Astronomy was first cultivated in Al-Andalus, the part of the Iberian Peninsula under Islamic rule, during the early ninth century. This was mainly due to the fact that astronomy was necessary for the practice of astrology. The Muslim rulers relied on the predictive powers of a team of astrologers to provide them with useful information for decision-making. A group of poet-astrologers who served the courts of the emirs al-Ḥakam I (r. 796–822) and his son ʽAbd al-Raḥmān II (r. 822–852) are well attested in historical sources. The historian Ibn Ḥayyān recorded their names in his al-Muqtabis fī tārīẖ al-Andalus. A chapter titled “Anecdotes of the Astrologers with the Emir ʽAbd al-Raḥmān II,” describes an attempt by the sovereign to test the accuracy of the predictions made by his astrologers. It is clear from this account that ʽAbd al-Raḥmān II and the members of his court were greatly interested in both astrology and astronomy. The emir himself is credited with the ability to calculate planetary positions, and a musician like Ziryāb is presented as having a deep knowledge of both disciplines. Ibn Ḥayyān also sheds light on the books brought to Córdoba from Baghdad by the astrologer ʽAbbās b. Nāṣiḥ (fl. ca. 800–850). Included is a list of what are presumably astronomical tables—known as zījes in Arabic—titled al-Zīj, al-Qānūn, al-Sindhind, and al-Arkand. The reference to al-Zīj is too general for the purposes of identification, but Al-Qānūn probably refers to Ptolemy’s Handy Tables. Al-Sindhind is likely the Indo-Iranian zīj compiled by al-Khwārizmī in Baghdad during the first half of the ninth century; its use in Al-Andalus is well documented a century later. And al-Arkand is another set of Indian astronomical tables, introduced in Baghdad in the eighth century.
At the time, astronomy raised suspicions in orthodox circles due to its connections with astrology, and could only be cultivated under the rule of open-minded authorities. It is for this reason that there is little surviving information about astronomical and astrological practices following the death of ʽAbd al-Raḥmān II in 852. It was not until a century later that astronomy seems to have been revived, reaching maturity with the important figure of Maslama al-Majrīṭī (d. 1007). Maslama revised and adapted the coordinates of al-Khwārizmī’s Sindhind tables to Córdoba. He also studied Ptolemy’s Almagest, as well as the Ptolemaic tables compiled by al-Battānī (c. 858–929). Maslama was particularly interested in stereographic projection, as used in the making of the astrolabe and similar instruments, and improved Ptolemy’s Planispherium, the classical work in which this type of projection was described. Two of his disciples, Ibn al-Ṣaffār and Ibn al-Samḥ, applied his findings in treatises on the construction and use of the astrolabe. These works were introduced in the Latin world through two compilations, De compositione and De operatione astrolabii, made during the twelfth and thirteenth centuries.1 Through these compilations, Maslama’s influence can be seen in treatises on the astrolabe written during the thirteenth and fourteenth centuries: one in Castilian by Alfonso X, another in French by Pèlerin de Prusse, and a third in English by Geoffrey Chaucer.
Orthodoxy returned to Al-Andalus under the leadership of al-Manṣūr ibn Abī ʽĀmir (981–1002), prime minister for the child emir Hishām II, who was too young to rule. Under the caliphate of Hishām’s father, al-Ḥakam II (961–976), Al-Andalus had basked in one of the most accomplished periods of its cultural history. Al-Manṣūr destroyed this legacy, ordering selective manuscripts from the great library of al-Ḥakam II to be burned, including books on astrology and astronomy. Soothsayers and astrologers were arrested, tortured, and executed for predicting the end of al-Manṣūr’s regime. Such predictions were still being made long after al-Manṣūr’s death, during the period when his two sons held political power. Maslama, among others, predicted that the conjunction of Saturn and Jupiter in 1007 would portend the overturn of the regime, that the state would fall into other hands, and that there would be killings and famine. He was proved right. After the deaths of al-Manṣūr’s sons in 1008 and 1009, a period of anarchy and civil wars followed. Between 1009 and 1031, seven different monarchs occupied the caliphate.
