Medieval Science, Technology and Medicine

Abraham Bar Hiyya

Abraham Bar Hiyya (c. 1065–c. 1140) is the genuine pioneer in the rise of medieval Hebrew science, a process in which Jewish scholars gradually abandoned Arabic and adopted Hebrew as the language for expressing secular and scientific ideas. After the completion of the Islamic conquests in the eighth century, Jews had willingly adopted the Arabic language, spoke it fluently, and participated, together with Muslims, Christians, and members of other religions, in the reception and integration of the Greek worldview into Arabic culture and language. This honeymoon between Jewish intellectuals and the Arabic language did not, however, outlast the successive invasions of Muslim Spain by the fundamentalist Berber dynasties of the Almoravides (1090) and the Almohades (1145). As a result, a remarkable transition from Arabic to Hebrew ensued, of which Abraham Bar Hiyya was the first, and perhaps the greatest, exponent.

Little is known about Abraham Bar Hiyya’s life. However, he left significant information about his scientific career in the final paragraph of an epistle that he addressed at an elderly age to Rabbi Judah ben Barzilai of Barcelona. In it he reports that he was held in high esteem by grandees and kings, and that he was engrossed from his youth by learning, dealing with, inquiring into, and teaching the so-called “science of the stars”—hokhmat ha-kokhavim, a calque translation of the Arabic ‘ilm alnujum, a term employed by *al-Farabi (c. 870–c. 950) in his Ihsa al-‘ulum (Classification of the Sciences). Like al-Farabi, Bar Hiyya defined the “science of the stars” in two of his works as a composite body of learning that included astronomy as well as *astrology.

Bar Hiyya’s reference to his connections with grandees and kings is borne out by his appellation “Savasorda,” a corruption of sahib al-shurta (chief of the guard). It has been surmised by some commentators that he lived in Huesca, in the Arabic kingdom of Zaragoza-Lerida, where he attained mastery of Arabic sciences and high dignity under the rule of the Banu Hud dynasty. Bar Hiyya was probably also a scion of an important Jewish family, a fact which is indicated by his title ha-Nasi (the Prince).

Abraham Bar Hiyya’s scientific work is truly encyclopedic and covers five main areas of medieval science: astronomy, mathematics, the Jewish *calendar, astrology, and philosophy. Whereas the astronomical, mathematical, and philosophical components are clearly flagged in the list of Bar Hiyya’s scientific works, none of his output has astrology in its title. Nonetheless, substantial astrological material may be found in three of his non-astrological works. All of Bar Hiyya’s original scientific works were written in Hebrew, thus testifying that he developed his scientific career principally among Jews. His scientific works are now presented separately.

Yesodey ha-tevuna u-migdal ha-’emuna (Foundations of Understanding and Tower of Faith) is the first medieval Hebrew encyclopedia of science. The title suggests that it was planned as a work in two parts, the first covering all scientific learning and the second intended as a summary of religious knowledge. Only the introduction and the beginning of the first part are extant, and it is not clear if Bar Hiyya ever completed his encyclopedia. In the introduction, Bar Hiyya informs the reader that he wrote the encyclopedia at the request of the Jews of France, i.e., Provence; he elaborates on wisdom and the tripartite human soul, and gives a hierarchical classification of the sciences, presenting a table of contents of the whole planned encyclopedia. The first part of the extant segment follows Nicomachus of Gerasa and *Muhammad ibn Musa al-Khwarizmi and deals with the theory of numbers, arithmetical operations, and rules for mercantile calculations (regula mercatorum); the second part follows *Euclid, Menelaus of Alexandria, *Archimedes, Hero, and notably al-Farabi, and deals with geometry, optics, and music.

Hibbur ha-meshiha ve ha-tishboret (Treatise on Mensuration and Calculation) is a mathematical work conceived as a nontechnical textbook for the use of land-holders and judges. Bar Hiyya, however, went far beyond the practical needs of elementary land measurements and added in many cases relevant theorems and their mathematical demonstrations. The work was translated into Latin by Plato of Tivoli under the title Liber embadorum, Bar Hiyya perhaps collaborating in the enterprise. The treatise is divided into four parts: the initial section defines general concepts and terms such as point, straight line, area, and various types of angles. The second part, the largest section of the treatise, is devoted to problems of mensuration; the third follows a lost work by Euclid and deals with the division of parcels of land, while the fourth is devoted to the calculation of the volume of various bodies. A main characteristic of this treatise is that Bar Hiyya consistently avoided the measurement of angles, with the exception of right angles.

Astronomy in Bar Hiyya’s oeuvre is represented by two treatises—Surat ha-ares (The Shape of the Earth) and Heshbon mahalakhot ha-kokhavim (Computation of the Motions of Stars)—and a set of astronomical tables. The treatises were written in Barcelona in 1136 and are presented in the introduction to Surat ha-ares not as isolated works but, together with an astrological work that is not extant, as an interwoven trilogy meant to deal with the various features of the science of the stars. Surat ha-ares follows al-Farghani’s Kitab fi harakat alsamawiyya wa yawami ‘ilm al-nujum (Treatise on the Motion of the Heavens and the Complete Science of the Stars), and its rationale was presented by Bar Hiyya as the need to deal with the “shape of the configuration in the heavens and in the earth, and the order of the motion visible in the skies and in the stars, and its path and measure in each of them, and the proofs demonstrating it.” Bar Hiyya drew up a set of planetary tables called Luhot ha-nasi (Tables of the Prince) or Jerusalem Tables since their radix is Jerusalem. The canons of these tables are found in Heshbon mahalakhot ha-kokhavim, a work that follows closely *al-Battani’s Zij al-Sabi, and which was aimed by Bar Hiyya at expounding the “way of computing the course of these moving celestial bodies, and how you can ascertain the position of the stars in the sky at any time you may wish.”

On the subject of the Jewish calendar, Bar Hiyya wrote Sefer ha-‘Ibbur (Book of Intercalation), which was in all likelihood the first Hebrew work of this type. This treatise includes, beside typical calendrical material and a strong dose of polemics, rich astronomical materials whose counterpart may be found in Bar Hiyya’s astronomical work. The first part introduces basic astronomical and cosmographic concepts, such as lunar and solar motions, and the relation of the seven climates and latitudes to the duration of day and night. The second and third parts of the book deal respectively with the lunar month and the solar year, their astronomical characterization and calendrical implications.

Astrological Predictions

Bar Hiyya devoted the whole of Megillat ha-megalleh (Scroll of the Revealer) to foretelling the exact date of the coming of the Messiah, mainly by means of Scriptural data. Its fifth chapter, however, is an impressive astrological work in which Bar Hiyya included a voluminous Jewish and universal astrological history, and provided a parallel astrological prognostication of the days of coming of the Messiah. Four main parts may be discerned. Its introduction is devoted to a justification of the use of astrology to predict the time of coming of the Messiah, in particular, and to analyze the course of history in general. In the second part, Bar Hiyya correlates the biblical account of Jewish history, from the birth of Moses and the exodus from Egypt to the destruction of the second temple, with a series of consecutive conjunctions of Saturn and Jupiter, as well as other celestial phenomena. Next, Bar Hiyya shows the correspondence between the subsequent conjunctions of Saturn and Jupiter and a general universal history, from the birth of Jesus and the founding of the Christian religion to the conquest of Palestine by the Crusaders. In the fourth and final part, Bar Hiyya utilizes the ensuing Saturn–Jupiter conjunctions to provide a futuristic view of world history from the beginning of the first quarter of the twelfth century, that is, from his own times, to the coming of the Messiah, which, according to his calculations, should have supervened in 1448 or 1468. The most marked feature in the astrological history is the interpretation of horoscopes cast at the vernal equinoxes of the years in which there are conjunctions of Saturn and Jupiter. Besides the three traditional types of conjunctions (small: every 20 years; great: every 238 years, and strong: every 953 years), Bar Hiyya introduced an unprecedented “huge” conjunction with a period of 2,869 years, which serves as the chronological framework into which he built his complete astrological history.

Bar Hiyya also wrote a long, apologetic epistle to Rabbi Judah ben Barzilai of Barcelona, justifying the study and use of a specific astrological approach. Bar Hiyya shows that his permissible version of astrology is in perfect harmony with main tenets of Judaism, as well as closely related to astronomy, but disconnected from astrological magic. From this epistle we may infer that Bar Hiyya endorsed the main tenets of astrology and that he integrated astrological considerations into his tasks as a rabbi. We know also from this letter that his astrologically oriented activities while serving as a rabbi aroused sharp criticism and that he adopted an apologetic stance vis-à-vis his attackers. We know for certain from the introduction to Surat ha-ares that Bar Hiyya planned a whole astrological textbook. This book, however, is not extant; the possibility should not be excluded that it was never written. The last three chapters of the Heshbon mahalakhot ha-kokhavim were devoted to the explanation of astronomical procedures which actually embody typically astrological tasks such as the calculation of the twelve astrological houses and of the astrological aspects. It has been suggested that Bar Hiyya assisted Plato of Tivoli in the translation of astrological works into Latin.

Besides the first part of Megillat ha-megalleh, Bar Hiyya expounded his Neoplatonic philosophical thinking in Hegyon ha-nefesh ha-asuvah (Meditation of the Sad Soul). In the first cosmological part of this work Bar Hiyya deals with the creation of the world as it is narrated in Genesis. The three other chapters are devoted to morality and penitence, repentance, good and evil, and the saintly life. The emphasis is ethical, the approach is generally homiletical and based on the exposition of biblical passages. It is less frequently quoted than Bar Hiyya’s other works.

See also Astrolabes and quadrants; Optics and catoptrics

Bibliography

Baron, S. A Social and Religious History of the Jews. New York: Columbia University Press, 1958.

Langermann, Y.T. The Jews and the Sciences in the Middle Ages. Brookfield, Vt: Ashgate/Variorum, 1999. I: 10–16, 32.

Lévy, T. Les débuts de la littérature mathématique hébraïque: La géométrie d’Abraham Bar Hiyya (XIe–XIIe siècle). Micrologus, Nature, Sciences and Medieval Societies (2001) 9: 35–64.

Sela, S. Abraham. Ibn Ezra and the Rise of Medieval Hebrew Science. Leiden: E.J. Brill, 2003.

Sirat, C. A History of Jewish Philosophy in the Middle Ages. New York: Cambridge University Press, 1990.

Steinschneider, M. “Abraham Judaeus—Savasorda und Ibn Esra.” In Gesamelte Schriften. Berlin, 1925: 327–387

Stitskin, Leon D. Judaism as a Philosophy—The Philosophy of Abraham Bar Hiyya (1065–1143). New York: Bloch, 1960.

