F

Farabi, al-

Al-Farabi (Abu Nasr Muhammad ibn Muhammad ibn Tarkhan ibn Awzalagh) (c. 870–950 C.E.) was well known among medieval Muslim intellectuals as “The Second Teacher,” and as “Abunaser” or “Alfarabius” to medieval Christians. In view of his distinction, it is surprising how little we actually know of the life of this highly significant Neoplatonic philosopher. As his name implies, he was born in the Farabi district of Wasij, a town in Turkestan, a region that comprised the northeast border of the Islamic world until after his death. According to geographers, the town of his birth was a fortress, which accords well with the tradition that his father was an officer in the Turkish guard of the Caliph of Baghdad. In spite of that connection, al-Farabi does not appear to have been part of the court circles. It is believed that he learned Arabic in Baghdad and then philosophy from Yuhanna ibn Haylan, a Nestorian Christian who came to that city around 908 C.E. However, it is possible that he studied with Yuhanna before that scholar came to Baghdad from Merv. Whichever is the case, despite being a Muslim, al-Farabi was clearly part of the circle of Christian Aristotelian scholars that flourished in Baghdad in the first half of the tenth century, studying with Abu Bisr Matta ibn Yunus and teaching Yahya ibn Adi. Beyond these sketchy details, there are numerous legendary stories attached to al-Farabi by medieval biographers which attempt to give us a view of his personality; none is entirely trustworthy. In addition to his education, the one fact that is certain is that around 942 he moved from Baghdad to the court of the Shi’ite ruler of Aleppo, Sayf al-Dawla, who became his patron, and in whose company he remained until his death about eight years later.

We do not know where and in what circumstances al-Farabi wrote most of his works, but the principal reasons for his reputation as the second most important philosopher after Aristotle were the volume and the clarity of his writings on philosophy. While al-Farabi was not a scientist per se, he understood and advocated the notion that truth is discoverable by reason. In the late Abbasid period, because the earlier Mu’tazilite controversy had created friction between faith and reason, there was strong suspicion among the orthodox Sunnite theologians that Hellenistic rationalism created heretics. This controversy, which had played out in the generation before al-Farabi’s birth, made it difficult for Muslim thinkers to pursue philosophy in its own right. Those who wanted to study philosophy had always to take account of religious thought and the theologians. Al-Farabi does not appear to have been intimidated by studying in such an atmosphere (although it may explain why he studied with Christian teachers), and in fact he may have paved a way for Muslim intellectuals to approach Aristotle. Before him, as a matter of practice, Christian and Islamic scholars had read the Organon only as far as Prior Analytics I.7; the material after this point had come to be called by a sort of technical term: “the part that is not read.” In a curious episode, it appears that al-Farabi and his teacher Yuhanna ibn Haylan may have been the first to break that barrier in Baghdad; significantly, another of al-Farabi’s teachers, Abu Bishr Matta ibn Yunus, was the translator of the Posterior Analytics. As Ibn Abi Usaybia relates this story, after al-Farabi the reading of “the part that is not read” became standard in logical study. In this way, al-Farabi is a pivotal figure in reinstating philosophical study (particularly of logical demonstration) to the status it had before religious strictures were placed on its instruction.

However, al-Farabi was not a thoroughgoing Aristotelian who had no room for revelation in his epistemology, for he clearly recognized that there were two ways of knowing, by philosophy or religious belief, and he did not see them as contradictory. In the chapter of the Enumeration of the Sciences (Ihsa’ al-culum) devoted to “Divine Science,” he shows how all being is derived from “the first being, to whom nothing is able to be prior and to whom nothing is able to take precedence.” He goes on to conclude that this first being “is more worthy of the name and all that is signified by Unity and Being and Truth and the First,” and “that this, such as is of its own nature, ought to be believed to be God” (Enumeration, Ch. 4). It is from this being, through a series of Neoplatonic emanations, that humans ultimately gain life and knowledge. So while al-Farabi preserves a place for God and revelation in his metaphysics and epistemology, in his writings there was still a clear preference for rational comprehension: “In everything demonstrated by philosophy, religion employs persuasion” (Attainment of Happiness, 44). To any reader familiar with the Aristotelian system, demonstration attained on the basis of syllogistic logic was far superior to persuasion in pursuit of the truth. Al-Farabi says this explicitly in the excursus on the art of demonstration which forms the concluding section of the chapter on Logic in the Enumeration of the Sciences. He makes it clear that “certain knowledge of the truth is not to be had except through demonstration.” He goes on to say that all the other parts of logic and all the kinds of argumentation—including persuasion—are, in one sense or another, subservient to demonstration, as taught in the Posterior Analytics. Because his conclusions were based on demonstration, the assertions of the philosopher demand assent and represent a kind of knowledge “fixed in the soul.” Thus the philosopher came to certain knowledge, not mere belief. Al-Farabi’s Neoplatonic system seemed to many of his contemporaries to bridge the gap between the “religious” and the “foreign” sciences. Of The Philosophy of Plato and Aristotle, the book in which al-Farabi explained this difference between the two ways of knowing, *Sa‘id al-Andalusi wrote: “I do not know of a more helpful book for the study of philosophy, because it explains the common ground of all the sciences and provides the specifics for each one of these sciences.”