In 1031, the Córdoban caliphate came to an end. Political unity was lost, and the state was divided into a set of petty kingdoms. This arrangement lasted from 1031 to 1085, a period that could be considered the golden half-century of Andalusian science. The loss of political unity had two contradictory consequences. On the one hand, the number of patrons who fostered scientific research grew. Each sovereign was interested in having at his service physicians, astrologers, and poets who would enhance his glory and importance. On the other hand, Andalusian scientists of this period seem to have believed that an adequate scientific education could be obtained without the riḥla, or traditional journey, to the East, which completed the standard education of any young man belonging to a family who could afford it. None of the sovereigns of the petty kingdoms seem to have been able to afford the expense involved in receiving information about, let alone buying, new publications from Eastern capitals. The result was a long period of cultural isolation. As a result, a distinctive approach to astronomy developed in Al-Andalus during this period, one that differed markedly from its Eastern counterpart.
Toledo, City of Science and Learning
During the eleventh century, Toledo became well known as a center for astronomical activity. This reputation was maintained in the twelfth and thirteenth centuries by the ongoing process of translating Arabic scientific texts into Latin.2 Yaḥyā al-Ma’mūn, who reigned between 1044 and 1075, was a member of the Banū Dhī l-Nūn, a Berber dynasty who ruled the kingdom of Toledo during the eleventh century. Yaḥyā’s honorary name, al-Ma’mūn, was likely chosen to emulate an Abbasid caliph with the same name, who had patronized the first program of astronomical observations undertaken in Baghdad and Damascus in around 830. Al-Ma’mūn sponsored numerous technological marvels, contributing to Toledo’s international reputation as the city of knowledge.3 During his reign, the engineer Aḥmad or Muḥammad ibn Khalaf al-Murādī published his Kitāb al-asrār fī natā’ij al-afkār (Secrets of the Results of Thoughts),4 which contains descriptions of 18 clepsydras, or water clocks. In the same period, Abū l-Qāsim b. ʽAbd al-Raḥmān, also known as al-Zarqāl, built a clepsydra-calendar that was used to mark the date of the lunar month.5 According to a description by the geographer al-Zuhrī (d. 1137), al-Zarqāl built two large basins in a house outside Toledo on the banks of the Tagus, near the Bāb al-dabbāghīn (Door of the Tanners). The basins were filled and emptied in consonance with the lunar phases. When the new moon appeared, the water began to flow, and the water level rose by 1/14 of the total volume of the basin per day. On the fourteenth day of the lunar month, the basin was full and, on the fifteenth, the level of water began to fall at the same rate. By the end of the month the basin was empty. If anyone removed or added water to the basin, the system automatically compensated for the excess or shortfall.
Another patron of astronomy in Toledo, even more important than al-Ma’mūn, was the qāḍī, or judge, Ṣāʽid (1029–1070).6 He became known as a historian and the author of the Kitāb ṭabaqāt al-umam (Categories of Nations), a world history of science containing abundant details about the development of science in Al-Andalus between the ninth and eleventh centuries.7 The Ṭabaqāt reveals the astronomical sources that were available in Toledo toward the middle of the eleventh century: Ṣāʽid knew the Greek classics, particularly Ptolemy’s Almagest, Geography, and Tetrabiblos, as well as Theon of Alexandria’s commentary on the Almagest and the Handy Tables. References are also made to Eastern Islamic sources of the ninth and tenth centuries, especially al-Khwārizmī, al-Ḥasan ibn al-Ṣabbāḥ, Thābit ibn Qurra, Abū Maʽshar, Ibn al-Ādamī, and al-Hamdānī. The Ṭabaqāt gives no indication that Ṣāʽid knew of any Eastern Islamic books published after 950, confirming that Andalusian culture was isolated after the fall of the Córdoban Caliphate.8
Ṣāʽid was himself an astronomer and a patron of astronomical research. The fourteenth-century astronomer Isaac Israeli, in his Yesod ha-ʽOlam, recounts that Ṣāʽid gathered a team of about twelve people, mostly comprising Muslims, but also including some Jews. They consecrated their lives to scientific and astronomical research, while Ṣāʽid furnished them with adequate means for their living. Israeli notes that they used instruments built and adjusted by an astronomer called Ibn al-Zarqālluh.
