The great scientists and philosophers of the Islamic West were as much at home in the Maghrib, as they were in al-Andalus. Some of them travelled widely in both the Muslim and Christian worlds, which from the late eleventh century onwards were beginning to share ideas in philosophy and science, particularly in Spain, North Africa, Sicily and southern Italy.
The first of the important translators of Graeco-Islamic science from Arabic into Latin is Constantine the African (fl. 1065–85). An account of his early life is given by a twelfth-century Salerno physician known only as Magister Mattheus F.
According to this account, Constantine was a Muslim merchant from North Africa who visited the Lombard court at Salerno in southern Italy, where he learned that there was no medical literature available in Latin. According to the Salerno physician’s account, he went back to North Africa and studied medicine for three years, after which he returned to Salerno with a collection of medical writings in Arabic, perhaps as early as 1065.
The story goes that a few years later he converted to Christianity and became a monk in the Benedictine Abbey at Monte Cassino. There, under the patronage of the famous abbot Desiderius, later Pope Victor III, he spent the rest of his days in making Latin translations or compilations from Arabic medical texts.
Petrus Diaconus, historian of the monastery at Monte Cassino, lists a score of translations by Constantine, including works of Hippocrates and Galen as well as those of the Jewish physician Isaac Israeli and the Arabic writers Ibn al-Jazar and ‘Ali ‘Abbas. His most ambitious work was the Kitab al-Maliki of ‘Ali ‘Abbas, which he translated as the Pantegne, divided into two ten-chapter sections, theorica and practica, suppressing the name of the author and thus leaving himself open to charges of plagiarism. Constantine appears to have translated only about half of this work, which seems to have been completed by his student Johannes Afflacius.
There is no direct evidence to connect Constantine with the Medical School of Salerno, founded in the mid-eleventh century. Johannes Afflacius seems to have taught there and introduced Constantine’s translations into the curriculum under the title of Ars medicine or Articella, which formed the foundation of a large part of European medical education on into the sixteenth century. Constantine had always emphasised that medicine should be taught as a basic part of natural philosophy, and the theorica section of the Pantegne provided the basis for this integrated study.
The systematic study of Aristotelian philosophy in al-Andalus began with Abu Bakr Muhammad ibn Yahya ibn al-Sa’igh ibn Bajja, known in Latin as Avempace. Ibn Bajja was born in Saragossa ca. 1070, and in the years 1110–18 he served as vizier to the Almoravid governor of the city, Ibn Tifilwit. After the Christian conquest of Saragossa he spent the rest of his life in Almoravid territory, moving in turn to Almeria, Granada and Seville. While in Seville he was imprisoned before being released due to the intervention of Ibn Rushd al-Jadd, grandfather of the philosopher Ibn Rushd (Ibn Rushd al-Jadd literally means ‘grandfather of Ibn Rushd’). After his release he moved first to Jaen and then to Fez in Morocco, where he died in 1128. Tradition says that he died after eating an eggplant poisoned by his rivals, intellectuals in the Almoravid court in Fez. According to Ibn Tufayl, Ibn Bajja ‘was so preoccupied with material success that death carried him off before his intellectual storehouses could be cleared and all his hidden wisdom known’.
Thirty-seven of Ibn Bajja’s numerous works survive, many of them commentaries on the works of Aristotle, Galen and al-Farabi, along with three of his own works. His ideas influenced the thought of Ibn Tufayl (Abubacer), Ibn Rushd (Averroës) and Maimonides. There were few Latin translations of his works, nevertheless they influenced St Thomas Aquinas, who incorporated some of Ibn Bajja’s ideas into his theology.
Ibn Bajja seems to have been the first Arabic philosopher in al-Andalus to oppose the Ptolemaic planetary model. He rejected the use of epicycles as being incompatible with Aristotle’s doctrine of celestial motion, in which the planets move in perfect circles about the earth as a centre. But, according to Maimonides, he did use eccentric circles, i.e., circular orbits whose centres did not coincide with that of the earth.