SHLOMO SELA

Abu Ma‘shar

Abu Ma‘shar Ja’far ibn Muhammad ibn ‘Umar al-Balkhi (Albumasar) is the best-known astrologer of the Middle Ages. He was born in Balkh in the Persian province of Khurasan in 787 C.E., and died in al-Wasit in central Iraq in 886. He apparently spent most of his life in Baghdad, where he lived by the Khurasan Gate. His extant works were written in Arabic, but he retained his allegiance to the Persian cause; he refers to Persian astronomical tables (the zij al-Shahriyar), and he gave currency to an account of the history of science which privileged the Persian contribution. According to a story in the *Fihrist, Ibn al-Nadim’s tenth-century bio-bibliography, Abu Ma‘shar was a student of Islamic tradition, until, at the age of forty-seven, he was tricked into studying *arithmetic and geometry by the “Philosopher of the Arabs,” *al-Kindi, and consequently turned to the study of the stars. Although there is one arithmetical work, on amicable numbers, attributed to Abu Ma‘shar, and references to astronomical tables drawn up by him, all the other texts that survive in his name are on the subject of *astrology. The best-known of these is his Great Introduction to Astrology. This work, of which two versions appear to have been written, one in 848 and the other in 876, sets astrology firmly within the framework of Aristotelian natural philosophy, and provides, in the first of its eight books, a detailed defense of astrology. His Book of Religions and Dynasties (known in its Latin version as On the Great Conjunctions) is of similar dimensions, and deals with the effects on whole nations, on dynasties, and on rulership, of conjunctions of the superior planets, and of other celestial phenomena. Other works deal with the remaining principal branches of astrology: natal horoscopes, anniversary horoscopes, choices, questions, and weather forecasting. Abu Ma‘shar is eclectic by nature, drawing on both ancient Greek astrology (especially *Ptolemy’s Tetrabiblos and Dorotheus’s Carmen Astrologicum), and Middle Persian sources (which in turn incorporate Indian elements), apparently using previous translations and interpretations of the Greek and Persian material (especially those of *Masha’allah) rather than the original texts directly. His work became well known in Western Europe, first through the translation of a shorter version of his Great Introduction to Astrology by *Adelard of Bath, then through two independent translations of the Great Introduction itself made by *John of Seville (1133) and *Hermann of Carinthia (1140), and finally by translations of his major works in the various branches of astrology made in the circle of John of Seville in *Toledo in the mid-twelfth century, with two texts translated from Greek by Stephen of Messina in the mid-thirteenth century: De revolutionibus nativitatum (on anniversary horoscopes), and Albumasar in Sadan (anecdotes concerning Abu Ma‘shar recorded by his pupil Shadhan). Abu Ma‘shar’s discussions of natural science and astrology were an important source for Western writers on philosophy in the twelfth century (especially Hermann of Carinthia and Daniel of Morley); his “conjunctionalism” became very popular in the political and eschatological astrology of the later medieval and early modern period (e.g., *Pierre d’Ailly), while his defense of astrology was the starting point of many of the arguments for and against the science (e.g., those of Pietro Pomponazzi and Giovanni Pico della Mirandola).

Bibliography

Primary Sources

Abu Ma‘shar. The Abbreviation of the Introduction to Astrology, together with the Medieval Latin Translation of Adelard of Bath. Edited and translated by C. Burnett, K. Yamamoto, and M. Yano. Leiden: E.J. Brill, 1994.

———. On Historical Astrology. Edited by Keiji Yamamoto and Charles Burnett, 2 vols. Leiden: E.J. Brill, 2000.

Abu Ma‘sar al-Balhi. Liber introductorii maioris ad scientiam judiciorum astrorum. Edited by Richard Lemay. 9 vols. Naples: Istituto universtaria orientale, 1995–1996, vol. V.

Albumasaris De revolutionibus nativitatum [Greek translation]. Edited by David Pingree. Leipzig: Teubner, 1968.

Secondary Sources

The Fihrist of al-Nadim. Translated by Bayard Dodge, 2 vols. New York: Columbia University Press, 1977.

Lemay, Richard. Abu Ma‘shar and Latin Aristotelianism in the Twelfth Century: The Recovery of Aristotle’s Natural Philosophy through Arabic Astrology. Beirut: American University of Beirut, 1962.

Pingree, David. The Thousands of Abu Ma‘shar. London: Warburg Institute, 1968.

———. “The Sayings of Abu Ma‘shar in Arabic, Greek, and Latin.” In Ratio et Superstitio: Essays in Honor of Graziella Federici Vescovini, ed. G. Marchetti, Orsola Rignani, and Valeria Sorge. Louvain-la-Neuve: Fédération Internationale des Instituts d’Études Médiévales, 2003, pp. 41–57.

Saliba, George. Islamic Astronomy in Context: Attacks on Astrology and the Rise of the Hay’a Tradition. Bulletin of the Royal Institute of Inter-Faith Studies (2002) 4: 24–46.

Smoller, L.A. History, Prophecy and the Stars: the Christian Astrology of Pierre d’Ailly, 1350–1420. Princeton: Princeton University Press, 1994.

CHARLES BURNETT

Adelard of Bath

Adelard of Bath was a pioneer in introducing Arabic science into the Latin curriculum of the liberal arts. Born c. 1080 in Bath in the west of England, he went abroad to study—first to France, and then, following in the wake of the First Crusade, to the Principality of Antioch, Magna Graecia (Southern Italy), and Sicily. After seven years’ absence he returned to England, probably spending most of his time in Bath, but during the troubled years of the civil war (1135–1154) he seems to have joined the household of the Duke of Normandy, since he dedicated his De opere astrolapsus (On the Use of the Astrolabe), to Henry, the son of the Duke, and the future King Henry II, early in 1150. Since we have no later record concerning him, Adelard may have died soon after this dedication. His works were well known both in northern France (e.g., at Mont-Saint-Michel and Chartres), and in England, where several students and followers of his can be identified.

Adelard regarded “philosophy” (the seven liberal arts that were the backbone of education in the secular arts since late antiquity) as a single entity, whose parts could not be studied without each other. He aimed to show this in an exhortation to the study of philosophy, which he called De eodem et diverso (On the Same and the Different), in which each of the seven liberal arts is described in a dramatic setting. Some notes on music theory survive, and there is evidence that Adelard wrote a text on rhetoric. Nevertheless, it is to geometry and astronomy that he paid most attention. He made the first complete translation (from Arabic) of *Euclid’s Elements, and his adaptation of this version for teaching (the so-called Adelard II Version) became the standard geometry textbook for several generations of students. He also translated a set of astronomical tables by *al-Khwarizmi (early ninth century), together with the rules for using them. The starting-point of the tables is 1126, and one of the half-dozen extant manuscripts preserves a copy made in the scriptorium of Worcester Cathedral before 1140. The tables follow the Indian models of computation that had been used by early generations of astronomers of the Abbasid period in Baghdad, but which had been superseded by Ptolemaic models in the Islamic Orient by Adelard’s time. Adelard’s treatise on the astrolabe (De opere astrolapsus) draws on his translation of the Elements and on the Tables, as well as on earlier texts on the instrument, and includes a summary of Ptolemaic cosmology. Adelard regarded the ultimate aim of astronomy as enabling one “not only to declare the present condition of earthly things, but also their past or future conditions,” and to further this aim he translated two Arabic texts on *astrology: the Abbreviation of the Introduction to Astrology of *Abu Ma‘shar, and the Hundred Aphorisms attributed falsely to *Ptolemy. To Adelard or his circle also belong some marginal notes comparing the doctrines of Arabic astrology to those of the Latin textbook of Firmicus Maternus. Another application of astronomy was magic, to which Adelard contributed by translating a text on the manufacture of talismans by *Thabit ibn Qurra.

Luminary Among Mathematicians

Through his translations of Euclid’s Elements and the Tables of al-Khwarizmi, Adelard considerably expanded the range of the traditional seven liberal arts (both texts were included in the well-known two-volume “Library of the Liberal Arts”—the Heptateuchon of *Thierry of Chartres of the early 1140s). His version or versions of Euclid’s Elements in particular gained him a reputation as one of the “luminaries among geometricians,” according to a comment in a mid-twelfth century manuscript from Coventry. However, he also ventured outside this curriculum by introducing the science of nature, or physics, in the form of a series of questions concerning topics arranged in ascending order, from the seeds within the Earth to the highest heaven (his Quaestiones naturales). The physical questions concerning the heavenly bodies include: “Why is the Moon deprived of light?”; “Why do the planets not move with a constant motion?”; “Why do the planets move in the opposite direction from the fixed stars?”; “Why do stars appear to fall from the sky?”; and “Whether the heavenly bodies are animate.” Adelard alleges that the teaching in this book comes from the “Arabic studies” (studia Arabica) to which he devoted himself during his seven-year absence from England. While it is likely that he took part in scientific discussions in the Middle East (he refers to meeting a philosopher in Tarsus, and experiencing an earthquake in Mamistra), no specific Arabic source is cited or identifiable in his work. It is possible that he knew some Greek medical and philosophical works (by Hippocrates and Nemesius) that had been translated into Latin from Arabic in southern Italy. However, it is not his doctrine so much as his method that he attributes to the Arabs: that of finding the causes of things through the use of reason rather than by following authorities. The Quaestiones naturales exemplifies this method throughout, by using the dialogue situation to counter one argument with another, taking observations from nature, and using analogy.

Adelard’s influence on the teaching of geometry in Western Europe was much greater than on that of astronomy, since the Tables of al-Khwarizmi were soon eclipsed by those of *Toledo, and other texts on the astrolabe and astrology issuing especially from Toledo proved more popular than his own. However, the popularity of the Quaestiones naturales ensured that his discussions of cosmology were well known, and at least one English scholar, Daniel of Morley (fl. 1175), knew the cosmological section of the De opere astrolapsus, which he quotes in his own cosmology, the Philosophia. The Quaestiones naturales were printed three times in the Renaissance (twice in 1475, and again between 1488 and 1491), and were still being quoted by scholars such as Pico della Mirandola and Elias Ashmole.

See also Astrolabes and quadrants; Cosmology; Magic and the occult; Music theory; Quadrivium; Translation movements; Translation, norms and practices

Bibliography

Primary Sources

Adelard of Bath: Conversations with His Nephew: On the Same and the Different, Question on Natural Science and On Birds. Translated and edited by Charles Burnett, et al. New York: Cambridge University Press, 1998.

Boncompagni, Baldassare. Regulae Abaci di Adelardo di Bath. Bulletino di bibliografia e di storia delle scienze matematiche e fisiche (1881) 14: 1–134.

Dickey, Bruce G. “Adelard of Bath: An Examination Based on Heretofore Unexamined Manuscripts.” Unpublished Ph.D. dissertation, University of Toronto, 1982 (includes De opere astrolapsus).

Suter, H., A. A. Bjørnbo and R. O. Besthorn. Die astronomischen Tafeln des Muhammed ibn Musa al-Khwarizmi in der Bearbeitung des Maslama ibn Ahmed al-Madjriti und der latein. Ubersetzung des Athelhard von Bath. Det Kongelige Danske Videnskabernes Selskab, Skrifter, 7 Række, hist.-filos. Afd. 3, Copenhagen, 1963.

Secondary Sources

Burnett, C., ed. Adelard of Bath: An English Scientist and Arabist of the Early Twelfth Century. London: The Warburg Institute, 1987 (Warburg Surveys and Texts 14).

Cochrane, L. Adelard of Bath: The First English Scientist. London: The British Library, 1994.

CHARLES BURNETT

Agriculture

Medieval agriculture was a knowledge-intensive activity. That is, its practice was predicated on local knowledge guiding the application of generalized tool-kits to specific micro-regional settings. Technological constraints made for a medieval agricultural which, although low in yields by modern standards, was surprisingly resilient and endowed with enough flexibility to permit a fine-tuned relationship with the environment. In general terms, traditional agro-systems were surprisingly well-adapted to their environments. Although Arab, Mediterranean, and northern European agricultural will be dealt with separately here, a number of introductory considerations provides context for all cases. First, because of relatively small yields, medieval agriculture was highly sensitive to adverse weather conditions, both summer droughts, winter freezes, and periods of overabundance of rain. This meant that a certain level of crop variety was necessary as insurance against the possible destruction of an important staple. Therefore, all viable local microclimates tended to be used. Moreover, since medieval farmers lacked the technical ability to be able to standardize seeds or even to sort them by variety, sown cereals always involved some kind of mixture (where for example, spelt and emmer, growing as weeds, would turn up in a wheat field). All crop varieties changed over time, in obedience both to natural selection, which fine-tuned the adaptation of varieties to local habitats, and also to unconscious selection of cultivars. Thus, while we know in a general way what was planted (e.g., bread wheat, oats, rye, and so forth) we cannot specify the exact make-up of local varieties (at least, not without paleobotanical evidence).