Ibn al-Zarqālluh and the Toledan Tables
Although he became known as Ibn al-Zarqālluh, his full name was Abū Isḥāq Ibrāhīm ibn Yaḥyā al-Naqqāsh al-Tujībī.9 He had been born near Toledo and trained as a metalsmith, becoming an instrument maker for Ṣāʽid, al-Ma’mūn, and, in 1048, the young ʽAbbādid prince of Seville, among others.10 Ibn al-Zarqālluh’s patrons in Toledo lent him the necessary literature to teach himself astronomy. He soon assumed a prominent position in the group assembled by Ṣāʽid, who mentions him in his Ṭabaqāt as belonging to the younger Toledan generation. Israeli reports that precision instruments were used by the group, but there is otherwise little further information about them.11
Ṣāʽid’s group had begun making observations by at least the early 1050s, leading to the compilation of a set of astronomical tables known as the Toledan Tables. These were adapted to the coordinates of Toledo using tabular information derived from al-Khwārizmī’s (fl. ca. 800–950) and al-Battānī’s Eastern zījes.12 The set survives through three Latin translations or adaptations, one of which has been attributed to Gerard of Cremona (d. 1187), and through a Greek translation made ca. 1330–1340. More than 128 manuscripts of these translations have survived, an indication of the compilation’s success throughout Europe.13 Chaucer mentions the Toledan Tables in his Canterbury Tales:
His tables Toletanes forth he broght,
Ful wel corrected, ne ther lakked noght,
Neither his collect ne his expans yeres,
Ne his rotes ne his othere geres,
As been his centres and his arguments,
And his proporcionels convenients
For his equacions in every thing.14
As can be seen from the work of the Toledan astronomers, Western Islamic medieval astronomers developed original and highly influential treatments of the precession of the equinoxes. Precession had been discovered by Hipparchus of Rhodes in the second century BCE. He became aware that the so-called fixed stars had a slow motion, from west to east, of about one degree per century. This parameter was confirmed four centuries later by Ptolemy. When Muslim astronomers began making observations in Baghdad and Damascus around the year 830, they discovered that the motion was considerably faster: one degree every 66 years. This was confirmed by their successors in the ninth and tenth centuries. The Toledan astronomers of the eleventh century were inclined to trust the validity of the observations made by all their predecessors. When faced with this discrepancy, the Toledan astronomers concluded that the motion of precession was not uniform.
This assessment meant that a new geometrical model was needed that could justify variable precession and remain in agreement with past observations. At least three scholars in the Toledan team worked on this problem and recorded their observations: Ṣāʽid himself, Ibn al-Zarqālluh, and Abū Marwān al-Istijī.15 The earliest known results of this work appear in the Liber de motu octave spere, extant in a twelfth-century translation from a lost Arabic original. Among its contents is a description of the model (Figure 1).16 The Liber de motu also contains a set of tables, designed for the computation of precession on a given date, which were included in the Toledan Tables.
Figure 1. Model of precession, as described in the Liber de motu octave spere.
As shown in Figure 1, the mean equinox, point A, is determined by the intersection of the equator QQ’ and the mean ecliptic AC. Point B rotates uniformly on the small equatorial epicycle B1B2 with center A. Its motion drags the ecliptic, whose point of intersection with the equator, or equinox, moves back and forth, always keeping the common point C at 90º from A. As shown in Figure 1, there are two positions for the moving ecliptic: E1B1C and B2E2C. E1 and E2 are the equinoxes corresponding to the moments at which point B occupies the positions B1 and B2. The arcs of the moving ecliptic E1B1 and B2E2 determine the increase in longitude due to precession at the two moments in question. Angle i is an arc GB, measured from the equator, which determines the position of point B on the equatorial epicycle. In this model a second equatorial epicycle must also exist, one whose center is located at a distance of 180º from point A. Precession will increase when point B rotates in the upper half of the equatorial epicycle, and it will decrease in its lower half. This is why the sources refer to an accession and recession motion.
Ibn al-Zarqālluh in Toledo and Córdoba
After the deaths of his patrons qāḍī Ṣāʽid in 1070 and al-Ma’mūn in 1075, Ibn al-Zarqālluh’s life in Toledo likely became increasingly difficult. Historical sources indicate that he left Toledo either at the beginning of the reign of al-Ma’mūn’s successor, Yaḥyā II al-Qādir (1075–1085), or as a result of the conquest of Toledo by Alfonso VI, king of Castile, in 1085. He moved to Córdoba, which belonged to the kingdom of Seville, where al-Muʽtamid (r. 1069–1091) reigned. Ibn al-Zarqālluh had already worked for this ruler in 1048, who was at the time the young ʽAbbādid prince of Seville.