Wideranging Influence

Al-Farabi was an unparalleled thinker, but he was first and foremost a teacher. We do not know the names of all the scholars he taught personally, but his writings served as both fundamental and advanced instruction for those who sought to truly know a subject. As logic was the foundation of all further study, including the sciences, reading al-Farabi’s books was considered essential prerequisite preparation for anyone who wished to understand any field of knowledge. Sa‘id al-Andalusi said that al-Farabi “surpassed all Muslim scholars in his knowledge of logic and in his research in the field. He explained its obscurities, uncovered its secrets, and facilitated its understanding.” *Maimonides, too, added his recommendation in a letter to his pupil Samuel Ibn Tibbon in which he wrote: “Do not concern yourself with books on logic except for what the philosopher Abu Nasr al-Farabi composed.” Al-Farabi’s works were even helpful to some of the greatest thinkers of the Islamic world. The famous passage from *Ibn Sina’s Autobiography is instructive: in it he states that he had read Aristotle’s Metaphysics thirty times without understanding it and then, after reading al-Farabi’s commentary on the work, he finally comprehended. Al-Farabi’s works were useful not only to scholars of Ibn Sina’s caliber: they were also greatly beneficial to students. The Book of the Enumeration of the Sciences, for example, was intended as a kind of description of all the “well-known sciences,” and was of particular value to students of philosophy. More than that, the book also functioned as a kind of prescriptive syllabus. In the ninth and tenth centuries, many such texts were written as Muslim scholars attempted to come to grips with the ways in which Hellenistic science and philosophy could be useful. Because of the Mu’tazilites, teaching such subjects—especially in mosques where most teaching was done—was problematic. There was a need for an instructional resource from which students could discover which books they needed to read in order to truly learn a subject. In addition, scholars who wished to add a field of knowledge, or who wished to examine someone else’s expertise, could use this book to “get up to speed” in each discipline. In the five books that comprised this work, al-Farabi outlined the major divisions of knowledge. While his categorization is based on earlier schemas, the divisions are uniquely his own: the first section was the Science of Language; the second the Science of Logic; the third, the Mathematical Sciences that include Arithmetic, Geometry, Optics, Astronomy, the science of weights, and the science of the Making of Mechanical Devices; the fourth section was about Physics and Metaphysics; the fifth dealt with Civil Science and its parts, including both the science of jurisprudence and the science of theology. Within these divisions are subdivisions in which al-Farabi discusses some thirty-six sciences in all.

In each of these divisions, al-Farabi outlined the content of the discipline (its “parts”), and at the end usually provided a list of the books to be read in order to comprehend this field of study. One can understand why Sa‘id al-Andalusi said: “The student of any of the sciences cannot do without it or proceed without its guidance.” In fact, that is probably exactly how it was used: students who wished to know some field of study not taught in the “circles” of professors in the mosque schools, could use this book to find out what they needed to read in order to be (or appear to be) learned in any science.

Al-Farabi also advocated the application of a rudimentary scientific method to various fields of inquiry. In discussing the ways in which the ruler should work to find the right stimuli for citizens in the state, he says that the power of a ruler consists of two strengths: one is awareness of the force of universal rules; the other is the faculty a man acquires by long, arduous study of operations of civil societies, of the deeds of one particular city, of individuals within a specific city, and of practical experience by experimentation and long observation, following the example of medical treatment. For a doctor only comes to a perfect treatment by two methods: first from the strength derived from knowing the universal conceptions and rules which he acquires from medical books; second, from the faculty which comes from long observation of the working of medicines on the disease and the practical experience which comes from long trials and observation of the bodies of individuals. By this power, the physician is able to decide the remedies and medical treatments required for each body and each condition. What goes for the practice of medicine also holds true for political leadership (Enumeration, Ch. 5).

Here we see the elements of a scientific method that is based on knowledge of universal principles and on testing hypothetical treatments and observing the results. The body of knowledge in a particular discipline grows from these experiments.

Outside the Islamic world, this text was rendered into Latin by two of the most prolific twelfth-century translators. One of them, *Domingo Gundisalvo, combined parts of his translation with other works on the knowledge of the sciences to produce a pastiche entitled De Divisione Philosophiae. Since the time of *Boethius, the study of anything beyond the trivium and theology had been minimal. Gundisalvo’s translation and adaptation of al-Farabi’s work introduced Christian scholars to an expanded *quadrivium that had long been in place in the Muslim world. It had an immediate effect. Recent scholarship has suggested that the text was instrumental in guiding the twelfth-century Christian translators in *Toledo and elsewhere in Spain to the very books they needed as they sought to gain the doctrina Arabum. Furthermore, within a century of the translations the nascent universities of Europe were requiring readings in these new sciences and the “new” Aristotle.

In addition to this broad introduction to the fields of knowledge, al-Farabi wrote several introductory books on logic, explaining for beginners the terminology and the logical expressions in easy-to-understand presentations. He also wrote at least two books extolling the virtues of philosophy as the “way to happiness” for a thinking person. He is perhaps best known for his book on political philosophy, The Perfect State. This work is often compared to Plato’s Republic because of its orientation and structure; however, it is more than an adaptation of that great text and includes a place for the transcendent God of Neoplatonism while holding to the idea that only the city that adopts goodness and happiness as its goals will be virtuous or perfect. Finally, The Great Book on Music was the only work by al-Farabi on a specific “science.” In the anecdotal materials, he is often presented as a very competent practicing musician as well as a theoretician.

Al-Farabi’s influence was widespread in both the Christian and Islamic worlds of the Middle Ages. Netton (1992) has written of a “school of al-Farabi” that includes the philosophers al-Sijistani, al-‘Amiri, and al-Tawhidi. Many other later Muslim thinkers, including *Ibn Rushd and Ibn Sina, were influenced by his thought; even as late as fifty years after it was translated and circulated in the Latin West, Muslim scholars such as Ibn Tumlus still depended heavily on al-Farabi’s Enumeration. Maimonides knew al-Farabi’s work and thought highly of it. Other Jewish scholars in the cultural orbit of al-Andalus were also interested in the issues raised by the classification of the sciences and were influenced by al-Farabi; both *Abraham ibn Ezra and Bayha ibn Paquda adapted the Farabian curricular scheme to their own purposes, as did Judah ha-Levi and Maimonides. In the Christian West, al-Farabi certainly was read by *Roger Bacon, who refers to him frequently. It has been argued that *Aquinas derived some of his ideas from al-Farabi through the medium of the Avicenna Latinus (Latin translations of Ibn Sina’s works). In terms of scientific theory and methods, Ibn Sina certainly follows al-Farabi’s conception that universals are known first and that experimentation comes in their wake. Ibn Sina’s Canon, which was authoritative in medical circles until the eighteenth century, expounded this principle. Because nearly all of al-Farabi’s Enumeration of the Sciences was included in both Gundisalvo’s De Divisione Philosophiae and *Vincent of Beauvais’ Speculum doctrinale, al-Farabi’s conceptualization of the number and hierarchy of the sciences became widespread in the Latin West.

See also Aristotelianism; Music theory; Translation movements; Translation norms and practice

Bibliography

Primary Sources

Al-Farabi. Al-Farabi on the Perfect State. Translated and edited by Richard Walzer Oxford: The Clarendon Press, 1985.