All three agricultural systems had a standard approach to the balance among agricultural sectors: cereal cultivation, livestocking, and arboriculture, including grapevines. By livestocking, we refer not to transhumant or nomadic herding, but to local herds, specifically the number of animals that could be wintered over, which in turn set the level of cereal production, especially in northern Europe. Because medieval cultivators knew of no way to refurbish soil fertility other than fallowing and letting the local herds graze the fallow fields, supplying them with their manure. Domestic animals, in any case, can easily be switched from one agricultural role (e.g., source of dietary protein) to another (e.g., food stored against possible need; or, a medium of exchange) and as such are key elements in the agricultural economy.

Northern European Regimes

The Germans of late antiquity were a semi-nomadic hunting and grazing people. When they farmed they would cultivate new land for a while, until it was exhausted, then move on. Low population density is a prerequisite for this kind of agriculture. Because the barbarians generally (not just the Germans, but Slavs, Mongols, Huns, etc.) could not produce enough cereals, they needed to maintain large herds. And because they devoted so much space to their herds, they could not produce enough cereals. This kind of agricultural economy had some advantages over that of the Romans: it produced a more varied diet, with more protein. Semi-nomadic peoples had greater familiarity with domestic animals than the Romans had, and more animals were available to the peasant, for leaving manure on fallow fields. Medieval agriculture as it developed was a mixture of Roman and German styles.

Open Fields

The style of cerealculture that developed in northern Europe is known as the open field system. Open field agriculture is based on the heavy or wheeled plow, which is capable of turning over a furrow. This required a heavy team to pull it along, typically with eight oxen. Since it was cumbersome to turn a big team very often, fields tended to be about ten times longer than they were wide. The heavy plow enabled farmers to cultivate the lowland clay-earth areas of the northern European river valleys which had been uncultivatable with the Roman plow.

Open fields refer to fields surrounding a village. Toward the end of the first millennium the most common format was a system of two fields, one sown in wheat or rye (“wintercorn”), the other lying fallow with animals grazing on it. This was called biennial rotation; villagers had strips in each field and all had to follow the same rotation of crops. In the later Middle Ages, three-field agriculture became the dominant form. The third field was devoted to “springcorn”—oats, peas, beans, and barley—sown in the spring, and harvested in the fall. Note that oats, peas, and beans are nitrogen-fixing. Medieval farmers did not know any method of restoring exhausted land except to leave it alone and put as much manure on it as possible. Nor did they know anything about planting hay: it was always gathered wild. Meadowland—land in hay—was always more valuable than arable because the extent of meadow determined the number of animals you could keep through the winter. Feudalism privileged wheat in that, when rents were paid in kind, wheat was normally the specific medium of payment.

According to White’s famous hypothesis the European economy entered a long phase of growth around 1000 C.E. as a result of the conjunction of three different technical elements. The first was the shift from the Roman plow (generically called an ard) to the heavy plow. The share of an ard does not turn over the soil and makes cross-plowing necessary. A single plowing will leave a wedge of undisturbed soil between each furrow. Cross-plowing pulverizes the soil, which prevents excessive evaporation of moisture in dry climates and helps keep fertility high by bringing up subsoil minerals through capillary action. The heavy plow had three advantages over the ard: (1) It was so powerful it broke up the clods without the need for cross-plowing. This saves the peasant’s time and increases the areas of land which he can cultivate in a day; (2) It changes the shape of fields from squarish to long and narrow. With the passage of the years the ridges and furrows became accentuated. The farmer could be sure of getting a crop on the ridge in a wet year and one in the furrow in a dry one. It promoted more efficient drainage; (3) The heavy lowland soils which it could plow gave higher yields than the light upland soils plowed with the scratch plow.

The second element was the development of a new system of animal traction that included the modern harness, harnessing in file, the whippletree, traces, and horseshoes. Oxen had been used as the plow beast of choice because they suffer less from hoof breakage than do either horses or mules. Horses’ hooves are especially sensitive to moisture, meaning that they could not be used in northern Europe before the introduction of the nailed horseshoe. The first common references to shod hooves are found in the ninth century. But a shod horse is useless for plowing unless it is harnessed in a way that utilizes its power. The yoke harness was well suited to oxen, but was applied to horses in such a way that from each end of the yoke two flexible straps encircled the belly and neck of the horse. As soon as the horse began to pull, the neck strap pressed on its windpipe and jugular vein, choking it and cutting down the circulation of blood to its brain. The modern harness of a work horse has a padded collar which rests on the horse’s shoulders, permitting free breathing and circulation, and attached with traces so that the horse can throw its whole weight into pulling. A horse can pull four or five times more with a collar harness than with a yoke harness. The Germans appear to have learned about the horse collar from the Slavs in the late eighth or early ninth century, earlier than harnessing in file (tenth or eleventh centuries) and the whippletree (twelfth century).

The third element is three-field rotation. Again, the earliest documented evidence appears in the late eighth century. If a village had 600 acres (242 hectares), in the two-field system half of that area would have crops and the other half would lie fallow. In a three-field system, there would be 400 acres (160 hectares) under crops. In both systems all 600 acres must be plowed (800 if the fallow were plowed twice), but 100 more acres are producing than was the case before. White viewed the spread of three-field agriculture as a major impetus in bringing new land into cultivation, reclaiming swamps, and cutting down forests.

Three-field agriculture also had the crucial effect of diversifying crops. The spring crops (oats, peas, beans, and barley) while not as remunerative as wheat, brought a number of benefits. It lessened the risk of hunger in a bad cereal year. Spring crops provided a large amount of vegetable proteins which diversified a diet that had been top-heavy with carbohydrates. With triennial rotation, northern European peasants were able to grow enough oats—and oats of a high enough quality—needed to support plow horses. Southern European peasants had no choice between the ox and horse: they could not grow enough oats in a biennial rotation to support horses. Where the horse was the plow animal, the harrow was also found (this instrument seems not to have been much drawn by oxen). The harrow was used to remove weeds, to break up heavy clods, and to spread manure. (For the harrow to be much used, therefore, all the rest of the elements of the complex—plow, horse harness, horseshoes, oat supply—have to be in place first.)

White correctly identified the most important elements of a technological complex typical of the agriculture of medieval northern Europe whose key element was the moldboard plow. Rather than a revolution however, medieval agricultural change was gradual, incremental and, in many areas, incomplete. In specific places, such as southern Jutland, however, the technological changeover appears to have happened according to the chronology suggested by White, that is around 900–1000 C.E., while for Scandinavia as a whole, three-field agriculture appears gradually in the course of the eleventh through thirteenth centuries. According to data presented by Langdon for England, although plow horses (equi arantes) are documented in the tenth century, and the use of horses increases to the end of the twelfth, oxen predominated overall. By 1500, rather than a wholesale replacement of oxen by horses there was patchwork of horse-only and oxen-only areas. The choice between the horse and the ox was determined by a complex set of factors, including the availability of pasture and meadows, soil (and therefore plow) type, and climate. Areas where oxen predominated used swing or foot plows on heavy lowland terrain with wetter climates, and used two-course rotations. With horses, one finds wheeled plows upland, drier climate with lighter soils, and three-course rotation schemes. In economic terms, horses represented lower costs, not increased production. Lords continued to prefer eight-oxen teams, while peasant teams were typically of four oxen or four horses. The fewer the draft animals a farm had, the more likely it was that those animals would be horses; hence peasants were more apt to adopt the horse than were lords. Langdon’s conclusions with respect to the Middle Ages generally, that smallholders were the technologically most progressive sector of society, agree with those of Bois for the early medieval expansion that made seizure of peasant property by the emerging feudal nobility such an attractive course.

An overly sharp distinction between two- and three-field systems may also be an oversimplification. According to Hilton, the rotation was among strips (furlongs, as the basic unit of cultivation) rather than fields. The reduction of fallowing was not necessarily the result of the introduction of spring crops, nor were they planted as massively as White pretends.

To a great degree, the classical “Mediterranean triad” of wheat, the olive tree, and grapevines continued to dominate the agricultural landscape of this region in the Middle Ages. Wheat was especially privileged in areas where feudal dues were taken in kind. Elsewhere cereal culture was better able to respond to local environments. The olive was widely grown wherever the environment could accommodate it; the northern climatic limit of olive cultivation in Spain was conterminous with the Christian/Muslim frontier of the early Middle Ages.

Mediterranean agricultural regimes were risk-driven. Because of the structural probability of summer drought, or torrential rains particularly in the autumn and spring, it was necessary to diversify crops to the maximum in order to ensure that at least some would survive. The diversification strategy was implemented in the context of a topography fragmented into microregions with different ecological characteristics and a variety of niches. In particular, it was common to grow a variety of cereals, not only wheat, but also spelt, barley, and millet or sorghum. Traditional wheat varieties were normally adapted to different microregional habitats over the course of centuries. Rough pasture, forests, and wetlands were all managed entities, integrated into agricultural economies. In addition, the numerous plants gathered wild were an important complement to cultivated crops.

Mediterranean agriculture was normally under a regime of two-course, biennial rotation. If the climate were arid enough, sometimes fields were fallowed for more than one year. In the Castilian system called año y vez, a field was planted to wheat one year and left fallow the next. In many areas of Spain no rotation was practiced, but in others a two-course rotation appeared when organized fallowing became an economic necessity. The advantage of a two-course rotation was that local herds could be grazed on half of the fields annually, a stratagem that was unnecessary as long as there was abundant uncultivated land (monte). In areas where local herding was particularly strong, a further adaptation was made by increasing the fallowing from one year to two (or more), which providing more fallow grazing. Given the summer aridity and the continued use of the light Roman plow, it was never feasible to introduce the northern European three-course rotation, with a spring sowing; the only way to increase wheat cultivation was by extending the arable land at the expense of pasture and woodland and, later, even of vineyards and irrigated fields. The increasing trend away from local towards transhumant herding—also an effect of increased use of land for agriculture—heightened the dependence of cultivators on fallowing, to make up for the loss of local sources of fertilizer. Yields were accordingly very low, from 3.4 to 4.2 to 1, for wheat and barley compared to the normal northern European yield of 5:1 for wheat and 8:1 for barley. When Christians captured irrigated huertas, like that of Valencia, what they did was install three-course rotation, grew the usual spring crops—oats, peas, and beans—and continued to fallow. As a consequence of cross-plowing, fields were square in shape and frequently bounded by irrigation canals or drainage ditches.