Returning to the patronage of al-Muʽtamid, Ibn al-Zarqālluh continued working on astronomical instruments, including an armillary sphere,17 a universal astrolabe, and an equatorium. The astrolabe is the standard instrument for solving problems of spherical astronomy in relation to the motion of the sun and the stars. It is easy to use, but has one major drawback: a specific plate is required for each latitude. If the appropriate plate is not available, time-consuming calculations are required that yield only approximate results. During his stay in Toledo, Ibn al-Zarqālluh and his colleague ʽAlī ibn Khalaf invented two astrolabes that were not latitude dependent (Figure 2). The instrument was called a ṣafīḥa, or saphea in Latin and azafea in Castilian. It contains two sets of coordinates. The most complete set is equatorial, the equator itself represented by the diameter which goes from the upper ring, used to hang the instrument, to the bottom of the instrument. A second diameter represents the ecliptic and forms an angle with the equatorial diameter, known as the obliquity of the ecliptic, of approximately 23º 30'. A second, incomplete set of coordinates corresponds to the great circles of ecliptical longitude passing through the beginnings of the zodiacal signs. A ruler that rotates around the center of the instrument (not shown in Figure 2) corresponds to the local horizon. Moving the ruler until its end forms an angle with the northern equatorial pole equal to the local latitude yields a perfect representation of the three basic astronomical planes—equator, ecliptic, and horizon—that can be used to solve all manner of problems in spherical astronomy. Ibn al-Zarqālluh made different versions of his saphea. Two of them were dedicated to his royal patrons: al-ṣafīḥa al-ma’mūniyya to al-Ma’mūn of Toledo and al-ṣafīḥa al-ʽabbādiyya to al-Muʽtamid of Seville, of the ʽAbbādid dynasty.
Figure 2. Ibn al-Zarqālluh’s saphea
Ibn al-Zarqālluh also designed another astronomical instrument for al-Muʽtamid. The equatorium, as it was known, allowed for a graphical determination of planetary longitudes using very little computation. It was based on a series of Ptolemaic planetary scale models. Computing the longitude of a planet using a standard set of astronomical tables requires about 30 minutes’ work for a competent astronomer. If asked to cast a horoscope, the astronomer must then compute the longitudes of the sun, moon, Mercury, Venus, Mars, Jupiter, Saturn, and the ascending lunar node—the intersection of the moon’s orbit with the ecliptic. This process requires about four hours of cumbersome computation. Further time is required to divide the ecliptic into twelve unequal astrological houses using complicated mathematical procedures. Finally, there is also the time needed for the analysis of the horoscope and the elaboration of a prediction. This lengthy process made horoscopes an expensive product to prepare. These overheads could be reduced by computing devices: an astrolabe made the division of the houses fairly simple, while the equatorium facilitated the determination of planetary longitudes.
This was not the only instance in which Ibn al-Zarqālluh simplified the work of astrologers. He also compiled a perpetual almanac using the goal-year cycles developed by Babylonian astronomers to predict planetary motion.18 These cycles are characterized by the number of solar years during which a planet makes a particular number of synodic and zodiacal revolutions. Both figures are expressed as integers. These goal years have an obvious advantage for the astronomer. Assuming that a high degree of precision is not required, they allow for the computation of planetary positions for whole cycles—for example, eight years for Venus. In the following cycles, these positions will be repeated on the same dates. In the case of Venus, its longitude will be the same on January 1 of the first year as it is on January 1 of the ninth year, January 1 of the seventeenth year, and so on.
Ibn al-Zarqālluh wrote two short treatises on the construction and use of an equatorium. The former is only known through the Alfonsine Castilian translation, while the latter is extant in the original Arabic.19 It seems that both works were written during Ibn al-Zarqālluh’s time in Córdoba. The latter treatise mentions the year 474H of the Hegira, which is 1081–82 CE. The Alfonsine text mentions year 473H, or 1080–81.
In his equatorium design, Ibn al-Zarqālluh concentrated all the circles corresponding to each planet on both sides of the same plate. This forced him to use different scales for each planet. For each planetary deferent, he placed the center of the epicycle in a position corresponding to the planet’s mean longitude. The situation was more complicated in the case of Mercury, for which the Ptolemaic model established that the center of the planet’s deferent rotates on a small circle whose center is located in the apse-line—a straight line that connects the planet’s apogee and perigee and passes through its center. As a result, Mercury’s deferent is not circular, but instead forms an undefined curve.