Ibn Bajja’s ideas on dynamics appear in his notes on Aristotle’s Physics. Here he attempted to replace Aristotle’s causal approach to dynamics with the notion of force as the cause of motion. He rejected the Aristotelian law of motion, which held that the velocity of a body is directly proportional to the motive power and inversely proportional to the resistance of the medium through which it moves. Instead, following John Philoponus, he said that motion would occur only when the motive power was greater than the resistance, and that the velocity was proportional to the difference between the power and the resistance. He argued further that even in a void a body had to traverse a definite distance in any given time, so that its velocity would be finite no matter how fast it was moving. This was counter to the Aristotelian notion that in a vacuum a body’s velocity would be infinite, which was impossible, so that a void could not possibly exist.
Ibn Bajja was also an accomplished musician and poet. According to the thirteenth-century Tunisian writer al-Tifashi, Ibn Bajja ‘combined the songs of the Christians with those of the East, thereby inventing a style found only in Andalus, toward which the temperament of its people inclined so that they rejected all others’.
Another contemporary of Ibn Bajja was the Jewish polymath Abraham ben Meir ben Ezra (1092–1167), known in Latin as Abenezra. Ben Ezra was born in 1092, either in Toledo or Tudela, and he lived in Cordoba before leaving Spain before 1140 to escape the persecution of Jews by the Almohads. He then travelled to the Maghrib, Egypt, Palestine, Italy, France and England, visiting London and Oxford in 1158, before returning to Spain, where he most likely died around 1167. His writings include poetry and works in Hebrew grammar and religious philosophy, as well as treatises in mathematics, astronomy, astrology and chronology. Ibn Ezra’s own writings include biblical commentaries that were much admired by Spinoza. His astrological works, were very popular in medieval Europe and were translated into French, Catalan and Latin, and later into other languages.
One of ben Ezra’s astronomical works is a Hebrew translation of a commentary on the Sindhind, the astronomical tables of al-Khwarizmi, by the tenth-century Andalusian mathematician and astronomer Ibn al-Muthanna.
Ben Ezra’s only extant mathematical work is his Sefer ha-Mispar, The Book of Number, written probably before 1160. This is of particular importance because it describes the so-called Hindu decimal positional number-system, which he represented using the first nine letters of the Hebrew alphabet with a circle for zero. He says in The Book of Number that this system originated with the ‘Wise men of India’, while in his translation of al-Muthanna’s commentary on the Sindhind he remarks that al-Khwarizmi was the first Arabic scholar to understand the Hindu numbers.
Adelard of Bath (fl. 1116–42) was one of the leading figures among those who were involved in the organic acquisition of Arabic science – patrons, translators, travelers and scholars. In the introduction to his Questiones Naturalis, addressed to his nephew, Adelard writes of his ‘long period of study abroad’, first in France, where he studied at Tours and taught at Laon. He then went on to Salerno, Sicily, Asia Minor, Syria probably, Palestine and Spain. It was probably in Spain that Adelard learned Arabic – though we do not know this for certain – for his translation of the Astronomical Tables of al-Khwarizmi was from the revised version of the Andalusian astronomer Abu Maslama al-Majriti. The Tables, comprising 37 introductory chapters and 116 listings of celestial data, provided Christian Europe with its first knowledge of Graeco-Arabic-Indian astronomy and mathematics, including the first tables of the trigonometric sine function to appear in Latin.
Adelard was also the first to give a full translation of the Elements of Euclid into Latin, beginning the process that led to Euclid’s domination of medieval European mathematics. He did three versions of the Elements, the first being from the Arabic of Al-Hajjaj, who probably had translated it from Greek for Caliph Harun al-Rashid.
Adelard says that his Questiones Naturalis was written to explain ‘something new from my Arab studies’. The Questiones are seventy-six in number, 1–6 dealing with plants, 7–14 with birds, 15–16 with mankind in general, 17–32 with psychology, 33–47 with the human body, and 48–76 with meteorology and astronomy. Throughout he looks for natural rather than supernatural causes of phenomena, a practice that would be followed by later European writers.
One particularly interesting passage in this work comes when Adelard’s nephew asks him if it were not ‘better to attribute all the operations of the universe to God’. Adelard replies: ‘I do not detract from God. Everything that is, is from him and because of him. But [nature] is not confused and without system and so far as human knowledge has progressed it should be given a hearing. Only when it fails utterly should there be a recourse to God.’