The Arab conquests of the seventh and eighth centuries created, in the Islamic Empire, a vast zone propitious for the diffusion of ideas and techniques, particularly from east to west through the great Eurasian continental land mass. Chief among these techniques were a roster of Indian cultivars (rice, sugar cane, citrus fruits, and old world cotton being the most important) grown under monsoon conditions in their hearths of origin, but which, when imported into the Mediterranean basin had to be grown under irrigation. The Arabs called the resultant style of cultivation “Indian agriculture” (filaha hindiyya). As this lore passed through Iran, it gained Persian accretions, both in crops and techniques. Thus the eggplant and the artichoke (Arabic baranjana and karshuf, respectively, both terms from Persian) were added to the crop roster; while irrigation technology picked up the qanat or filtration gallery and the waterwheel (in particular the fluvial *noria, generically called the Persian Wheel). In addition, specific plowing techniques, such as the comb furrow, known today from Afghanistan to Spain, probably represents a medieval irradiation both eastward and westward from a Persian hearth.

Inasmuch as these crops required heat, they were grown in the summer. Thus a rotation of crops became the norm, and irrigated fields yielded as many as four harvests yearly. The far greater number of annual plowings required by the new crop succession and the resultant water loss tended to make Muslim irrigators meticulous in their regard for the water-bearing capacities of each kind of soil. More kinds of soil were used than had been the custom in antiquity, and the agronomical handbooks indicate that each soil type should be fully exploited. The Andalusi agronomist Ibn Bassal, whose treatise was based completely on practical experience, distinguished between ten classes of soil, assigning to each a different life-sustaining capability, according to the season of the year, and he was insistent that fallow be plowed four times.

The Arabs were once thought responsible for the spread of hard wheat (Triticum durum), which was used for semolina, and could also be milled twice to make bread flour. It is now established that both the ancient Greeks and Romans had hard wheat, but when they made pasta from it, they cooked it fresh. The Arabs introduced dried pasta, which could be stored for long periods.

The Indian crops which were introduced into Europe through Spain were documented quite late, not before the tenth century. Noria pot finds around the same time suggest that the entire complex of crops and techniques was introduced together, as part of a unified peasant tool kit. Although medieval Arab historians have preserved anecdotes describing the introduction of specific varieties (such as the safarí pomegranate or the doñegal fig) by palatine officials, and an impressive set of agronomical books emerged from the opulent courts of the “Party” kings of the eleventh and twelfth centuries, it cannot be concluded that princely acclimatization gardens were the principal motor of agricultural change. Rather the interaction of tribal settlement and the broken topography that produced a plethora of local “microregions” had the effect of generating dozens of slightly differing agricultural systems that were an ideal locus for acclimatizing crops. Ultimately there can be no standard “agricultural revolution” in societies, like those of the Mediterranean basin, characterized by a crazy-quilt of environmentally different regions. According to Horden and Purcell, “New crops were inserted within a spectrum of preexisting strategies,” that is, the standard crops improved by generations of selection in the normal course of agricultural practice were more important in the long run than new cultivars.

See also Agronomy; Irrigation and drainage

Bibliography

Astill, Grenville and John Langdon, eds. Medieval Farming and Technology: The Impact of Agricultural Change in Northwest Europe. Leiden: E.J. Brill, 1977.

Bois, Guy. The Transformation of the Year One Thousand. Manchester: Manchester University Press, 1992.

Hilton, R. H. Technical Determinism: The Stirrup and the Plough. Past and Present (April 1963) 24: 01–100.

Horden, Peregrine and Nicholas Purcell. The Corrupting Sea. Oxford: Blackwell, 2000.

Langdon, John. Horses, Oxen and Technological Innovation. New York: Cambridge University Press, 1986.

Watson, Andrew M. Agricultural Innovation in the Early Islamic World: The Diffusion of Crops and Farming Techniques, 700–1100. New York: Cambridge University Press, 1983.

White Jr., L. Medieval Technology and Social Change. Oxford: Clarendon Press, 1962.

THOMAS F. GLICK

Agrimensores

Agrimensura—the Latin term for the practice of land surveying—was always held in high esteem by the ancients. The tradition of surveying dates back to Babylon and Egypt. The ancient Greeks based their town planning on rectangular forms, and their practices were later adopted in Rome, where the earliest reference to surveyors (agrimensores) is dated July 597, during the pontificate of Pope Gregory I. For hundreds of years surveying was numbered among the liberal arts (artes liberales).

Medieval surveyors performed a range of public functions. Their duties included marking out and signing borders, mediating border disputes, and conducting geodetic works for road marking and aqueduct construction. All the issues were described in writing at the time, but most of the texts were subsequently modified, and those that have survived have reached us only in severely modified and truncated form. Such documents are technical tracts dated between 75 and 110 C.E. The authors are Sextus Julius Frontinus, Hyginus Gromaticus and Balbus, Siculus Flaccus, and Agennius Urbicus. The works include many interesting remarks on the education of surveyors, the professional knowledge they had to apply, and their approach to the profession. Surveyors are known to have had excellent writing and drawing skills; knowledge of solid geometry, optics, arithmetic, cartography, and law; and they were generally educated in history, philosophy, literature, music, and medical science.

Land measurement was a basic activity of the agrimensores. The applied procedure (limitatio) was based on marking out parallel lines from east to west and from south to north—the divided land looked like a chessboard. Traces of these divisions are still visible today, especially in North Africa, where they show up in aerial photographs.

Of the very precise instruments used by surveyors for measurement the most important was the groma (surveyor’s cross), the main symbol of the profession, which was used for marking out angles and straight lines. Among the other commonly used instruments were chorobates, water tables with sighting devices, used for leveling, and decempeda, a ten-feet- (2.9m-) long measuring pole.

After measuring and dividing an area, the agrimen-sores then marked out its borders. The stones (termini) around the perimeter of the land were made of imported material so that they could be clearly distinguished from a distance; they were engraved with information, such as the location of the nearest river or lake.

Another of the surveyor’s important functions was to draw charts of the land. The maps thus produced were made in two copies on bronze plates, and were always saved as evidence. Local authorities kept one copy; the other was taken to the central archive.

Plotting the courses of roads was another job for the agrimensores. The network of roads crossing the whole territory of the Roman Empire is shown on one of the oldest maps, Tabula Peutningeriana, the surviving twelfth-century copy of which is based on a map made in the third or fourth century C.E. The road lines marked on it are supplemented by distances, estimated traveling times, and information about the accommodation available in various places. In the Middle Ages travelers and pilgrims used copies of the maps made by Roman surveyors. These maps were made in the form of portable paper rolls.

In the early Empire agrimensores became imperial officials and carried out great geodetic operations that were usually connected with registering population and real estate in the Empire and were performed for fiscal reasons. One such survey of Orange, in the South of France, conducted in 77 C.E., gives information on private areas and includes a map.

Medieval Surveying

The art of surveying declined considerably during the early Middle Ages but was revived in the ninth and tenth centuries after the discovery of Roman surveyors’ tracts (gromatici veteres), which were then transcribed. Authorship of the tracts is attributed to either *Boethius or *Gerbert of Aurillac. These works were quite common in the tenth and eleventh centuries, but they were used more for teaching than for practical applications in the countryside.

From the ninth century extensive if simple measurements were made of wide areas of Europe from England to Catalonia in order to evaluate the revenue due from the land. The range of measurements made for fiscal reasons was limited—land title books were very often made on the basis of the owner’s declaration. The first real land registers date from the twelfth century.

It is difficult to date the first appearance of surveyors as a professional group. The earliest authorized source mentioning area measurement was written in 1139. From the early fourteenth century, however, there were numerous references to officials involved in measurements for royal properties in France.

By the late Middle Ages the measurement of land and the estimation of income from real estate for fiscal reasons had become commonplace. Literate and numerate people began to specialize in surveying, and by the fourteenth and fifteenth centuries surveying had become a profession, and practitioners began to write descriptions of their practical activities. One of the earliest works of this type, by Bernard Boysset of Arles (fourteenth century) is a comprehensive tract, illustrated by the author, that includes extensive information on the surveyor’s profession, the techniques applied, and local customs. It reveals that surveyors of that epoque were involved in marking out the borderlines of the property, placing border stones, calculating the area of properties (which were typically divided into triangles and rectangles), compiling reports on all the activities performed, and even verifying weights and measures. The instruments used by medieval surveyors were simple and easy to construct: a wooden pole and a string marked for distance measurements, a T-square, and a trammel. As in the Roman period, border stones were regarded as sacrosanct: any violation of them or attempt to alter their positions was severely punished.

Bibliography

Campbell, Brian. The Writings of the Roman Land Surveyors: Introduction, Text, Translation and Commentary. London: Society for the Promotion of Roman Studies, 2000.

Guerreau, Alain. Remarques sur l’arpentage selon Bertrand Boysset (Arles, vers 1400–1410). In Campagnes médiévales: l’homme et son space: études offertes à Robert Fossier, ed. Elisabeth Mornet. Paris: Publications de la Sorbonne, 1995.

Dilke, Oswald A.W. The Roman Land Surveyors: An Introduction to the agrimensores. Newton Abbot, England: David and Charles, 1971.

ANNA PIKULSKA

Agronomy

In traditional societies, agronomy was the learned reflection of agricultural practice. It had both theoretical and applied components, bundled together in an attempt to synthesize a vast body of data.

The Roman agronomy tradition—De re rustica, the title of successive works by Cato, Varro, and Columella—was the immediate source of medieval writing on the subject. Cato the Censor (mid-second century B.C.E.), the first Roman agronomical writer, was said by Columella to have taught agriculture to speak Latin. His work was a compendium of practical information on estate management. Varro’s treatise (37 B.C.E.) emphasizes the predominance of grapevines and fruit trees in Italian agriculture. Lucius Junius Columella (fl. mid-first century C.E.) was from Gades (Cádiz) in Roman Hispania. His book of the same title aimed, through a detailed presentation of agriculture techniques and farm management, to restore agriculture to its former primacy as a form of land investment, in a period when the aristocracy was investing in pasture. Finally Palladius (fl. late fourth century C.E.) in his Opus agriculturae, although as much as one-third of the work was based on Columella, became the most influential of Roman agricultural writers in medieval times (at least until the rediscovery of Columella in 1418) because his presentation—in the form of a calendar of agrarian tasks—proved more in tune with medieval farming. Palladius was well known in England through a versified Middle English translation titled On husbondrie. The hallmark of Roman agronomy was the interdependence of the various elements of mixed intensive farming: cereal and legume field crops, vineyards, fruit and olive trees, and animal husbandry whose close association with cultivation was stressed in particular by Varro.

English Estate Books

A common genre of agronomical writing is estate books, which describe managerial strategies for large estates, somewhat in the tradition of Varro and other Roman writers. First come various recensions of *Robert Grosseteste’s rules (Statuta) for estate managers which he composed between 1235 and 1242 in Latin for the use of the management of his own household, as bishop of Lincoln. A French recension was later made for the Countess of Lincoln, and this version circulated widely. Grosseteste advised that crop yields be estimated in advance of harvesting so that lords could plan their budgets effectively.

Next came an anonymous treatise in French for the instruction of stewards and bailiffs called the Seneschaucy, written in the 1260s or 1270s. Stewards, it instructs, must keep track of how much of each crop of wintercorn (wheat, rye and barley) and springcorn (peas and beans) are sowed per acre; and what the plowing requirements of each is. The bailiff is in charge of soil quality (marling and manuring) and the apportionment of work between customary tenants and hired labor. In all estate books, these issues constitute the primary focus. Walter of Henley, a knight who later became a Dominican friar, wrote the most famous of these treatises, known as the Husbandry, also in French and based somewhat on the Seneschaucy, around 1285. The book is mainly about plowing, sowing and harvesting, in particular how costs and profits are to be calculated. Interestingly, Like the Seneschaucy Walter’s treatise was read by and designed for not the owners of manors but rather estate lawyers, men trained in the common law on the particulars of estate management, conveyancing, and accounting in view of the demand for such services, whether in management or litigation.