———. Ihsa’ al-culum. [Enumeration of the Sciences]. Catálogo de las Ciencias. Edited by Angel González Palencia, 2nd ed. Madrid: CSIC, 1953.

———. The Attainment of Happiness. Edited and Translated by Muhsin Mahdi. In The Philosophy of Plato and Aristotle. New York: Free Press, 1962.

Dunlop, D. M. Chapters on What is Useful in the Art of Logic. Islamic Quarterly (1955) 2: 264–282.

———. Al-Farabi’s Isagoge. Islamic Quarterly. (1956) 3: 117–138.

Najjar, Fauzi M. “Alfarabi: The Enumeration of the Sciences.” In Lerner and Mahdi, eds, Medieval Political Philosophy. Ithaca: Cornell University Press, 1978, pp. 22–30.

Saliba, George. The Function of Mechanical Devices in Medieval Islamic Science. Annals of the New York Academy of Sciences (1985) 441: 141–151.

Sa‘id al-Andalusi, Tabaqat al-Umam (Categories of the Nations). Translated and edited by Salem and Kumar. Science in the Medieval World. Austin: University of Texas Press, 1991.

Secondary Sources

Abed, Shukri B. Aristotelian Logic and the Arabic Language in al-Farabi. Albany: SUNY Press, 1991.

Burnett, Charles S. F. “The Institutional context of Arabic-Latin Translations of the Middle Ages: A Reassessment of the ‘School of Toledo’.” In Vocabulary of Teaching and Research between Middle Ages and Renaissance. Edited by Olga Weijers. Turnhout: Brepols, 1995, pp. 214–255.

Butterworth, C.E. and B.A. Kessel. The Introduction of Arabic Philosophy into Europe. Leiden: E. J. Brill, 1994.

Fakhry, Majid. A History of Islamic Philosophy, 2nd. ed. London: Longman, 1983.

Farmer, Henry George. The Influence of al-Farabi’s Ihsa’ alculum. Journal of the Royal Asiatic Society (1932) 561–592.

Lindberg, David C., ed. Studies in Medieval Science. Chicago: University of Chicago Press, 1989.

Muhsin, Mahdi. “Science, Philosophy, and Religion in Al-Farabi’s Enumeration of the Sciences.” In The Cultural Context of Medieval Learning, edited by John Murdoch and Edith Sylla. Dordrecht and Boston: D. Reidel Publishing, 1975, pp. 113–150.

Netton, Ian R. Al-Farabi and his School. London: Routledge, 1992.

Rescher, Nicholas. Al-Farabi: An Annotated Bibliography. Pittsburgh: University of Pittsburgh Press, 1962.

———. “Al-Farabi on the Logical Tradition.” Journal of the History of Ideas (1963) 24: 127–132.

Young, M.J.L., J.D. Latham, and R.B. Serjeant. Religion, Learning and Sciences in the Abbasid Period. New York: Cambridge University Press, 1990.

MICHAEL C. WEBER

Fibonacci, Leonardo

Leonardo Fibonacci (Leonardus Pisanus, Leonardo Pisano, Leonardo da Pisa) was born in Pisa in about 1170, and died there in or after 1240 or 1241.

According to Fibonacci himself in the prologue of the Liber abaci (Book of the Abacus), he began his study of mathematics in Bugia, a Pisan colony on the Barbary Coast of Africa (modern Bejaïa, Algeria), where he joined his father, Guglielmo Bonacci, who was working as publicus scriba (public notary). The young Fibonacci learned the “nine figures of the numbers used by the Hindus,” i.e., Arabic ciphers. Later he became a merchant, visiting Egypt, Syria, Greece, Sicily, Provence, and Byzantium, and observing the manner in which mathematics was taught there. Fibonacci himself tells us that, on his travels, he engaged in public disputations and addressed specific mathematical questions posed to him by scholars of several countries, but especially at the court of the Holy Roman Emperor *Frederick II, including John of Palermo, “Master Theodoric,” and, above all, *Michael Scot, the imperial astronomer, astrologer, and philosopher, who encouraged him to revise the Liber abaci. Originally completed in 1202, a new edition of the work was produced in 1228. In 1240 or 1241 the citizens of Pisa awarded Fibonacci twenty pounds (denarii) in recognition of his lifetime’s service to the city state.

Fibonacci’s works have been preserved in numerous manuscripts. The original Liber abaci is lost, but the later edition survives. Although it is based largely on the work of *Euclid and the Islamic mathematicians *al-Khwarizmi and Abu Kamil, it is not without original contributions by Fibonacci himself. It is composed of a prologue and fifteen chapters in which the arrangement of the material both conforms to and reflects principles of order and systematization. The result is a summa, a complete encyclopedia of the most advanced mathematical learning of the period, which influenced mathematicians for several centuries.

Chapters One to Seven deal with elementary notions of arithmetic: Hindu numbers, the advantages of their use, their representation using the fingers of the hand; the four operations with whole numbers; the criteria of divisibility by 2, 3, 5, and 9; the proofs for casting out 7, 9, and 11; and the method of finding the common denominator of fractions. The Liber abaci also treats more difficult concepts, such as those of arithmetical progressions, their addition and their squares, and of equations of the first degree, whose solution is found through the method of the false position. Chapter Twelve, the most extensive of the work, is dedicated to a great number of curious problems, the most famous of which concerns the multiplication of rabbits. Supposing that any newborn pair of rabbits requires one month to reach maturity, and that thereafter it reproduces itself every month, the question is: how many pairs will there be at the end of n months? The answer is u_n where every number in the series is the sum of the preceding two—1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on. Fibonacci was able to demonstrate the truth of his theory, but he could not prove it. The principle of the Fibonacci Series is closely related to that of the Golden Ratio—a geometric proportion of ancient origin in which a line AB is divided at a point C such that AC:AB = CB:AC, which can be expressed numerically as:

$$\frac{1+\sqrt{5}}{2}=1.618033989$$

By dividing adjacent numbers in the Fibonacci Series it is possible to obtain an approximation of this ratio which becomes more and more precise as you go further up the series, tending to a limit that is the ratio at infinity. The Golden Ratio appears extensively in nature: the shells of snails, the heads of sunflowers, and phyllotaxy all conform to it. There are also instances of it in art and literature. A notable example of the use of the Golden Section in architecture is the Castel del Monte, a mysterious building in Apulia that was started during Fibonacci’s lifetime, possibly under his influence. This high, isolated landmark is built around an octagonal courtyard in two stories of eight rooms. Strangely, in view of its location and period, it is not fortified. It is unknown whether those parts of the Castel’s structure that reflect the Golden Ratio do so fortuitously or by design.