In a paper published in 1955, Willy Hartner established that the curve described by the center of Mercury’s epicycle becomes practically identical with an ellipse according to the parameters provided in the Almagest. This configuration is not affected by Ibn al-Zarqālluh’s slight modification to Ptolemy’s parameters. Hartner also noted that the Alfonsine translation of Ibn al-Zarqālluh’s lost Arabic original was the first explicit description of Mercury’s true deferent.20 This curve is identified as an ellipse in the Castilian translation of Ibn al-Zarqālluh’s Arabic text on the construction of the instrument. In an English approximation of the enigmatic Castilian text, “The deferent circle will have the shape of the deficient section [ellipse], of those sections which appear in the pineal figure [cone].”21
Figure 3. Circles for Mercury, the moon, and the sun in Ibn al-Zarqālluh’s equatorium according to a reconstruction by Mercè Comes and Honorino Mielgo. Note the oval shape of Mercury’s deferent.
This is likely the first use of such a conic section in astronomy. Ibn al-Zarqālluh had no theoretical pretensions in his use of an ellipse and employed it only to simplify the design of an equatorium.22 Similar developments took place in the Islamic East during the fifteenth century, in which al-Kāshī’s equatorium used an oval curve for Mercury’s deferent, as well as in Europe. Georg von Peuerbach (1423–1461) was the first European scholar to identify the oval curve of Mercury’s deferent in Ptolemaic theory. Erasmus Reinhold (1511–1553) subsequently found that this was not only the case for Mercury, but also for the moon.23
Ibn al-Zarqālluh and Astronomical Theory
Beginning around 1050, Ibn al-Zarqālluh made observations of the sun for the following 25 years and the moon for 37. He started in Toledo, probably while working with Ṣāʽid’s team, and continued during his stay in Córdoba where, according to his own account, he was helped by one of his disciples, likely Ibn al-Kammād. He used the mid-seasons method, observing the sun in the midpoints between equinoxes and solstices. In his Yesod ha-ʽOlam, Israeli offers some details about Ibn al-Zarqālluh’s determination of the autumn equinox which took place in Toledo on September 17, 1075, at 4 hours and 18 minutes after noon. The modern calculated value for this particular equinox is September 17, 1075, at 5 hours, 30 minutes, and 40 seconds after noon. The year 1075 also seems to have been when Ibn al-Zarqālluh made crucial observations that allowed him to determine the solar parameters. Observations of stellar longitudes made in 1063 and 1080 are mentioned in his Treatise on the Motion of the Fixed Stars. This task was continued until at least 1087 or 1088.
Ibn al-Zarqālluh wrote several important works based on these long periods of observation. One of them, not extant, was entitled On the Invalidity of Ptolemy’s Method to Obtain the Apogee of Mercury. The title implies that he was aware that Ptolemy’s apogee for Mercury, 190º, was inaccurate by about 30º. In his Treatise on the Motion of the Fixed Stars, Ibn al-Zarqālluh improved the trepidation model that was likely designed by Ṣāʽid with other members of the Toledan team. He introduced a secondary model that allows for the calculation of the obliquity of the ecliptic, the angle between the ecliptic and the equator. The model implies that the changes in the obliquity are cyclical between a maximum of 23º 53', attained near Ptolemy’s time,24 and a minimum of 23º 33', obtained in the time of Ibn al-Zarqālluh. This finding reappeared in all his theoretical efforts, in which his geometrical models justified historical changes to astronomical parameters.