Walter’s treatise can be viewed as an operationalization of open field agriculture, whether with two- or three-course rotation. Walter based his cost calculations on a standard unit of 240 acres (97.1 hectares), the equivalent both of 160 acres (64.7 hectares) in a two-field system, with the fallow plowed twice, and 180 acres (72.8 hectares) in a three-field system, with the fallow plowed once. He then estimated the distance a team would travel per day in each system and, on this basis, calculated the labor requirements. Walter’s theory of agriculture was roughly based on notions of the balance of the four qualities (dung is too “hot” to be used without cooling by mixing it with earth, for example.) Drainage was also a theme that Walter stressed in conjunction with soil types and quality: pooling water was an obvious cause of soil imbalance. The second part of the book is devoted to animal husbandry. As a counterpart to Walter’s primer for lawyers, an anonymous Husbandry, copied mainly in monasteries, appears to have circulated mainly among estate owners and was probably designed to aid account audits.

Taken as a group, these didactic estate treatises reveal a characteristic pattern of linguistic *communication. Stewards and lawyers alike had to know both French and Latin. Accounts were always written in Latin, but French was the language of the nobility who owned and managed the estates.

Pietro de Crescenzi (1233–1321), a judge from Bologna, wrote the first medieval Latin work in the tradition of classical agronomy. His Opus ruralium commodorum (Book of Practical Agriculture) was based both on Roman authors and his own observations, was quickly translated into Italian, then French (by order of Charles V in 1373), and became the first agricultural work to be printed (Augsburg, 1471). He also drew on theoreticians like *Albertus Magnus and *Ibn Sina for information on plant growth. The work is divided into twelve books, covering farm location; practical botany; cereal cultivation; arboriculture and horticulture (with an account of one hundred eighty-five edible or medical plants); meadows and woods; gardens; animal husbandry; hunting; a recapitulation and summary; and finally a calendar of the farmer’s year.

Ambrosoli characterizes Crescenzi’s Opus as a reordering of medieval thought equal to that of Dante or *Aquinas. It is based mainly on Palladius, whose texts were frequently read together and compared with it. He provides general rules for growing every common field and garden crop and tree, in such a way that farmers with different requirements could mold his prescriptions to their own needs. In this sense, the Opus was an open text: readers practicing agriculture from different perspectives and under different conditions could adapt it to their needs. The French translation was at the same time an adaptation of Crescenzi’s original text to the agrarian geography of France. He was read by persons interested in estate management, and also by those seeking information on specific agricultural products. He goes into great detail on the differences between emmer and spelt, although it is not clear whether he had direct experience of emmer or only knew of it through classical authors.

The Islamic Tradition

The Nabatean Agriculture, a tenth-century treatise, was a mixture of practical techniques and theosophical ideas compiled by Ibn Wahshiyya, reflecting the agricultural practice of central Mesopotamia (around Kufa). By “Nabatean” is meant the Syriac-speaking rural population. Although the treatise enjoyed wide fame in the Arabic-speaking world, the text reflects traditional agriculture in lowland Mesopotamia; there is only perfunctory mention of the new Indian crops, like rice, sugar, and cotton. The number of cultivated plants and fruit trees is substantially greater than those described in the Byzantine Geoponika (one hundred six versus seventy), with new coverage of garden vegetables (which became a hallmark of Arab agriculture) and medicinal plants, with strong integration of horticulture and arboriculture. The eleventh-century Andalusi agronomist, Ibn al-‘Awwam, self-consciously relied on the Nabatean Agriculture, which he cites five hundred forty times, because the Middle East was located in the same clime as al-Andalus, as he ascertained by comparing harvest dates.

Acclimatization gardens were favored by the kings of the independent states that sprang up in eleventh-century al-Andalus in the wake of the dissolution of the Caliphate. Thus Ibn Bassal was employed as royal gardener in Toledo, Ibn al-‘Awwam in Seville. Oddly, Andalusi agronomists devote scant attention to irrigation, even though it was central to the agricultural wealth of the country. Discussion of irrigation is limited to specifications about norias, with no mention of surface irrigation from canals. Ibn al-‘Awwam describes a method of linking wells drawing from the same water table, adjacent with the depth stepped so that subsidiary wells supply water to the main one. This is the application of the filtration gallery (qanat) principle to noria wells, an example of which was excavated at an archeological site (Les Jovades) in Gandia, Spain. Abu’l-Khayr gives specifications regarding the kinds of wood appropriate to various noria components and how the pots should be arrayed on the rope of the pot-garland wheel.

On the other hand, considerable attention is paid to the water requirements of plants and how to design fields to facilitate irrigation. Homely surveying methods provide furrows with enough gradient to ensure both the flow of water and the equality of water depth throughout the area irrigated. All writers stress the objective of attaining equilibrium between plant, soil, and water.

The Arabic word filaha meant both agriculture and agronomy, as its study. For Ibn Khaldun filaha was both a science, a branch of physics, and a craft. As a science, “It concerns the study of the cultivation and growth of plants through irrigation, proper treatment, improvement of the soil… and the care for them by applying these things in a way that will benefit them and help them grow.” The ancients, he goes on to say, considered plants not only with respect to their planting and cultivation, but also their properties and the relationship of their spiritual properties (ruhaniyyat) to that of the celestial bodies. He believes that the Nabataean Agriculture was a translation of a Greek work combining both agricultural and magical lore, and that Ibn al-‘Awwam had abridged it, excluding the magical portion which was transmitted separately by *Maslama of Madrid (III, 151–152). Agriculture was also the oldest craft, prior to and older than sedentary life (II, 356–357).

The Andalusis extended Ibn Wahshiyya’s emphasis on soil types. Ibn Bassal describes ten such types, organizing them according to the Hippocratic four qualities (hot, cold, moist, and dry). The system functions analogically like that of humoral pathology. Soils must be balanced; therefore, water (cold and moist) can temper the overly hot and dry soils of arid and semi-arid regions. Plowing restores heat to soil which is cold and dry by nature. Similarly, fertilizers can supply heat. Ibn al-‘Awwam—less theoretical—stressed the organic content and permeability of soils.

The Andalusis relied on the Nabatean Agriculture, but divested it of its neo-Platonic underpinnings and created a unique body of agronomical lore by conjoining the new Indian Agriculture with the collected experience of Andalusi peasant agriculture, systematized according to the Roman agronomical tradition, especially Columella, whom the Arabs knew as Yunius. In terms of theory, this was an agronomy of the tradition of Aristotle and Theophrastus which recognized the complexity of agricultural practice. It was also related to the traditions of classical *botany and *pharmacology. Ibn Wafid, for example, wrote on both agronomy and materia medica.

Indian agriculture (filaha hindiyya) followed the same path of diffusion as that taken by Indian *arithmetic (hisab al-hind)—from India to Persia to the Arabic-speaking world, to Spain. “Indian agriculture” referred to the particular roster of plants originating under monsoon conditions in India—rice, sugarcane, oranges and lemons, watermelon, old world cotton—together with the techniques—mainly Persian—required to irrigate them under the conditions of aridity prevailing in the Islamic world. In Persia, several additional crops—the artichoke and the eggplant—were assimilated to the roster of Indian cultivars.

The Chinese agronomical tradition was isolated from that of Europe until the eighteenth century. The earliest complete agronomical text that survives is the Chhi Min Yao Shu (“Essential Techniques for the Peasantry,” c. 535 C.E.), by Chia Ssu-Hsieh. He says he wrote the book for his own children; therefore the text is plain and lacking in the rhetorical flourishes of the literary culture of the day and his approach is pragmatic. He describes crop rotations (e.g., beans rotated with millet) which permitted constant cropping without fallowing. He names nearly one hundred varieties of millet. A later treatise was the Nung Shu (1313) by an official named Wang Chen. He apparently wrote for the bureaucratic class, because he believed that only official direction and instruction could improve peasant agriculture. He stresses the comparative advantages of northern (dry farming) and southern (irrigation agriculture) methods, and includes useful information on novel agricultural tools or techniques.

If one compares citations of authors in medieval Arab and Latin treatises and those of the Renaissance, the flow of information over time is sharply revealed. Ibn al-‘Awwam’s Kitab al-filaha contains one thousand nine hundred direct and indirect citations. Six hundred fifteen of these, or 32.5 percent, are to Byzantine sources, especially the Geoponika of Cassianus. Five hundred eighty-five (31 percent) are to near eastern sources and 85 percent of these are to Ibn Wahshiyya. Six hundred ninety citations (36.5 percent) are of earlier Sevillian agronomical writers. Classical sources were especially significant in the areas of arboriculture, olive and grape cultivation, and cereals, Near Eastern on soils and fertilizers, and Andalusi on irrigation, grafting and pruning, garden vegetables, condiments, and flowers.

In his Opus, Crescenzi cites thirty-four authors in four hundred twenty-eight citations. Palladius leads with one hundred twelve (26 percent of all citations), then Ibn Sina and Varro, fifty-nine (13.75 percent) each; and Albert the Great tied with Pliny, twenty-four (5.6 percent) each. There are thirteen mentions of Columella, whose work was not known first-hand to Crescenzi.

Gabriel Alonso de Herrera’s Obra de agricultura is a sixteenth-century Spanish work that recapitulates the medieval tradition. The author’s appetite for referencing dwarves that of his predecessors: he offers a total of 3,684. His top five are Crescenzi, eight hundred eighty-eight (24 percent), Pliny, six hundred ninety-two (16 percent), Palladius, five hundred twenty-nine (14.4 percent), Columella, five hundred seventeen (14 percent), and Theophrastus, two hundred sixty-two (7 percent). Two Muslim authorities, Ibn Sina and Ibn Wafid are cited one hundred forty-seven (4 percent) and one hundred two (3 percent) times, respectively.

Butzer concludes that the Mediterranean agrosystem, whether exploited by Greeks, Romans, Muslims or medieval Europeans, is “essentially the same, in terms of crops, methods, and strategies.” There are only regional or cultural differences in crop emphasis and small-scale irrigation, while “At the academic level [agronomy proper] there are additional differences in the perception of agricultural goals or the different priorities set by religion, economics, or values.” The problem is then how to interpret vastly different economic outcomes in the face of long-term continuity of agronomic ideas. The solution would seem to lie first in the application of similar principles and practices (“tool kits”) to the myriad microregions of the Mediterranean world and second in the changing modalities of social appropriation of peasant work.

See also Agriculture; Elements and qualities; Noria

Bibliography

Bolens, Lucie. Les méthodes culturales au Moyen-Age d’après les traités d’agronomie andalous: Traditions et techniques. Geneva: Ed. Médicine et Hygiène, 1974.

Butzer, Karl W. The Islamic Traditions of Agroecology: Crosscultural Experience, Ideas and Innovations. Ecumene: A Journal of Environment, Culture, Meaning (1994) 1: 7–50.

Comet, Georges. “Le statut intellectuel des savoirs agricoles au Moyen Age.” In Traditions agronomiques européennes. Élaboration et transmission depuis l’Antiquité. Edited by Marie-Claire Amouretti and F. Sigaut. Paris: CTHS, 1998, pp. 27–41.

———. “Les céréales du bas-Empire au Moyen Age.” In The Making of Feudal Agricultures? Edited by Miquel Barceló and François Sigaut. Leiden: E.J. Brill, 2004, pp. 131–176.

