabi planetarum theorica physicis rationibus probata nupperime latinis litteris mandata a Calo Calonymos hebreo napolitano(Venice, 1531).

II. Secondary Literature. See F.J.Carmody, “Regiomontanus Notes on alBitrûjî’s Astronomy,” in Isis, 42 (1951), 121–130; and “The Planetary Theory of Ibn Rushd,” in Osiris, 10 (1952), 556–586; J.L.E.Dreyer, A History of AQstronomy from Thales to Kepler(repr.New York, 1953), 264–267, 278; P.Duhem, Le système du monde,II(Paris, 1914), 146–156; Léon Gauthier, “Une réforme du système astronomique de Ptolémée tentée par les philosophes arabes duXII e siècle,” in Journal asiatique, 14 (1909), 483–510, reproduced, with simplifications and additions, in Gauthier’s Ibn Rochd(Avèrroes)(Paris, 1948), 113–127; Bernard R.Goldstein, “On the Theory of Trepidation According to Thābit b.Qurra and al-Zarqāllu and Its Implications for Homocentric Planetary Theory,” in Centaurus, 10 (1964), 232–247; and “Preliminary Remarks on Levi ben Gerson’s Contributions to Astronomy,” in Proceedings of the Israel Academy of Sciences and Humanities, 3 (1969), 239–254; E.s.Kennedy, review of Carmody’s De motibus, in Speculum, 29 (1954), 246–251; Bruno Nardi, “Dante e Alpetragio,” in Giornale Dantesco, 29 (1926), 41–53; E.Rosen, “Copernicus and al-Bitrūjī,” in Centaurus, 7 (1961), 152–156: and George Sarton, Introduction to the History of Sciences, II(Baltimore, 1931), 399–400, also 18, 620, 749–750, 757, 925, 930, 937, 952, 956, 964, 990, 995; and III(Baltimore, 1947–1948), 440, 539, 544.

Julio SamsÓ

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Al-Biṭrūjī Al-Ishbīlī, Abū Isḥāq

also known as Alpetragius

(his surname probably derives from Pedroche, Spain, near Cordoba; fl. Seville, ca. 1190)

astronomy, natural philosophy.

Al-Biṭrūjī’s only extant work is De motibus celorum, originally written in Arabic. He was a contemporary of Ibn Rushd (Averroës), and his astronomical system aroused much interest among such Chiristan natural philosophers as Albertus Magnus, Robert Grosseteste, and Roger Bacon. For a detailed study of his life and work, see Supplement.

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"Al-Biṭr." Complete Dictionary of Scientific Biography. . 23 Aug. 2017 <>.

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"Al-Biṭr." Complete Dictionary of Scientific Biography. . Retrieved August 23, 2017 from