The Questiones Naturalis remained popular throughout the rest of the Middle Ages, with three editions appearing before 1500, as well as a Hebrew version. Adelard also wrote works ranging from trigonometry to astrology and from Platonic philosophy to falconry. His last work was a treatise on the astrolabe, in which once more he explained ‘the opinions of the Arabs’, this time concerning astronomy. The treatise describes the workings of the astrolabe and its various applications in celestial measurements, using Arabic terms freely and quoting from Adelard’s other works, particularly his translations of Euclid’s Elements and the planetary tables of al-Khwarizmi.
Little is known about John of Seville, who in the years 1135–53 translated a score of Arabic works, most of them astrological, but also including an astronomical manual by al-Farghani and a treatise on arithmetic by al-Khwarizmi in which he describes the Hindu number system. The best known work by John of Seville is his partial translation of the medical section of the pseudo-Aristotelian Secretum secretorum (The Secret of Secrets). A more complete translation was subsequently made by Philip of Tripoli, who in his preface describes how he was in Antioch when he discovered ‘this pearl of philosophy...this book which contains something useful about almost every science’.
Toledo became a centre for translation from the Arabic after Alfonso VI, king of Castile and Leon, carried out the first major triumph of the reconquista, the Christian reconquest of al-Andalus, and captured the city in 1085.
Gundissalinus, archbishop of Segovia, did several translations and adaptations of Arabic philosophy, including works by al-Kindi, Ibn Rushd, al-Farabi, al-Ghazali and Ibn Sina, as well as one by the Jewish physician Isaac Israeli. The translations attributed to Gundissalinus were probably done by him in collaboration with others who were fluent in Arabic, though only in one work, the De anima of Ibn Sina, is his name linked with that of a co-author. There his collaborator was a Jew named Abraham ibn David, the Latin Avendaut, w ho is usually identified with the translator known as John of Seville.
Gundissalinus also wrote five philosophical works on his own, based largely on the books that he had translated as well as on Latin sources. He is credited with introducing Arabic-Judaic Neoplatonism to the Latin West and blending it with that of St Augustine and Boethius. His De divisione philosophiae, which incorporates the systems of both Aristotle and al-Farabi as well as others, is a classification of the sciences transcending the traditional division of studies in the trivium (grammar, rhetoric and logic) and quadrivium (arithmetic, geometry, astronomy and musical theory), and it influenced later schemes of classification.
Plato of Tivoli is known only through his work, at least part of which he wrote in Barcelona between 1132 and 1146. His name appears only as an editor of translations from the Arabic and Hebrew in collaboration with the Jewish mathematician and astronomer Abraham bar Hiyya ha-Nasi, also known as Abraham Judaeus, or, in Latin, Savasorda, a corruption of the Arabic Sahib al-shurta.
Savasorda’s most important work is his Hebrew treatise on practical geometry, which he and Plato of Tivoli translated into Latin in 1145 as the Liber Embadorum. This was one of the earliest works on Arabic elementary, geometry and arithmetic to be published in Latin Europe, and it contains the first solution of the standard quadratic equation to appear in the West. It was also the earliest to deal with Euclid’s On Divisions of Figures, which has not survived in Greek and only partially in Arabic. This work influenced Leonardo Fibonacci, who in his Practica geometriae, written in 1220, devoted an entire section to division of geometrical figures.
Savasorda also collaborated with Plato of Tivoli in translating the Spherica by Theodosius of Bithynia, and the two may also have worked together on books by Ptolemy and al-Battani, as well as on Abu Maslama al-Majriti’s treatise on the astrolabe. The translations from the Arabic of seven other works are attributed to Plato, with or without Savasorda, five of them astrological, one on divination, and one medical, now lost. One of these works is Ptolemy’s great treatise on astrology, the Tetrabiblos, which Plato of Tivoli translated into Latin as the Tetrapartitium. This was the first Latin translation of Ptolemy, appearing before the Almagest and the Geography, evidence of the great popularity of astrology in medieval Europe. It has also been suggested that Plato is the author of the Latin translation from the Arabic of Archimedes’ De mensura circuli. Plato’s translations were used by both Fibonacci and Albertus Magnus, and printed editions of some of them were published in the late fifteenth and early sixteenth centuries.