Glick, Thomas F. “Introduction.” In Gabriel Alonso de Herrera, Obra de agricultura [1513]. Valencia: Hispaniae Scientia, 1979, pp. 14–49.

Ibn Khaldun. The Muqaddimah. An Introduction to History. Translated by Franz Rosenthal. 3 vols. Princeton: Princeton University Press, 1958.

Oschinsky, Dorothea. Walter of Henley and other Treatises on Estate Management and Accounting. Oxford: Clarendon Press, 1971.

THOMAS F. GLICK

Albert of Saxony

Albert of Saxony—otherwise known as Albert of Helmstedt, Albert of Rickmersdorf, or Albertutius—was one of the most influential Parisian masters of the fourteenth century, his works remaining widely read until the late sixteenth century. He was a secular cleric who taught at the Parisian Arts Faculty from 1351 to 1361/1362; he then helped to found the University of Vienna for Duke Rudolph IV of Austria (1363/64–1366), and died as Bishop of Halberstadt July 8, 1390.

The first secure biographical date is that of his determination at the Parisian Arts Faculty under master Albert of Bohemia in March 1351. Since the statutes of Paris require an age of at least twenty years to become a bachelor, Albert will have been born before 1331, probably rather around 1320. Before coming to Paris, he may have studied in Halberstadt, Magdeburg or even Erfurt, but not in Prague, which he probably visited later. After his determination and inception Albert probably started lecturing on Aristotle’s Physics and other textbooks of *natural philosophy. In June 1353, Albert was elected rector of the Faculty (for three months of office), and from 1352 to 1362 he represented the English Nation on several occasions. Thus, in 1358, he took part in negotiations with the Picardian Nation concerning the border line of both nations—together with *John Buridan—and in 1361 he became receptor of the English Nation. He had more than fifty students that took at least one of the three parts of the master’s examination under his supervision. After 1353, he probably also started studying in theology at the Sorbonne although he never finished his studies.

By November 1362 Albert had left Paris, for in that month he was named as a prebend at the cathedral chapter of Mainz on the yearly roll sent by the University of Paris to the pope to secure provision for its masters. Albert then probably went to Avignon, where he may have come into contact with the Austrian duke in July 1363, and followed Rudolph IV on a visit to Prague in April and May 1364. In September 1364 he returned to Pope Urban V as Austrian ambassador (and parish priest of Laa), and he achieved papal support for Rudolph’s plan to establish a university in Vienna. Following Rudolph’s foundation charter in March 1365, Albert secured a papal bull which established the Faculties of Arts, Law and Medicine—but not a Faculty of Theology, perhaps because the emperor, Charles IV, had intervened. When Duke Rudolph died in July 1365, Albert reached an agreement over the endowment of the university. He became the first rector and imported the Parisian model for the first statutes, but actually only the Arts Faculty had been founded when he left Vienna (the university was re-founded in 1383/1384 by Duke Albert III).

Peak of Career

In October 1366 Albert was appointed Bishop of Halberstadt, and took office in February 1367; in doing so he became involved in politics. In September 1367 he lost a battle against Bishop Gerard of Hildesheim, and afterwards engaged in regional peace alliances. In 1372 he was suspected of determinism when Pope Gregory XI wrote to German inquisitors, but it seems that he was never formally accused. He stayed in office and remained quite successful until his death.

Probably mainly during his time in Paris, Albert wrote and published about thirty texts on logic and natural and moral philosophy, mainly commentaries on Aristotle, but also independent treatises. Although at times he relied heavily on Buridan or the highly original *Nicole Oresme, and also used the works of *William of Ockham, Walter Burley, *Thomas Bradwardine, and *William of Heytesbury (the last named is the only contemporary author he mentions explicitly), Albert was a quite independent thinker who sometimes combined the theories of his predecessors (especially those of Buridan, Oresme, and the English and Parisian masters) or chose to present problems in a didactic manner. His main contributions to the history of science concern “modern” logic, the theory of motion, and geology.

In *logic, he probably commented on the Ars Vetus, the Prior and Posterior Analytics and perhaps also on the Topics, although only one question on the latter is known to have survived (and some relevant problems also appear in his Perutilis Logica). Aside from some smaller texts, his main logical works are two different versions of Questiones logicales, his Perutilis Logica (or Logica nova), and his Sophismata, all of which survive in several manuscripts. The Perutilis Logica (which may even have influenced Buridan rather than vice versa) follows Ockham, but expands the problems of “modern” logic considerably into a handbook which is divided in six parts: the first deals with the elements of propositions, the second with the properties of terms, the third with different types of proposition, the fourth with consequences and syllogisms, the fifth with fallacies, and the sixth with insolubles and obligations. The work was very influential, and Albert’s theory of consequences was an important step forward in the medieval theory of deduction by systematizing the forms of inference. The Questiones logicales, which have been termed “metalogical,” treat various problems of logic and semantics, as well as of reference and truth. The Sophismata follow William of Heytesbury and deal intensively with infinity and the divisibility of the continuum.

In natural philosophy, Albert of Saxony contributed to the propagation of Bradwardine’s Law (by his own Tractatus proportionum and in his commentary on the Physics), and of Buridan’s concept of *impetus. His writings comprise different commentaries on the Physics, questions and an expositio on De Caelo, commentaries on De generatione, De anima (now lost), the Metheora and the Parva Naturalia. He also commented on *John of Sacrobosco’s De Sphaera and perhaps on the so-called Philosophia pauperum, and a Questio de quadratura circuli has been attributed to him. His earlier questions on the Physics are an important work which influenced Buridan’s ultima lectura. Although Albert took over Buridan’s concept of *impetus or rather virtus impressa (impetus is the term used only in the ultima lectura) as not self-exhausting, and therefore had no problems explaining the celestial motions by an impressed force, there are also some changes in relation to Buridan’s tertia lectura: he transferred the discussion of projectile motion into Book Eight, discussed also a different theory of motion similar to that of Ockham or Olivi, and was even more pragmatic. He was also the first to introduce the distinction between kinematics and dynamics into the Physics (relating them to Book Six and Book Seven, respectively), and he included an expanded discussion on vacuum. In the context of discussions on place and space, he also developed a theory of small movements of the Earth as a whole caused by erosion of earth by winds and rivers and resulting in geological changes which elevate lower layers. His Tractatus proportionum, which was widely copied and read, offers a more popular explanation than earlier texts of Bradwardine’s Law.

Albert also contributed extensively to the field of moral philosophy through one widely read commentary on the Nicomachean Ethics and another on the Oeconomica. He lectured on the Aristotelian Politics, although no manuscripts of the text are known.

Many of the works of Albert of Saxony were distributed in several manuscripts and printed during the Renaissance period. They found wide reception at the central European and Italian universities, where they were known to a wide range of people including Leonardo da Vinci and the teachers of Galileo. In the end, even the concept of impetus was mainly linked with Albert’s name (as well as with that of *Thomas Aquinas), not with Buridan’s.

See also Aristotelianism; Logic; Nature: diverse medieval interpretations

Bibliography

Primary Sources

Albert of Saxony’s Twenty-five disputed questions on logic: a critical edition of his Quaestiones circa logicam, ed. Michael J. Fitzgerald. (Studien und Texte zur Geistesgeschichte des Mittelalters, 79.) Leiden: E.J. Brill, 2002.

Albert von Sachsen. Tractatus proportionum, ed. Hubertus L. L. Busard. In Denkschriften der Österreichischen Akademie der Wissenschaften, math.-naturwiss. Kl. 116, 2. Wien: Springer in Komm 1971, pp. 43–72.

———. Questiones subtilissime in libros De celo et mundo, ed. Hieronymus Surianus. Venice: Bonetus Locatellus for Octavianus Scotus, 1492.

———. Perutilis Logica, ed. Petrus Aurelius Sanutus. Venice: Heredes Octaviani Scoti 1522; repr. Hildesheim-New York: Olms, 1974.

———. Sophimata, ed. Anthonius Chapiell. Paris: Dionysius Roce, 1502, repr. Hildesheim-New York: Olms, 1975.

Beltrán de Heredia, Vicente. Commentarios de San Alberto Magno [recte: de Saxonia] a los Económicos de Aristóteles. La ciencia tomista (1932) 46: 406–432.

Expositio et Quæstiones in Aristotelis Physicam ad Albertum de Saxonia Attributæ, ed. Benoît Patar. 3 volumes. (Philosophes médiévaux, XXXIX-XLI) Louvain-Paris: Institut supérieur de philosophie, Peeters, 1999.

Le Questiones de sensu attribuite a Oresme e Alberto de Sassonia, ed. Jole Agrimi. (Pubblicazioni della facoltà di lettere e filosofia dell’università di Pavia, 29) Firenze: La Nuova Italia, 1983.

Secondary Sources

Berger, Harald. “Albert von Sachsen.” In Die deutsche Literatur des Mittelalters, Verfasserlexikon. 2nd ed. Berlin-New York: De Gruyter, 2000. Vol. 11, fasc. 1, col. 39–56.

———. “Bischof Albrecht III. (1366-1390) als Gelehrter von europäischem Rang (Albert von Sachsen).” In Halberstadt. Das erste Bistum Mitteldeutschlands. Edited by G. Maseberg and A. Schulze. (Veröffentlichungen des Städtischen Museums Halberstadt 29) Halberstadt: Städtisches Museum Halberstadt, 2004, pp. 81–92.

———. Albert von Sachsen († 1390), 4. Fortsetzung und Ergänzungen zur Bibliographie der Sekundärliteratur. Acta Mediaevalia (2004) 17: 253–279.

———. Albertus de Saxonia († 1390), Conradus de Waldhausen († 1369) und Ganderus recte Sanderus de Meppen († 1401/06). Eine Begegnung in Prag im Jahr 1364. Mitteilungen des Instituts für österreichische Geschichtsforschung (1998) 106: 31–50.

Biard, Joel, ed. Itinéraires d’Albert de Saxe, Paris-Vienne au XIV siècle: actes du colloque organisé le 19-22 juin 1990 dans le cadre des activités de l’URA 1085 du CNRS à l’occasion du 600e anniversaire de la mort d’Albert de Saxe. (Études de philosophie médiévale, 69). Paris: J. Vrin, 1991.

———. “Albert of Saxony.” In The Stanford Encyclopedia of Philosophy. Edited by Edward Zalta. (Spring 2004 Edition). (http://plato.stanford.edu/entries/albert-saxony).

Kann, Christoph. Die Eigenschaften der Termini. Eine Untersuchung zur Perutilis logica Alberts von Sachsen. (Studien und Texte zur Geistesgeschichte des Mittelalters, 37.) Leiden: E.J. Brill, 1994.

Sarnowsky, Jürgen. “Albert von Sachsen und die ‘Physik’ des ens mobile ad formam.” In The Commentary Tradition on Aristotle’s De generatione and corruptione. Ancient and Medieval and Early Modern. Edited by J.M. Thijssen, H. Braakhuis. (Studia artistarum, 7) Turnhout: Brepols, 1999, pp. 163–181.

———. “Nicole Oresme and Albert of Saxony’s Commentary on the Physics: the Problems of Vacuum and Motion in the Void.” In Quia inter doctores est magna dissensio. Les débats de philosophie naturelle à Paris au XIV siècle. Edited by Stefano Caroti, Jean Celerette. Firenze: Leo S. Olschki 2004, pp. 161–174.