Chapter Thirteen of the Liber abaci concerns problems reducible to systems of five equations which Fibonacci solves using a method of double false position, the most advanced stage of pre-algebraic mathematics. Chapter Fourteen deals with the extraction of square and cubic roots, and with the problem of irrational squares. The last chapter (Chapter Fifteen) focuses on the theory of proportions, and “the method of algebra.” Here Fibonacci explains how to solve equations of the first and second degree, sometimes using irrational coefficients and geometrical demonstrations, all explained through one hundred concrete problems. Not all the Liber abaci is theoretical, however: chapters Eight to Eleven treat *“commercial arithmetic,” and suggest solutions to numerous commercial problems, especially those arising from the need to divide profits fairly in proportion to the amount of capital invested by each member of a company.

Fibonacci dedicated his Practica geometriae, written in 1220, to his friend the astrologer Domenico Ispano. Divided into eight parts, the work defines fundamental geometrical concepts (point, line, surface, angle, triangle, quadrangle); states the rules for extracting square and cube roots and shows some of their possible uses; and gives the formula for Heron’s triangle. It gives solutions to various practical problems of geometry, such as rules for measuring the length and surface area of land, and formulae for calculating the surface areas and volumes of plain and solid figures. It also describes methods for comparing values in different monetary currencies. In addition, the Practica geometriae contains several other important techniques, including a simplification of the Archimedean method of calculating pi, the use of the quadrant to measure altitudes, and examples of indeterminate analysis. In the mid-fourteenth century, the first four parts of the work were translated into Italian, under the title Savasorra id est libro di geometria.

It is uncertain whether the Castel del Monte in Apulia fortuitously conforms to the theories of Fibonacci or was designed deliberately to illustrate them. (AKG Images/Schütze/Rodemann)

In 1225 or 1226 Fibonacci responded to various questions that had been put to him by Giovanni of Palermo and other scholars at the imperial court in two further works, the Liber quadratorum, which remained unfinished and was for a long time considered lost, and Flos supersolutionibus quarundam questionum ad numerum et ad geometriam vel ad utrumque pertinentium. The former is devoted to the solution of problems concerning quadratic numbers and their reciprocal relations. The latter features the first complete equation of the third degree. Fibonacci returned to equations in his Quaestio mihi proposita a Magistro Theodoro domini imperatoris phylosopho. He was also the author of Trattato di minor guisa (a résumé of the Liber abaci), and a Commentary on the Tenth Book of Euclid, but both works have been lost.

See also Algebra; Arithmetic; Khwarizmi, al-

Bibliography

Primary Sources

Fibonacci, Leonardo. Liber abaci. In Baldassarre Boncompagni: Scritti di Leonardo Pisano, matematico del secolo decimoterzo, Vol. I. Il Liber Abbaci di Leonardo Pisano secondo la lezione del Codice Magliabechiano C.I, 2616, Badia Fiorentina, n.73. Roma: Tipografia delle scienze matematiche e fisiche, 1857, pp. 1–459.

———. Liber quadratorum; Flos super solutionibus quarundam questionum ad numerum et ad geometriam vel ad utrumque pertinentium; Questio mihi proposita a magistro Theodoro domini imperatoris phylosopho. In Baldassarre Boncompagni: Scritti di Leonardo Pisano, matematico del secolo decimoterzo. Vol. II. Opuscoli di Leonardo Pisano secondo un Codice della Biblioteca Ambrosiana di Milano contrassegnato E. 75. Parte superiore. Roma: Tipografia delle scienze matematiche e fisiche, 1862, pp. 227–283.

———. Practica geometriae. In Baldassarre Boncompagni. Scritti di Leonardo Pisano, matematico del secolo decimoterzo. Vol. II. La Practica geometriae di Leonardo Pisano secondo la lezione del Codice Urbinate n. 292 della Biblioteca Vaticana. Roma: Tipografia delle scienze matematiche e fisiche, 1862, pp. 1–224.

———. La pratica di geometria: volgarizzata da Cristofano di Gherardo di Dino, cittadino pisano, dal codice 2186 della Biblioteca Riccardiana di Firenze. Edited and with an Introduction by Gino Arrighi. Pisa: Domus Galilaeana, 1966.

———. É chasi della terza parte del XV capitolo del Liber abaci nella trascelta a cura di maestro Benedetto, secondo la lezione del Codice L.IV.21 (sec. XV) della Biblioteca comunale di Siena. Edited with an introduction by Lucia Salomone. Siena: Servizio editoriale dell’Università di Siena 1984.

———. Fibonacci’s Liber abaci: a translation into modern English of Leonardo Pisano’s Book of calculation. Translated by Laurence E. Sigler. New York: Springer, 2002.

———. The Book of Squares. Translated by Laurence E. Sigler. Boston: Academic Press, 1987.

———. Le livre des nombres carrés. Translated by Paul Ver Eecke. Bruges: Desclée de Brouwer, 1952.

Secondary Sources

Bartolozzi, Margherita and Raffaella Franci. La teoria delle proporzioni nella matematica dell’abaco da Leonardo Pisano a Luca Pacioli. Bollettino di Storia delle Scienze Matematiche (1990) 10: 3–28.

Folkerts, Menso. “Gli albori di una ‘matematica pratica’: Leonardo Fibonacci.” In Storia della Scienza. Medioevo. Rinascimento. Vol. 4, Roma: Istituto dell’Enciclopedia Italiana, 2001, pp. 320–321.

Franci, Raffaella and Laura Toti Rigatelli. Towards a history of algebra from Leonardo of Pisa to Luca Pacioli. Janus (1985) 72: 17–82.

Gies, Joseph and Frances Gies. Leonard of Pisa and the new mathematics of the Middle Ages. New York: Crowell, 1969.