Translations were also sponsored by Bishop Michael of Tarazona during the years 1119–51, as evidenced by a dedication to him by Hugo Sanctallensis. This appears in Hugo’s translation from the Arabic of an abridged version of Ptolemy’s Tetrabiblos, entitled Centiloquium. Hugo’s preface says that the Centiloquium was commissioned by Michael to serve as a guide to the many astrological works that had been made available to the bishop. Hugo’s other translations, all from Arabic sources, are on astrology and various forms of divination, including aeromancy, hydromancy and pyromancy, prognostication by observing patterns in air, water and fire, respectively, as well as two short treatises on spatulamancy, foretelling the future by examining the shoulder blades of slaughtered animals.
Gerard of Cremona (1114–87) was the most prolific of all the Latin translators, by far. The few details that are known of Gerard’s life come mostly from a short biography and eulogy written by his companions in Toledo after his death, together with a list of seventy-one works that he had translated. This document was found inserted at the end of Gerard’s last translation, that of Galen’s Tegni with the commentary of ‘Ali ibn Ridwan. It notes that Gerard completed his education in the schools of the Latins before going to Toledo, which he would have reached by 1144 at the latest, when he would have been thirty years old. The vita goes on to say that it was his love of Ptolemy’s Almagest, which he knew was not available in Latin, that drew Gerard to Toledo, and ‘there, seeing the abundance of books in Arabic on every subject...he learned the Arabic language, in order to be able to translate’.
Gerard also lectured on Arabic science, as evidenced by the testimony of the English scholar Daniel of Morley, who had first gone to Paris, but had left there in disappointment, going to Toledo to hear the ‘wiser philosophers of the world’, as he remarks in his Philosophia. Daniel gives a detailed account of meeting ‘Gerard of Toledo’ and listening to his public lectures on Abu Ma’shar’s Great Introduction to the Science of Astrology. He also listened to lectures by Gallipus Mixtarabe, a Mozarab who collaborated with Gerard in his translation of the Almagest, which they seem to have completed in 1175. Otherwise Gerard appears to have worked alone, for no collaborators are listed in any of his other translations.
Gerard’s translations included Arabic versions of writings by Aristotle, Euclid, Archimedes, Ptolemy and Galen, as well as works by al-Kindi, al-Khwarizmi, al-Razi, Ibn Sina, Ibn al-Haytham, Thabit ibn Qurra, al-Farghani, al-Farabi, Qusta ibn Luqa, Jabir ibn Hayyan, al-Zarqallu, Jabir ibn Aflah, Masha’allah, the Banu Musa and Abu Ma’shar. The subjects covered in these translations include 24 works on medicine; 17 on geometry, mathematics, optics, weights and dynamics; 14 on philosophy and logic; 12 on astronomy and astrology; and 7 on alchemy, divination and geomancy, or predicting the future from geographic features.
Gerard may also have published a number of original works, and several have been tentatively attributed to him, including two glosses on medical texts by Isaac Israeli as well as treatises entitled Geomantia astronomica and Theorica Planetarium. However, it is possible that the latter treatise is a work of John of Seville, whose style Gerard adopted in his translations.
More of Arabic science passed to the West through Gerard than from any other source. His translations produced a great impact upon the development of European science, particularly in medicine, where students in the Latin West took advantage of the more advanced state of medical studies in medieval Islam. His translations in astronomy, physics and mathematics were also very influential, since they represented a scientific approach to the study of nature rather than the philosophical and theological attitude that had been prevalent in the Latin West.
An older contemporary of Gerard, Abu Marwan ‘Abd al-Malik ibn Abi’l ‘Ala’ ibn Zuhr (c. 1092–1162), the Latin Avenzoar, was born in Seville and studied in Cordoba. He belonged to the Banu Zuhr family, which produced five generations of physicians, including two women doctors, who served the Almoravid dynasty in the Maghrib and al-Andalus. Ibn Zuhr served as personal physician to the emir ‘Ali ibn Tashfin (r. 1106–43) in his palace at Marrakech, but because of a misunderstanding he was imprisoned by his patron.