———. Die aristotelisch-scholastische Theorie der Bewegung. Studien zum Kommentar Alberts von Sachsen zur Physik des Aristoteles. (Beiträge zur Geschichte Philosophie und Theologie des Mittelalters, N.F. 32), Münster: Aschendorff, 1989.

———. Place and Space in Albert of Saxony’s Commentaries on the Physics. Arabic Sciences and Philosophy (1999) 9: 25–45.

Thijssen, J.M.M.H. The Buridan School Reassessed. John Buridan and Albert of Saxony. Vivarium (2004) 42, 1: 18–42.

JÜRGEN SARNOWSKY

Albertus Magnus

Albertus Magnus (known in English as Albert the Great) was born shortly before 1200 in Lauingen (present-day Swabia) into a knightly family in the service of the counts of Bollstadt. He died in Cologne on November 15, 1280. As a youth he was sent to study the liberal arts in Padua, where he probably began to read Aristotle and showed signs of an early interest in the study of the natural world. In the summer of 1223 he entered the Dominican order as a result of the preaching of Jordan of Saxony (the second master general of the order). Albert studied theology at the priory of Cologne, becoming lector (lecturer) there in 1228. He afterwards taught theology in various German Dominican priories (Hildesheim, Freiburg, Regensburg, and Strassburg), and during his wanderings visited the mines of the Harz mountains. During this period he wrote his first work, De natura boni, a theological treatise in which he cited several of Aristotle’s books on nature. In the early 1240s he was sent to Paris to lecture on the Sentences of *Peter Lombard, and in 1245 he became Master of Theology, lecturing for three consecutive years at the Dominican priory of St.-Jacques, while he was engaged in the writing of a large theological work, the Summa de creaturis. Although at that time the ban on Aristotle’s libri naturales (books on natural philosophy) decreed in 1210 and 1215 was still in effect at the University of Paris, Albert was able to absorb much of the new Aristotelian knowledge. He left Paris in 1248 together with *Thomas Aquinas (who had arrived in the city three years earlier) to serve as Regent Master at the recently established Dominican studium (college) in Cologne, where he remained until 1254. It was in Cologne that Albert finished his commentaries on Lombard and on the pseudo-Dionysian corpus begun in Paris. The period during which Albert wrote his paraphrase of Aristotle’s works has long been a controversial issue, but in the most informed opinion it spanned about two decades, from 1250–1252 to 1270. Albert was elected provincial of the German province of the Order of the Preachers in 1254 and remained in office until 1257. He first traveled to Italy in 1256–1257, when he visited the papal court at Anagni. From 1257 Albert was back as lector at the Dominican study of Cologne, and in January 1260 he was appointed bishop of Regensburg by Pope Alexander IV, holding this office for almost two years. In the summer of 1261 Albert returned to Italy, where he remained until early 1263, initially at Viterbo and later at Orvieto. Immediately afterward he was sent to preach throughout Germany the crusade to the Holy Land launched by Pope Urban IV. From the end of 1264 to 1267 Albert lived in Würzburg and, after a short stay in Strassburg in 1268, he remained in the Dominican convent in Cologne as lector emeritus from 1269 until his death. Albert’s reputed participation in the Council of Lyons (1274) and his trip to Paris on the occasion of the condemnations of 1277 have been questioned by scholars.

Albertus Magnus taught Aristotelianism at the University of Paris. Thomas Aquinas was among his pupils. Albertus was canonized in 1931. (National Library of Medicine)

Historical Significance and Scope

Albert the Great made available to the West a first complete, comprehensive version of the Aristotelian *scientia. What could be taken as characteristic of Albert’s approach to Aristotle—in contradistinction to that of authors such as *Robert Grosseteste and *Roger Bacon—is his emphasis on the observational, “empirical” branches of the Aristotelian encyclopedia of natural knowledge. Albert filled in the gaps in the sequence of the Aristotelian libri naturales with works of his own. Foremost among these were his treatises On Plants and On Minerals and his massive work On Animals, which remained influential well into modern times. Moreover, Albert’s treatment of physics, *cosmology, and the elements of matter provided a consistent interpretation of Aristotelian natural philosophy which was energetically pursued by Dominican authors, foremost among them Albert’s disciple Aquinas. In the wake of the translation movement and the reception in the West of Aristotle, by the mid-thirteenth century the Christian world was confronted with the challenge of a comprehensive and consistent system of knowledge, a substantial part of which was related to the explanation of the natural world. Albert, a theologian turned philosopher, refurbished the Aristotelian encyclopedia to make it compatible with the Christian worldview, eliminating the tenet of the eternity of the world and considering nature as the result of divine creation. But while it seems legitimate to distinguish between Albert’s philosophy and his theology inasmuch as he himself argues for it, his inquiry into nature is an integral part of his philosophy. What is sometimes termed Albert’s “science” is actually natural philosophy (philosophia naturalis), a part of Aristotelian scientia and as such an intellectual program that anticipates the modern distinction between science and philosophy.

Albert intended to make Aristotle “intelligible to the Latins.” While at Cologne in the early 1250s he was asked by fellow Dominicans to write a paraphrase of Aristotle’s Physics. He did more than that: he provided them with an exposition of the whole of natural knowledge along Peripatetic lines. In his works Albert repeatedly claims that what he intends to do is to expound the philosophy of the Peripatetics as faithfully as possible, correcting and completing it as necessary. His technique of commentary was the paraphrase of the Aristotelian text, which gave him the freedom to expound his own opinions as “digressions,” to include a vast array of materials from other authors—in particular Arabic interpreters such as *Ibn Sina (Avicenna) and *Ibn Rushd (Averroes)—and to assimilate different kinds of disciplinary traditions and literary genres. Crucial to his project was the manner in which he handled and articulated different bodies of knowledge identified with authoritative authors. Albert himself distinguished between different fields of inquiry in terms of the authorities on whom he relied: Augustine in theology, *Galen and *Hippocrates in medicine, Aristotle “or anyone experienced in natural things” in matters of nature.

The Structure of Albert’s Natural Philosophy

Albert adopts the Aristotelian scheme of a threefold division of philosophy into *metaphysics (concerning the intelligible), mathematics (dealing with the intelligible and imaginable), and physics (treating the intelligible, the imaginable, and the sensible). The object of physics is the natural, real body, considered with motion and sensible matter. Mathematics abstracts from real existence and deals with one aspect of body: its quantity as reconstructed in the imagination. Albert rejected the “Platonic” view supported by authors such as Grosseteste and Bacon that natural philosophy is founded on the principles of mathematics, and that mathematics in turn is founded on the principles of metaphysics. He endorsed the Aristotelian view that each science is autonomous within the limits of its principles, and that mathematics is only an aid to natural philosophy. Also, the ascent to metaphysics—the subject of which is not God but being as being—is through the natural sciences. The only known mathematical work ascribed to Albert is a commentary on the first four books of *Euclid’s Elements which drew on a commentary by al-Narizi (Anaritius).

In the first book of the Meteorology Albert expounded his plan of commenting on Aristotle’s libri naturales. According to this account, natural science (scientia naturalis) would involve three stages, considering: (1) The simple mobile body (Physics, On the Heavens, On Generation and Corruption); (2) The simple changeable body on its way to mixture (Meteorology); and (3) The mixed changeable body (minerals, plants, and animals). The Physics treats the principles of the mobile body, On Heavens discusses the motion from place to place of simple bodies, and On Generation and Corruption deals with simple bodies undergoing other kinds of change. In this section should also be included Albert’s On the Nature of Places—a “physical *geography” which discusses coordinates and geographical accidents in terms of the seven climatic zones of the Earth—and On the Causes of the Properties of the Elements, which deals with the four elements and the action of the planets on them. The first three books of the Meteorology are about all the meteorological and geological phenomena resulting from the transition to mixture; the fourth book examines the compounds (a sort of “chemistry”). The third part of Albert’s philosophia naturalis deals with the changeable body contracted to mineral, vegetal, and animal species. Thus, it comprehends inanimate bodies, which are discussed in his On Minerals, as well as bodies with soul, i.e., plants and animals, including human beings. Albert’s exposition of living creatures opens with On the Soul, which is followed by a group of short treatises on the vital functions of living beings grouped under the title Parva naturalia—four of them were original works. Then came the treatise on plants and the various works on animals. Albert also wrote a commentary on the pseudo-Aristotelian On Causes, a work much influenced by pseudo-Dionysian philosophy.

Physics, Astronomy, and Alchemy

In his Physics, Albert affirms that the subject of natural science is the body as it undergoes any kind of natural change: generation and corruption (substantial change), increase and diminution (quantitative change), alteration (qualitative change), and local movement (locomotion). The principles of form and matter, characteristic of the doctrine of *hylomorphism, are also the active and passive principles of change. Explanations of the phenomena of change should be framed in terms of the four Aristotelian causes: material, formal, efficient, and final cause.

Albert drew a distinction between mathematical astronomy, subordinated to mathematics and providing hypotheses designed to “save the phenomena,” and physical astronomy, which was concerned with the physical description of the universe and causal explanations. Albert depended on the geocentric physical world-pictures of Aristotle and al-Bitruji (Alpetragius) but did not altogether exclude *Ptolemy’s system of mathematical astronomy, although he did not spell out the articulation of both approaches. He seems to have preferred the simpler system of the twelfth-century Arab astronomer, although he was aware that it was unable to explain the retrograde motion of the planets. Beside the first mover in the outermost sphere, identified with God and the ultimate cause of all movement in the universe, Albert postulated individual spiritual substances as movers for each sphere. The attribution of the Speculum astronomiae to Albert is considered doubtful by many scholars. Albert dealt with *astrology in several of his works and mostly in On the Causes of the Properties of the Elements. His principal authorities were Ptolemy and Albumasar (*Abu Ma‘shar). Albert believed in the influence of heavenly bodies on natural and social events on Earth, but in his theological works he underscored that the stars could not interfere with the exercise of free will in humans.

Albert’s fame as an alchemist was great (as was his reputation as a magus), but it is now agreed that he did not write any work on *alchemy. Basing his conclusions mostly on Arabic sources, in the Meteorology and On Minerals Albert admitted the theoretical possibility of transmutation of metals but considered that it was very difficult to achieve. He was familiar with laboratory practice but was not himself an adept of the art and distrusted its hermetical and allegorical interpretations. In his theological works Albert condemned magic as the work of devils, but in his Aristotelian commentaries and original works his attitude is more nuanced: it seems as if he would have accepted “natural magic” as the result of the occult virtues of nature.

In On Minerals Albert deals with “stones,” “minerals,” and “intermediates.” Minerals and stones are considered with respect to their essences (“origin” in terms of the four Aristotelian causes), accidental properties and, finally, their individual properties. The work draws on Aristotelian, Avicennan, and alchemical theories, as well as on Albert’s considerable familiarity with metallurgical processes and his experience in the mining districts of Germany. Book II is a lapidary, preceded by a tract on “the causes and powers of stones” and followed by a treatise on sigils (images in stones) with a considerable amount of magical lore.

Plants and Animals

Two of the five books of On Plants are a commentary on the pseudo-Aristotelian De Plantis by Nicholas of Damascus; the remainder of the work is Albert’s own. From the examples used it is clear that Albert was well acquainted with the flora of western Europe. Particular attention is paid to the habitat of plants, and there are numerous morphological observations concerning individual plants. Albert divided the plant kingdom into trees, shrubs, olera virentia (large leafy stems), and herbs; besides, he added a doubtful category for fungi. Book VI is a herbal, and Book VII deals with *agriculture and contains information about domestic and economic uses of plants, transplanting, and grafting.