Giusti, Enrico. “Matematica e commercio nel Liber abaci.” In Un ponte sul Mediterraneo: Leonardo Pisano, la scienza araba e la rinascita della matematica in Occidente. Edited by Enrico Giusti with di Raffaella Petti. Florence: Edizioni Polistampa, 2002, pp. 59–120.

Lüneburg, Heinz. Leonardi Pisani Liber abbaci oder Lesevergnügen eines Mathematikers. Mannheim: B.I. Wissenschaftsverlag, 1992.

Pepe, Luigi. “La riscoperta di Leonardo Pisano.” In Un ponte sul Mediterraneo: Leonardo Pisano, la scienza araba e la rinascita della matematica in Occidente. Edited by Enrico Giusti with di Raffaella Petti. Florence: Edizioni Polistampa, 2002, pp. 161–175.

Picutti, Ettore. Il Libro dei quadrati di Leonardo Pisano e i problemi di analisi indeterminata nel Codice Palatino 577 della Biblioteca Nazionale di Firenze. Introduzione e commenti. Physis (1979) 21: 195–339.

———. Leonardo Pisano. Le Scienze. Quaderni (1984) 18: 30–39.

———. Sui numeri congruo-congruenti di Leonardo Pisano. Physis (1981) 23: 141–170.

Rashed, Roshdi. “Fibonacci e la matematica araba.” In Federico II e le scienze. Edited by Pierre Toubert and Agostino Paravicini Bagliani. Palermo: Sellerio, 1994, pp. 324–337.

Tavolaro Aldo. Federico II di Svevia Imperatore e Leonardo Fibonacci da Pisa Matematico. Bari: Edizioni Fratelli Laterza, 1994, pp. 15–23 (concerning the Castel del Monte and Fibonacci numbers, pp. 25–35).

Ulivi, Elisabetta. “Scuole e maestri d’abaco in Italia tra Medioevo e Rinascimento.” In Un ponte sul Mediterraneo: Leonardo Pisano, la scienza araba e la rinascita della matematica in Occidente. Edited by Enrico Giusti with di Raffaella Petti. Florence: Edizioni Polistampa, 2002, pp. 121–123, 155.

MARIA MUCCILLO

Fihrist

The Kitab al-Fihrist (“Book of the Index”) is a booksellers’ catalogue of books written in Arabic (or translated into Arabic), ostensibly available for copying and sale. It was written in Baghdad in 987 C.E. by a bookseller named Abu’l-Faraj Muhammad ibn al-Nadim al-Warraq (“Warraq” meaning “paper maker,” and by extension, copyist and bookseller). Ibn al-Nadim was a Shi’ite intellectual, whose father was also a bookseller; he lived in Baghdad and died there in 995.

The book is divided into ten sections (maqalat): (1) On language, calligraphy, and the various scriptural traditions; (2) On grammarians; (3) On historians and genealogists, government officials who wrote books, works by different courtiers, singers, jesters, and the like; (4) On poetry; (5) On speculative theology (kalam); (6) On the various schools and traditions of Islamic Law (fiqh); (7) On the ancient sciences (philosophy, mathematics, astronomy, and medicine); (8) On storytellers, magic, and fables; (9) On non-Abrahamic religions (Buddhism, Hinduism, etc.) together with information on India and China; and (10) Mainly on alchemical writers. The book circulated in versions of different lengths, some containing only the last four chapters.

The Fihrist was apparently intended to be a guide for booksellers presented with practical problems arising when a customer ordered a particular work to be copied. Ibn al-Nadim describes talking to book collectors and seeing what books they had on hand. He takes pains to declare that the information provided is either based on his personal experience or came to him on good authority. Thus he will interject phrases like “from what I have seen myself” or “I read what was written in the handwriting of….” There are details about who copied or corrected which book. So, for example, with regard to translations of *Plato (Dodge, 593): “Three dialogues which Ibn al-Batriq translated, and which *Hunayn ibn Ishaq either translated or else Hunayn corrected what Ibn al-Batriq had translated.” If there were multiple versions of the same work, that is, the dealer had to know what to look for or suggest, and the customer, which version to order (and in the case of commentaries, which commentator). With the works of *Galen, for example, (evidently reflecting the multiplicity of copies and formats), he provides the name of the book, the name of the translator, how many sections; which sections were corrected by whom, and so forth. In some instances he gives a rough estimate of the number of leaves in a specific work, and such figures are given for all works of poetry so that the customer can judge whether he has been cheated with an abridged version.

The Fihrist provides a vivid picture of the great density of activities related to ancient sciences at this time. In the first chapter he recounts as fact the caliph al-Ma’mun’s famous dream of Aristotle that ostensibly gave rise to his passion for Greek philosophy and science, and which led to his sending a delegation to Byzantium in search of manuscripts. There is dispersed, but detailed, information on how the translation movement was organized. For example, he says that the Banu Musa (three brothers, themselves mathematicians) financially supported a group of philosophers including Hunayn ibn Ishaq and *Thabit ibn Qurra: “Each month the translation and maintenance amounted to about five hundred dinars” (Dodge, 585). He describes the personnel and activities of various caliphal libraries, including the Bayt al-Hikma.

The Fihrist is well appreciated as an unusually complete documentation of the translation movement, and the introduction and growth of Aristotelian philosophy in the Arabic-speaking world. But it is also a key document of the cultural and intellectual impact of paper technology. Ibn al-Nadim provides copious details about the history of papermaking, although some details appear to be purely conventional. For example, he states that paper had been made of flax in Khurasan by Chinese craftsmen in imitation of Chinese paper, although modern studies of these same papers show them to be largely of rag (Bloom, 44–45). He identifies many different kinds of paper, ostensibly because they were identifiable to book dealers and were therefore another element in their ability to authenticate specific manuscripts. He calls papers made in Baghdad after the administrator who used it—an indication of the physical particularity of different paper stocks. He describes different kinds of script, in different alphabets, and the work originally included specimens of script forms as illustrations.

See also Aristotelianism; Paper; Translation movements

Bibliography

Bloom, Jonathan M. Paper before Print: The History and Impact of Paper in the Islamic World. New Haven: Yale University Press, 2001.

Dodge, Bayard, ed. and trans. The Fihrist of al-Nadim: A Tenth-Century Survey of Muslim Culture. 2 vols. (paginated consecutively). New York: Columbia University Press, 1970.