Ibn al-Zarqālluh’s book on the sun is also lost, although most of its contents have been recovered from quotations found in later Andalusian and Maghribi sources, as well as in the Tractatus super totam astrologiam by the thirteenth-century Franciscan Bernard of Verdun and in the Epitome of the Almagest by Regiomontanus in the fifteenth century.25 Ibn al-Zarqālluh’s book contained two original contributions. First, he discovered that the solar apogee had a motion of its own. While Ptolemy believed that the solar apogee was fixed and that its longitude was invariably 65º 30', observations made by Islamic astronomers in 829 and 831 yielded two different values of its position: 82º 39' and 82º 45', respectively. To reconcile these different measurements, astronomers concluded that the apogee advances 1º over 66 years, a parameter identical to the Ma’mūnī estimation of the precession of equinoxes. This was the origin of a general belief among Islamic astronomers that the solar and planetary apogees were sidereally fixed—that is, each was always pointing to a particular star, moving slowly with it as a result of precession.26 Even though this assumption resulted in disparities between calculated positions and solar observations, no Eastern Islamic astronomer dared to formulate an alternative. Ibn al-Zarqālluh established that the solar apogee moved faster than the stars, and suggested that its rate of motion was 1º in 279 years. His figure is close to the modern value: 1º in a little more than 310 years. Tables for the motion of the solar apogee based on Ibn al-Zarqālluh’s determination appear as part of later Andalusian and Maghribi astronomical tables.
Ibn al-Zarqālluh’s second original contribution was the design for a solar model with variable eccentricity. This was a work motivated by the fact that the eccentricity used by Ptolemy and Hipparchus was 2.5 parts, or 2;30p in sexagesimal notation, assuming that the radius of the solar orbit was 60p. Thābit ibn Qurra’s (d. 901) figure was 2;6,40p, while Al-Battānī and the Toledan Tables used an eccentricity of 2;4,46p. Ibn al-Zarqālluh had found a figure of 1;58p in observations made around 1075. In his solar model with variable eccentricity (Figure 4), S is the sun, which rotates uniformly about C, the center of its eccentric. C rotates very slowly, but also with uniform velocity, around the center G of the small circle C'C"E. O is the center of the earth. The solar eccentricity, OC, attains its maximum value (2;29,30p) when C is in C', and its minimum (1;50,56p) at E.
Figure 4. Ibn al-Zarqālluh’s solar model with variable eccentricity.
The Maghribi zījes based on Ibn al-Zarqālluh’s work contain tables from which the value of eccentricity can be calculated for a given date. Ibn al-Zarqālluh thought that the maximum value had been attained in the time of Ptolemy and that it was near its minimum in the second half of the eleventh century. This model passed into the medieval European astronomical literature and reappeared in De revolutionibus by Nicolaus Copernicus.27
A further innovation by Ibn al-Zarqālluh is mentioned in the testimony of Ibn al-Hā’im, an Andalusian astronomer of the early thirteenth century. In his Kāmil zīj, he states that he had read, in Ibn al-Zarqālluh’s own handwriting, a modification to a Ptolemaic lunar model: the center of the moon’s mean motion in longitude was not the center of the earth, as in Ptolemy, but was placed on a straight line linking the center of the earth with the solar apogee. The maximum correction in the lunar mean longitude amounted to 24'. Ibn al-Zarqālluh had reached this conclusion after a careful examination of Ptolemy’s lunar model, checking its results
in relation to many eclipses which took place in all parts of the ecliptic, during a long period of time of about thirty-seven years, according to what we found [in a text] written by his own hand. [He reached results] which did not disagree at all with [what] the Ancients said on this topic, with the only exception of the mean [lunar] motion in longitude.28
No other details have survived about this correction, other than it was introduced in later Andalusian and Maghribi zījes. The authors of these books recommend its use when a high degree of precision is required, particularly in relation to the computation of eclipses.
Legacy and Influence
Ibn al-Zarqālluh was one of the most important astronomers of the Islamic West. He was fortunate to be born in a time when the astronomical knowledge inherited from the Indo-Iranian and Greek traditions, as well as that produced in the Middle East during the ninth and tenth centuries, had been fully assimilated. The eleventh century was also a period in which Al-Andalus was culturally isolated. As a result, Andalusian science developed independently from Eastern Islam. The work of Ibn al-Zarqālluh is a case in point.
Together with his Toledan colleagues, Ibn al-Zarqālluh accepted the figures from earlier periods of observation, and developed models compatible with both old and new results. This approach yielded trepidation theory, the cyclical changes of the obliquity of the ecliptic, the discovery of the motion of the solar apogee and a solar model with variable eccentricity. His astronomical ideas and results proved extremely influential not only for astronomers in Al-Andalus and the Maghrib during the twelfth and the fifteenth centuries, but also in Europe where his work was passed on in Latin and Romance translations produced in twelfth-century Toledo. Ibn al-Zarqālluh’s innovations in instrument design and astronomical theory remained popular until the time of Copernicus.