When the Almoravids were overthrown by the Almohads, Ibn Zuhr was restored to favour by the new ruler, Abd al-Mu’min (r. 1145–63), who appointed him as his court physician and personal counsellor, with the rank of vizier. Ibn Zuhr dedicated two medical works to Abd al-Mu’min, the first of which was a treatise on therica, or antidotes to poisons, and the second on dietetics.
Ibn Zuhr’s medical writings were based on the works of Hippocrates and Galen as well as those of his Arabic predecessors and his own researches. His best-known work, al-Taysir fi’l-mudawat wa’l-’tadbir (An Aid to Therapy and Regimen), was dedicated to his friend Ibn Rushd (Averroës), who had encouraged him to write it. The text, which was in thirty treatises, was translated into Hebrew and Latin and remained in use up until the European renaissance.
The physician and philosopher Abu Bakr Muhammad Ibn Tufayl, known in Latin as Abubacer, was born ca. 1105 at Wadi Ash (Cadiz), north-west of Granada and studied medicine and philosophy at Seville or Cordoba. Working as a physician, he became secretary to the governor of Granada and then to the governor of Ceuta and Tangier. He was then appointed personal physician to the Almohad caliph, Abu Ya’qub Yusuf (r. 1163–84), becoming one of his boon companions. He retired in 1182 and moved to Marrakech in the Maghrib, where he died in 1185.
Ibn Tufayl is best known for his philosophical romance Hayy ibn Yaqzan (Living, Son of the Wakeful), about a feral youth living alone on a desert island in the Indian Ocean, who through his unaided reason reaches the highest level of knowledge. The novel was translated into Latin in 1671 by Edward Pococke the Younger, under the title Philosophus Autodidactus. The first English translation from the Arabic was done in 1708 by Simon Ockley. One of these translations may have inspired Daniel Defoe to write Robinson Crusoe, published in 1719. It has been suggested that Philosophus Autodidactus influenced Thomas Hobbes, John Locke, Isaac Newton, Gottfried Leibniz and Voltaire.
Ibn Tufayl was the first Andalusian thinker to make use of the works of Ibn Sina, though with some differences, such as his belief that there is no proof that the world is eternal rather than created in time. He also wrote an astronomical thesis, now lost, which is mentioned by his student Abu Ishaq al-Bitruji.
According to al-Bitruji, in this thesis Ibn Tufayl opposed certain aspects of Ptolemaic astronomy, apparently formulating a planetary model that avoided using the epicycles and eccentric circles of Ptolemy.
Ibn Tufayl’s researches in astronomy were continued by Abu Ishaq al-Bitruji, the Latin Alpetragius, who flourished in Seville ca. 1190. Al-Bitruji’s only known work is his Kitab fi’l-hay’a (Book of Astronomy), in which he says that he was a student of Ibn Tufayl.
Al-Bitruji acknowledged that Ptolemy’s theory gave an exact mathematical description of planetary motion. But he felt that the Ptolemaic model was unsatisfactory since its eccentrics, epicycles, equants and deferents were incompatible with Aristotle’s physical concept of the homocentric spheres. He also pointed out a problem involving Aristotle’s notion that the Prime Mover imparted motion to the ninth and outermost celestial sphere, and that this then was passed in turn to the inner spheres. If that were the case, he said, then the outer planets should move faster than the inner ones, rather than the other way round.
The Kitab fi’l-hay’a was translated into Hebrew and Latin, leading to the spread of al-Bitruji’s ideas through much of Europe from the thirteenth century on into the seventeenth. Al-Bitruji’s planetary model was used by those who were defending Aristotle’s theory of the homocentric spheres against the supporters of Ptolemy’s eccentrics and epicycles. Copernicus refers to al-Bitruji in connection with the order of the planets Mercury and Venus in his heliocentric theory of 1543.
Al-Bitruji was an older contemporary of the great Muslim geographer and cartographer Muhammad al-Idrisi (1100–ca. 1165). Al-Idrisi was born in Cueta, on the North African side of the Straits of Gibraltar, and studied in Cordoba. He travelled widely in the Maghrib and al-Andalus and also visited Asia Minor, France and England before moving to Palermo in 1138 on the invitation of Roger II (r. 1130–54), the Norman ruler of the ‘Kingdom of the Two Sicilies’.