THOMAS F. GLICK

Fishing

Fishing was practiced on inland and coastal waters nearly everywhere in medieval Europe, although the target species, intensity, and economic orientation of this activity varied. As medieval fisheries evolved in response to economic and environmental change, so did the importance and scale of chosen techniques for capture, preservation, and marketing of the catch.

Religious taboos and the prestige derived from eating a costly food shaped medieval demand for fish. Latin Christian rules allowed fish on the one day in three when they forbade animal flesh. For medieval elites, lay and clerical, fish on the table showed off wealth and piety. Poorer folk had to be content with small portions of disfavored varieties about as often as they ate comparable meats. From a subsistence activity of peasants and those serving great households, medieval fishing developed further as a small, then large-scale, commercial enterprise supplying urban markets.

Up to the central medieval centuries (roughly 1000–1300 C.E.), Europeans ate almost exclusively those fishes naturally present in local and nearby waters. Available transport and preservatives could not get fish to distant consumers for later use. Growing human numbers increased fishing pressure against limited and even depleted natural stocks of inland, migratory, and coastal fishes. This encouraged privatization of lucrative fishing rights, governmental regulation, and development of new marine and artificial fisheries. From even before 1200 innovations in preservation and marketing were as key as capture techniques for expanding use of, for instance, herring and cod from the North Atlantic Ocean and tuna from the Mediterranean Sea. About that same time inland estate managers learned how to rear certain freshwater fishes in ponds for fresh local consumption.

Consistent success called for good local environmental knowledge of the quarry and conditions across the diverse inland and marine waters of Europe. Fishers chose among traditional techniques still predominant as late as 1900. Simple movable gear targeting certain species or locations was ubiquitous. Some fishers knew how to catch fish by hand, incapacitate them with botanical, chemical, or primitive explosive preparations, or use a spear. The hand line with a single baited hook was normal for northern cod, southern hake, and many inland fishes. Besides live and prepared baits, medieval fishers made artificial lures from feathers or metal. Fish seeking food or shelter entered funnel-shaped basket traps (called retia, netz, weels, Reussen, vervaux, etc.) designed to prevent escape. These devices of wicker or webbing could be set independently in likely spots or as the operative element in a weir, sluice, or barrier trap.

One or two fishers could deploy larger panels of netting passively or actively. Nets stretched between poles in estuaries held fish, particularly seasonal migrants such as salmon and sturgeon. Hanging appropriate mesh on frames or with weights below a float line let desired fish put the head through, then caught the gill cover. Gill nets took whitefishes from cold inland lakes and, perhaps since the 700s, herring from the North Sea and the Baltic Sea. The seine, an elongate strip of netting, was actively maneuvered from one or both ends to encircle a school, then pulled to shore or into a boat to collect the catch. Various seines gave good catches from large coastal and inland waters of northern and southern Europe. The trawl, a bag of netting dragged behind a boat to scoop up fish, needed more powerful equipment, which limited its use. In 1376 fishers in eastern England complained that a new bottom trawl called wonderchoun harmed marine habitat.

More permanent installations called “fishery” (piscatura, piscaria) blocked, concentrated, and held especially fishes on seasonal migration. Perhaps every water mill had traps for eel or salmon in its race and spillway. Specialized fish weirs, fences of posts supporting brushwood or woven panels, angled across a current to funnel migrants into a trap or chamber. English rivers still contain traces of Anglo-Saxon and Norman weirs. Analogous structures of stone occur along French rivers and tidal coasts. Rows of close-set stakes channeled herring schools at the mouth of the Schlei estuary since at least the sixth century. On the north coast of Sicily post and net tuna traps (tonnara) extending as much as a kilometre seawards evolved from Arab and Byzantine prototypes and, since the thirteenth century, supplied a major export industry. Like big seines and trawls, fixed fisheries employed larger work crews.

Seasonal abundance required storage for later use. Smoking and light salting offered short-term solutions. Drying worked for non-oily varieties where the climate provided dry heat (Mediterranean hake) or cold (Norwegian “stockfish,” dried cod). Oil-rich herring, sardine, and mackerel had to be kept from the air or treated copiously with salt. Herring salted whole on North Sea beaches were sold in bundles of a thousand; they lasted the few cool months from late fall catch to Lenten consumption. A breakthrough came with probably thirteenth-century recognition that a partly gutted herring barrelled in salt brine kept much longer, allowing larger offshore catches to be shipped to consumers further inland. Similar packaging served Scottish salmon and Sicilian tuna. Much earlier many large consumers (castles, monasteries, towns) had facilities for live storage: net or wicker cages, wooden tanks, dug ponds (servatoria, vivaria, “stews”). This was not, however, aquaculture.

Fish farming meant control over selected animals for continual production. Probably in twelfth-century central France estate managers developed methods for controlling the water stored in dammed ponds, so that they could fill the pond to rear selected young fish and some years later drain it to harvest the adults. Specialized ponds for spawning selected brood stock and protecting the larvae followed. Techniques pioneered with a native western cyprinid, bream, were adapted around 1250 to the faster-growing carp, recently introduced from the Balkans, and spread across central Europe. Professional pond masters got big annual yields by staged rotation of several artificial water bodies, each covering hundreds of hectares.

See also Food storage; Shipbuilding; Watermills; Zoology

Bibliography

Aston, Michael, ed. Medieval Fish, Fisheries and Fishponds in England. 2 vols. BAR British series 182. Oxford: BAR, 1988.

Hoffmann, Richard C. Economic Development and Aquatic Ecosystems in Medieval Europe. American Historical Review (1996) 101: 631–669.

———. Fishers’ Craft and Lettered Art: Tracts on Fishing from the End of the Middle Ages. Toronto: University of Toronto Press, 1997.

———. “Medieval Fishing” In Working with Water in Medieval Europe: Technology and Resource Use, edited by Paolo Squatriti. Leiden: E.J. Brill, 2000.

Kowaleski, Maryanne. The Expansion of the Southwestern Fisheries in Late Medieval England. Economic History Review (2000) 2d series 53: 429–454.

RICHARD C. HOFFMANN

Food Storage and Preservation

Societies in the medieval period had developed primarily into settled agricultural communities and cities, which were subject to food availability based on seasonal cycles of bounty and dearth, unpredictable weather, and transportation delays. The preservation and storage of foodstuffs to sustain the population throughout the year was imperative for its survival.