The Normans had driven the Byzantines from their last footholds in southern Italy in the late eleventh century and then subdued the Arabs in Sicily. When Count Roger I conquered Palermo in 1091 it had been under Muslim domination for nearly two centuries. He reduced the Muslims to the status of serfs except in Palermo, his capital, where he employed the most talented of them as civil servants, so that Greek, Latin and Arabic were spoken in the Norman court and used in royal charters and registers. Under his son Roger II, Palermo became a centre of culture for both Christians and Muslims, surpassed only by Cordoba and Toledo. Beginning under Roger II, and continuing with his successors, the Sicilian court sponsored translations from both Greek and Arabic into Latin.
Roger II was particularly interested in geography, but he was dissatisfied with existing Greek and Arabic geographical works. This led him to write to al-Idrisi, who was already renowned as a geographer, inviting him to his court in Palermo, saying ‘If you live among the Muslims, their kings will contrive to kill you, but if you stay with me you will be safe’. Al-Idrisi accepted the offer and lived in Palermo under Roger II and his successor William I (1154–66), after which he returned to Ceuta and passed his remaining days there.
Roger commissioned al-Idrisi to create a large circular relief map of the world in silver, the data for which came from Greek and Arabic sources, principally Ptolemy’s Geography, as well as travellers and the king’s envoys. The silver map has long since vanished, but its features were probably reproduced in the sectional maps in al-Idrisi’s Arabic geographical compendium, Al-Kitab al-Rujari (Roger’s Book), also known as Kitab nuzhat al-mushtaq fi ikhtiraq al-afaq (The delight of him who desire to journey through the climates), which has survived.
The compendium deals with both physical and descriptive geography, with information on political, economic and social conditions in the lands around the Mediterranean and in the Middle East, and is thus a veritable encyclopedia of the medieval world. Al-Idrisi’s work was translated into Latin in part in 1619. A Latin translation was published at Paris in 1619, and a two-volume French translation was done in 1830–40, entitled Géographie d’Edrisi.
After the death of Roger II al-Idrisi wrote another and larger geographical compendium for King Willam I, entitled Rawd al-Nas wa-nuzhat al-nafs (Pleasure of Men and Delight of Souls). He also wrote a pharmacological work entitled Comprehensive Book of the Properties of Diverse Plants and Various Kinds of Simple Drugs.
Frederick II of Hohenstauffen (r. 1211–50), the Holy Roman Emperor and King of the Two Sicilies, was a grandson of Emperor Frederick I Barbarossa and the Norman king Roger II. Known in his time as stupor mundi, ‘the wonder of the world’, he had been raised from age seven to twelve in Palermo, where he grew up speaking Arabic and Sicilian as well as learning Latin and Greek. When he became emperor in 1211, at the age of fourteen, he turned away from his northern dominions to his Kingdom of the Two Sicilies, where, like his Norman predecessors, who were known as ‘baptised sultans’, he indulged himself in his harem.
Frederick was deeply interested in science and mathematics, and he invited a number of scholars to his brilliant court, most notably John of Palermo, Master Theodorus and Michael Scot, calling them his ‘philosophers’. He subsidised their scientific writings and translations, which included works of Aristotle on physics and logic, some of which he presented in 1232 to the professors at Bologna University. The letter that Frederick sent with the gift told of how he had loved learning since his youth, and of how he still took time from affairs of state to read in his library, where numerous manuscripts of all kinds ‘classified in order, enrich our cupboards’.
Frederick’s scholarship is evident in his famous book on falconry, De Arte Venandi cum Avibus, or The Art of Hunting with Birds. This is a scientific work on ornithology as well as a detailed and beautifully illustrated manual of falconry as an art rather than a sport. Frederick acknowledged his debt to Aristotle’s Zoology, which had been translated by Michael Scot earlier in the twelfth century. But he was critical of some aspects of the work, as he writes in the preface to his manual: ‘We have followed Aristotle when it was opportune, but in many cases, especially in that which regards the nature of some birds, he appears to have departed from the truth. That is why we have not always followed the prince of philosophers, because rarely, or never, had he the experience of falconing which we have loved and practiced always.’