Various methods of food preservation had developed prior to the Middle Ages and remained largely unchanged until the development of canning in the nineteenth century, but even then the principle of the technology remained constant. Simply put, food preservation results from killing, or greatly hindering, the efficacy of micro-organisms that cause decay and rot. Civilizations around the world used variants on universal methods that altered according to their climate and obtainable foodstuffs.

One way to preserve food was by physical means (drying or cooling), whereby the provisions were preserved for as long as the status remained unchanged. Air or sun provided the simplest means of preserving food by removing the moisture from it. Grains in Europe, rice in Asia, maize in the Americas—all staple products—were dried and stored in cellars or silos to use throughout the year. Fruits, including grapes (raisins), plums (prunes), and apricots, were sun-dried in the warmer climates of the Middle East, Mediterranean and Asia, while for more moderate temperatures, ovens dried out foodstuffs to be stored away in cellars, attics, or sometimes even in bedrooms. In the extreme north of Scandinavia, stockfish were left out in open to dehydrate in the cool, dry air, and South Americans in the altiplano freeze-dried potatoes. In the imperial palaces of China, ice was carried down from the mountains in the winter or spring and placed in deep pits to keep food frozen or cold during the summer months.

Le Menagier de Paris (1393) explains the common practice to preserve fish by drying:

“Cod. When it is taken in the far seas and it is desired to keep it for ten or twelve years, it is gutted and its head removed and it is dried in the air and sun….”

An alternative method of preservation was by chemical means (smoking, salting, brining, conserving, fermenting), which resulted in a shorter incubation period but offered alternatives that also enhanced or changed the flavors of the foods to be preserved. Smoking, by hanging the food in a chimney for several days, also dried food while imparting flavor to the food. To avoid feeding livestock through winters, extra animals were usually butchered in the fall, and chunks of meat, bacon, and sausages, as well as fresh- and salt-water fish were smoked and then hung from rafters away from rodents.

Salting food to extract moisture was common in various cultures, and in addition to meat and fish, vegetables were layered with salt and pressed into earthenware crocks and stored for the winter. Butter, too, was heavily salted. A variation of using salt as a preservative was pickling, or brining, whereby food was preserved in a salty liquid, sometimes with the addition of an acid (lemon, verjuice, or vinegar). The Arab cookery book Kitab wasf al- at’ima al-Mu’tada (c. 1373) lists turnips, cucumbers, eggs, plums, carrots, eggplants, hearts of garlic, and fish as ingredients to be pickled. The Chinese pickled crabs, while along the Mediterranean people stored pickled capers, eggplant, olives, limes, and fish in large jars until they were needed.

Preserves or comfits entailed the practice of covering foods with honey, or cooking them with sugar, which sealed the food from air and bacteria, while confits, or potting, preserved meats and poultry cooked in fat and stored in pots covered with fat. Again, this method was near universal, from cherries in China and oranges in France, to lamb in the Middle East.

So far from stopping or hindering living organisms from rotting foodstuffs, fermentation actually encouraged their introduction to convert desirable changes to provisions that made them more easily digestible and longer lasting. Throughout Europe, vintners turned grapes into wine, sometimes stored for years in wooden barrels and wine cellars. Alewives brewed grain into beer, a drink that provided a large part of the caloric makeup of peasants in Northern Europe. Andeans drank chichi, fermented grains and fruits, and in Mexico, the sap of the agave plant was fermented into pulque. In Asia, fermenting soy allowed easier digestion. The longevity of milk was also extended by fermenting it into cheese, which could be eaten immediately or salted and stored for years in a cellar. In al-Andalus, Spain, it was recommended that cheesemaking occur in March/April and that the product be left outside in the shade to cure until May. In India, earthen pots that held buttermilk (fermented milk) were stored underground and kept cold from Himalayan ice.

See also Agriculture

Bibliography

Carlin, Martha and Joel Rosenthal, eds. Food and Eating in Medieval Europe. London: The Hambleton Press, 1998.

Chang, K.E., ed. Food in Chinese Culture: Anthropological and Historical Perspectives. New Haven: Yale University Press, 1977.

Hörandner, Edith. “Storing and Preserving Meat in Europe: Historical Survey.” Food in Change: Eating Habits from the Middle Ages to the Present Day. Edited by Alexander Fenton and Eszter Kisban. Atlantic Highlands: Humanities Press, 1986.

Mennell, Stephen. All Manners of Food: Eating and Taste in England and France from the Middle Ages to the Present. Chicago: University of Illinois Press, 1985.

Power, Eileen. The Goodman of Paris. New York: Harcourt, Brace, 1928.

Prakash, Om. Food and Drinks in Ancient India. Delhi: Munshi Ram Manohar Lal, 1961.

Rodinson, Maxime, A.J. Arberry and Charles Perry. Medieval Arab Cookery. Devon, England: Prospect Books, 2001.

Superk, John C. Food, Conquest, and Colonization in Sixteenth-Century Spanish America. Albuquerque: University of New Mexico Press, 1988.

Wheaton, Barbara Ketcham. Savoring the Past: The French Kitchen and Table from 1300–1789. New York: Simon and Schuster, 1983.

BETH MARIE FORREST

Frederick II

Frederick Hohenstaufen, son of emperor Henry VI and Constance, heiress to the Norman kingdom of Sicily, was born in 1194 in the march of Ancona. Educated in southern Italy, Frederick was crowned Holy Roman Emperor in 1220 after more than two decades of virtual interregnum. Immediately after his accession he tried to impose a strong rule in Sicily, eventually succeeding and thus gaining a strong basis of economic power in the south. His conflict with the northern Italian cities, virtually declared in the imperial diet of Cremona in 1226, turned by 1235 into an open war between the empire and the Lombard League—a protracted confrontation that lasted until Frederick’s death in 1250 in Apulia. Reluctantly, Frederick led a crusade to the Holy Land between 1228 and 1230 with the diplomatic success of regaining Jerusalem for the West. His long struggle with Rome—which resulted in the emperor’s deposition by Pope Innocent IV in Lyons—prompted accusations of heresy from the papal party answered by imperial propaganda.