One of those with whom Frederick corresponded was the renowned mathematician Leonardo Fibonacci (ca. 1170–after 1240), who had been presented to him when he held court at Pisa about 1225. Leonardo had at that time just completed his treatise on squared numbers, the Liber quadratorum, which he dedicated to Frederick, noting ‘I have heard from the Podesta of Pisa that it pleases you from time to time to hear subtle reasoning in Geometry and Arithmetic.’
Leonardo was born in Pisa ca. 1170. He writes about his life in the preface to his most famous work, the book on calculations entitled Liber abbaci. His father, a secretary of the Republic of Pisa, was around 1192 appointed director of the Pisan trading colony in the city of Bugia (now Bejaia in Algeria). Leonardo was brought to Bugia by his father to be trained in the art of calculating, which he learned to do ‘with the new Indian numerals’. Around 1200 he returned to Pisa, where he spent the rest of his days writing the mathematical treatises that made him one of the most important mathematicians of the Middle Ages.
The five works of Leonardo that have survived are the Liber abbaci, first published in 1202 and revised in 1228; the Practica geometriae (1220–1), on applied geometry; a treatise entitled Flos (1225), sent to Frederick II in response to mathematical questions that had been put to Leonardo by John of Palermo at the time of the emperor’s visit to Pisa; an undated letter to Master Theodorus, one of the ‘philosophers’ in the court of Frederick II; and the Liber quadratorum (1225). The latter work contains the famous ‘rabbit problem’: ‘How many pairs of rabbits will be produced in a year, beginning with a single pair, if in every month each pair produces a new pair which become productive from the second month on?’ The solution to this problem gave rise to the so-called Fibonacci numbers, a progression in which each number is the sum of the two that precede it (e.g., 1, 1, 2, 3, 5, 8, 13, 21, etc.), a mathematical wonder that continues to fascinate mathematicians. Leonardo’s sources, where they can be traced, include Greek, Roman, Indian and Arabic works, which he synthesised and, adding to them with his own creative genius, undoubtedly helping to stimulate the beginning of the new European mathematics.
Leonardo dedicated his Flos to John of Palermo, whom he also mentions in the introduction to the Liber quadratorum. John’s only known work is a Latin translation of an Arabic treatise on the hyperbola, which may be derived from a work by Ibn al-Haytham on the same subject.
Master Theodorus, who is usually referred to as ‘the Philosopher’, was born in Antioch. He served Frederick as secretary, ambassador, astrologer and translator, from both Greek and Arabic into Latin, and he was also the emperor’s chief confectioner. One of his works is a translation of an Arabic work on falconry. He served the emperor until the time of his death around 1250, when Frederick regranted to another favourite the estate that ‘the late Theodore our philosopher held so long as he lived’.
Theodorus had probably succeeded Michael Scot as court astrologer. Michael was born in the last years of the twelfth century, probably in Scotland, though he might possibly be Irish. Nothing is known of his university studies, but his references to Paris indicate that he may have studied and lectured there as well as in Bologna, where he did some medical research in 1220 or 1221. He may have learned Arabic and some Hebrew in Toledo, where about 1217 he translated al-Bitruji’s On the Sphere, with the help of Abuteus Levita, a Jew who later converted to Christianity. By 1220 he had completed what became the standard Latin version of Aristotle’s On Animals, from a ninth-century Arabic version by al-Bitriq, as well as the De caelo and the De anima with Ibn Rushd’s commentaries.
When Leonardo Fibonacci completed his revised version of Liber abbaci in 1228 he sent it to Michael, who by that time seems to have entered the service of Frederick II as court astrologer. Michael wrote for the emperor a Latin summary of Ibn Rushd’s De animalibus as well as a voluminous treatise known in English as Introduction to Astrology. The latter work covers every aspect of astrology and divination including necromancy, or conjuring up the spirits of the dead to reveal the future or influence the course of coming events, as well as nigromancy, or black magic, dealing with dark things performed by night rather than by day.
Such was the astonishing variety of the scientific works transmitted between the Muslim Arabic and Christian Latin worlds in the West during the late medieval era, in a cultural interface that extended from the Maghrib to the Two Sicilies.