In the eyes of his admirers Frederick was a patron of learning, the animator of a vital cosmopolitan court resulting from the Sicilian mixture of Latin, Greek, and Arab cultures. According to other interpreters, he was not the enlightened despot of legend but an overripe medieval knight. If Frederick’s court culture were compared with that of thirteenth-century *Alfonso X, it would be to the disadvantage of the former. Frederick’s most significant scholarly achievement is his treatise On the Art of Falconry, of which two versions have been preserved, the larger in six books. It includes an original discussion on the nature, anatomy, and habits of birds which draws on the author’s experience and Aristotle’s works on animals. Frederick’s announcement that he will show “things as they are” and will oppose Aristotle on those matters in which he erred, has won for him a reputation as a “modern,” empirical observer of nature. Considered in terms of medieval *scientia, his treatise on hawking is hardly a “scientific” work and should be better seen as an accomplished example of technical literature. Besides, it has been claimed that Frederick’s strictures on Aristotle reveal his dependence on the medical approach to the study of living beings developed in *Salerno. Anyway, this work is an outstanding contribution to the princely literature on animals, for which he had a passion. Frederick’s itinerant court included a menagerie of exotic beasts with which he even crossed the Alps.

Frederick maintained a learned diplomatic correspondence, e.g., the “Sicilian letters,” a group of questions on controversial natural philosophical topics circulated among Muslim rulers and philosophers. He also addressed a famous questionnaire on cosmology to *Michael Scot, his court astrologer from around 1227 until the former’s death in 1236. Scot had translated Aristotle’s On animals while in Toledo and dedicated to Frederick his translation of *Ibn Sina’s Abbreviatio de animalibus. During his period in the emperor’s service he wrote astrological treatises and a book on physiognomy and translated commentaries by *Ibn Rushd. *Leonardo Fibonacci, who introduced Arabic numerals into the West, met Frederick in Pisa in 1225 and dedicated to Scot the revised edition of his Liber abaci, besides including in his Liber quadratorum the answers to questions posed to him by scholars of Frederick’s court such as Theodore of Antioch. Master Theodore succeeded Scot as Frederick’s astrologer, wrote a treatise on hygiene for the emperor and translated from the Arabic Moamyn’s On the Art of Hawking—it is said that Frederick himself supervised the translation. Jacob Anatoli, a Jewish scholar of the Ibn Tibbon family, enjoyed some kind of patronage from the emperor: he translated into Hebrew Ibn Rushd’s commentary on Aristotle’s logical works and Ptolemy’s Almagest.

Frederick founded in 1224 in Naples the first state university, where *Thomas Aquinas was taught natural philosophy by John of Ireland. In 1231 the emperor regulated the curriculum and the practice of medicine at Salerno, demanding one year of practical training after five years of study and the obligatory teaching of *anatomy to surgeons. Some medical literature arose in connection with Frederick’s patronage. *Petrus Hispanus (medicus) dedicated his treatise on diseases of the eye to a personage of the court and mentions Theodore as “my teacher.” Adam, a chanter of Cremona in the north, dedicated to Frederick a treatise on hygiene for the crusading army, and Peter of Eboli wrote for the emperor a poem on the baths of Pozzuoli. Jordanus Rufus of Calabria wrote under Frederick his Latin treatise on veterinary medicine, but the work was not completed until after the emperor’s death.

See also Natural history; Patronage of science; Translation movements; Zoology

Bibliography

Abulafia, David. Frederick II. A Medieval Emperor. Oxford: Oxford University Press, 1992.

Asúa, Miguel de. El De arte venandi cum avibus de Federico II. Veritas (1999) 44: 541–553.

Frederick II. The Art of Falconry being the De arte venandi cum avibus. Trans. by Casey A. Wood and F. Marjorie Fyfe. Stanford: Stanford University Press, 1943.

Haskins, Charles H. Studies in the History of Mediaeval Science. New York: Frederick Ungar, 1960.

Nitschke, August. “Federico II e gli scienziati del suo tempo.” In Atti del Convegno di studi su Federico II, Jesi, 28–29 maggio 1966. Edited by Edoardo Pierpaolo. Jesi: Biblioteca Comunale, 1976.

MIGUEL DE ASÚA

Frugard, Roger

Roger Frugard, an obscure teacher and surgeon who lived and worked in late twelfth-century Parma (c. 1170), was the first and perhaps the most important of the great medieval surgical authorities—a remarkable feat, given that he never actually wrote. It was Guido Arrezzo the Younger, himself the author of a handbook on medication, who, with the help of several of Roger’s pupils, organized sets of lecture notes into a head-to-toe exposition on surgical treatment in four distinct sections. The resulting book, the Chirurgia, inaugurated the long and distinguished tradition of medieval surgery. The Chirurgia, like Roger’s teachings on which it was based, was more empiric than academic, contained few references to established medical authorities, and reflected little of the Arabic scholarly activity that had perpetuated single-handedly the learned Greco-Roman traditions of medicine derailed in the fall of Alexandria. Nonetheless, the Chirurgia quickly captured the imagination of commentators at *Salerno, who produced “The First Salernitan Gloss” around the end of the century. In response, Roland, one of Roger’s disciples at Parma, added his own set of commentaries in an extremely popular version that would become known as the “Rolandino.” This version, in turn, was glossed yet further by the Salernitans, whose resulting text, known as “The Four Masters Gloss,” replaced Guido’s anatomical arrangement with one based instead on humors and pathology. The fame of Roger of Parma, as he eventually became known, was not confined to Salerno. Surgeons at Montpellier also found much to admire in the Chirurgia; not only the thirteenth-century surgeon and teacher Guillaume de Congenis but also one of his pupils wrote surgeries heavily indebted to Roger’s teachings. Indeed, twenty manuscripts survive in Latin along with numerous translations, including Catalan, Old French, Anglo-Norman, and Middle English versions.

See also Medicine, practical

Bibliography

Hunt, Tony. Anglo-Norman Medicine. Cambridge: D.S. Brewer, 1994.

———. The Medieval Surgery. Woodbridge: Boydell, 1992.

Siraisi, Nancy. Medieval and Early Renaissance Medicine: An Introduction to Knowledge and Practice. Chicago: University of Chicago Press, 1990.

JEREMY CITROME