Albert’s study of animals is embodied in several works; the widest ranging is On Animals, his commentary on Michael Scot’s Latin version of Aristotle’s History of Animals, On the Parts of Animals, and On Generation of Animals, together with two original books and a “dictionary of animals.” The last named drew heavily on *Thomas de Cantimpré’s encyclopedia On the Nature of Things, and treated humans, quadrupeds, birds, aquatic animals, serpents, and vermes (vermin). In Book XI Albert discussed his methodology, distinguishing a two-step approach between a “narrative method” concerned with description, and the ulterior search for causal explanation of the facts. Humans, considered as the summit in the hierarchy of sentient beings, are the point of reference for Albert’s study of animals. In On Animals Albert tried to reconcile the at times contradictory natural philosophical and medical doctrines of Aristotle and Galen and quite a lot of medical material—much of it taken from Ibn Sina’s Canon—entered the work, including an account of human anatomy and a long discussion of human generation.

In an effort to show that Albert was a “scientist” or at least a “precursor” of a given scientific discipline, some have extolled, at times exaggeratedly, his personal observations and “discoveries.” Undeniably, Albert had the cast of mind of a naturalist, a taste for the wilderness and the things of nature, and he was interested in the systematic and exhaustive study of all created beings. In philosophy, he argued for the need to arrive at general statements and principles proceeding from the study of particular species, and his understanding of Aristotle emphasized the latter’s concern for the empirical basis of all knowledge. But Albert was also a scholastic: just as significant as his study of *natural history is his deployment of rhetorical devices and textual strategies to unify into a coherent synthesis different traditions of knowledge about nature within a christianized *Aristotelianism.

See also Botany; Cosmology; Elements and qualities; Herbals; Lapidaries; Mineralogy; Natural history; Scientia; Translation movements; Universities; Zoology

Bibliography

Primary Sources

Albertus Magnus. Opera omnia (Editio Coloniensis). Edited by the Albertus-Magnus-Institut. Münster: Aschendorff, 1951.

———. Omnia opera. 38 vols. Edited by Auguste Borgnet. Paris: L. Vivès, 1890–1899.

———. De vegetabilibus libri septem. Edited by Ernst Meyer and Carl Jessen. Berlin: G. Reimer, 1867.

———. Albertus Magnus on Animals. A Medieval Summa Zoologica. Translated by Kenneth F. Kitchell, Jr., and Irven M. Resnick. 2 vols. Baltimore: Johns Hopkins University Press, 1999.

———. The Commentary of Albertus Magnus on Book I of Euclid’s Elements of Geometry. Edited by Anthony Lo Bello and Derek Robinson. Leiden: E.J. Brill, 2003.

———. Albertus Magnus. Book of Minerals. Translated by Dorothy Wyckoff. Oxford: Clarendon Press, 1967.

Secondary Sources

Anzulewicz, Henryk, ed. De forma resultante in speculo. Die theologische Relevanz des Bildbegriffs und des Spiegelbildmodells in den Frühwerken des Albertus Magnus. Eine textkritische und begriffsgeschichtliche Untersuchung. 2 vols. Münster: Aschendorff, 1999.

Asúa, Miguel de. “Minerals, Plants and Animals from A to Z. The Inventory of the Natural World in Albert the Great’s philosophia naturalis.” In Albertus Magnus. Zum Gedenken nach 800 Jahren: Neue Zugänge, Aspekte und Perspektiven. Edited by Walter Senner. Berlin: Akademie Verlag, 2001.

———. “The Organization of Discourse on Animals in the Thirteenth Century. Peter of Spain, Albert the Great, and the Commentaries on De animalibus.” Ph.D. Dissertation. University of Notre Dame, 1991.

Bonin, Therese M. Creation As Emanation: The Origin of Diversity in Albert the Great’s on the Causes and the Procession of the Universe. Notre Dame: University of Notre Dame Press, 2001.

Friedman, John B. “Albert the Great’s Topoi of Direct Observation and his Debt to Thomas of Cantimpré.” In Pre-Modern Encyclopaedic Texts. Edited by Peter Binkley. Leiden: E.J. Brill, 1997.

Jordan, Mark D. “Albert the Great and the Hierarchy of Sciences.” Faith and Philosophy (1992) 9: 483–499.

Köhler, Theodor W. Grundlagen des philosophisch-anthropologischen Diskurses im dreizenhten Jahrhundert. Die Erkentniss-bemühung um den Menschen im zeitgenössischen Verständniss. Leiden: E.J. Brill, 2000.

Price, Betsey Barker. “The Physical Astronomy and Astrology of Albertus Magnus.” In Albertus Magnus and the Sciences. Edited by James A. Weishepl, OP. Toronto: Pontifical Institute of Mediaeval Studies, 1980.

Stannard, Jerry. “The Botany of St. Albert the Great.” In Albertus Magnus Doctor Universalis, 1280/1980. Edited by Gerbert Meyer and Albert Zimmermann. Mainz: Matthias-Grünewald-Verlag, 1980.

Thorndike, Lynn. “Albertus Magnus.” In Lynn Thorndike, A History of Magic and Experimental Science. 8 vols. New York: University of Columbia Press (1923–1958).

Tilmann, Sister Jean P. An Appraisal of the Geographical Works of Albertus Magnus and His Contributions to Geographical Thought. Ann Arbor: University of Michigan Press, 1971.

Wallace, William. “The scientific methodology of St. Albert the Great.” In Albertus Magnus Doctor Universalis, 1280/1980. Edited by Gerbert Meyer and Albert Zimmermann. Mainz: Matthias-Grünewald-Verlag, 1980.

Weisheipl, James A, OP. “Albertus Magnus and the Oxford Platonists.” Proceedings of the American Catholic Philosophical Association (1958) 32: 124–139.

———. “The Life and Works of St. Albert the Great.” In Albertus Magnus and the Sciences. Edited by James A. Weishepl, OP. Toronto: Pontifical Institute of Mediaeval Studies, 1980.

MIGUEL DE ASÜA

Alchemy

In the narrow sense of the word, alchemy refers to the attempt to transmute base metals into gold. In the broader sense, alchemy includes the enquiry into the scientific, theoretical, philosophical, theological, and mystical frameworks that encompass the application of chemical operations. Historically, the art of alchemy attempted to achieve two goals: (a) To produce or counterfeit precious metals from baser metals; and (b) To attain longevity and immortality through the elixir vitae (elixir of life).

The etymology of the word “alchemy” is debatable. It has been attributed to the ancient Egyptian km (black) or kmt (the black land), suggesting one of the ancient names for Egypt in relation to its rich alluvial soil along the Nile River. However, it has been noted that the Coptic word keme is never attributed to the concept of alchemy. In addition, the Greek words kymeia (fusion), kyma (casting), and kymos (juice) have been associated with the origins of the English word; and it appears they were translated into the Syriac as kimiya, then into Arabic as al-kimiya, and later adopted by the Latin West in numerous phonetic forms (e.g., alchimia, alkimia, alquimia, chymiae).

The problem of identifying the origin of alchemy is further compounded when considering that early alchemical interests and efforts have been linked to ancient Mesopotamia, a point that becomes particularly complicated on the examination of specific equipment, technology, and religious beliefs of metallurgists and artisans at the time: (a) Sophisticated laboratory apparatuses (e.g., furnaces, bellows, crucibles, beakers, and weights); (b) Extant cuneiform tablets on the art of metallurgy (e.g., artificial lapis lazuli, copper, and silver); (c) The application of assaying gold by cupellation; and (d) The intrinsic association of metals and gods with *astrology. In addition, there appear to have been only minor technological advances made between Mesopotamian and Greek alchemical laboratory apparatus and those later adopted and improved by Muslim alchemists. For example, much of the equipment and many of the tools listed by the tenth-century Muslim physician and alchemist *Abu Bakr Mohammed al-Razi in his work Sirr al-asrar (Secrets of Secrets), are quite similar to earlier Mesopotamian technology: al-tannur (furnace), minfakh aw ziqq (bellows), bawtaqa (crucible), qawarir (flasks), etc. Furthermore, beginning in the fourth century B.C.E., over one hundred Taoist canonical texts covering the art of alchemy were written; many of the texts suggested that immortality was considered attainable through the application of medicines and other methods. Thus, by the first century B.C.E. a “gold elixir” (chin-tan) or “liquefied gold” (chin-i) appears in the texts; and as was true of Chinese alchemy, it appears most Muslim alchemical texts focused on the iksir (elixir). However, although similar ingredients and fractional distillation were employed by both cultures, the Muslim alchemists appear to have been introduced to the idea of the elixir by way of the Syriac term ksirin via the Greek word iksirat, representing powder used in medicine.

Even in light of these findings, it is still debatable whether or not Mesopotamian sources and Chinese alchemical literature were responsible for influencing the early Greek and Muslim alchemists. Moreover, it is not apparent when and what the Greeks truly knew about alchemy, since the majority of Greek alchemical texts are accessible only through uncatalogued and unpublished Arabic translations. Thus there are no extant Greek documents on the transmutation of base metals into gold until after the first centuries of the Common Era.

Early Alchemical Literature

At the same time, possibly the oldest Chinese alchemical treatise Chou i ts’ an t’ung ch’ i (The Concordance of the Three), which dates to c. 142 C.E., was considered to be an important interpretation of the I ching (Book of Changes), and used simple chemical operations to represent metaphorically the cosmic balance between yin and yang. Subsequently, in the work entitled Pao p’u tzu nei p’ien (The inner chapters of the philosopher Pao p’u tzu), written c. 320 C.E., the first notable Chinese alchemist Ko Hung (283–343 C.E.), whose pseudonym, Pao p’u tzu, is used in the title, advocated the pursuit of alchemy for the sake of pure knowledge. The chapters consist of a collection of instructions, transmitted to Ko Hung by his great-uncle Ko Hsuan (c. third century C.E.), on the production of arsenic, mercury, and counterfeit silver- and gold-based elixirs for, among other things, ailments, longevity, invulnerability, immortality, and resurrection. By the seventh century, perhaps the most famous Chinese alchemical text compiled was by the author Sun Su-mo (c. 581–673 C.E.), and it was entitled Tan ching yao chueh (Essential Formulas from the Alchemical Classics). In the treatise, Su-mo detailed the construction of furnaces and specified recipes and apparatus needed for producing medicinal remedies and elixirs of immortality; again, it appears that the technology was similar to, if not slightly more advanced than, that of earlier Mesopotamian models.

At about the same time (100–300 C.E.), a mass of Greek philosophical, astrological, magical, and alchemical texts, purportedly compiled by Egyptians in Alexandria, was being attributed to Hermes Trismegistus (“Hermes the thrice-greatest”). The texts are collectively referred to as Hermetic literature or Hermetica, and primarily reflect mystical teachings on philosophy, theology, occultism, and astrology via Platonic dialogues. In Egypt, the Greeks superlatively praised (i.e., “thrice greatest”) the Egyptian lunar deity Thoth or Djeheuty, whom they associated with Hermes, the messenger of the gods, the progenitor of writing, and the patron deity of good fortune, fraud, magic, and poetry. In addition, Hermes is frequently recorded by late antique and Byzantine writers as the initial transmitter of alchemy; and early Muslim scholars considered Hirmis (Hermes) to have been an exile of Babylonia, a Pharaoh of Egypt, a prolific commentator on magic, and the primary progenitor of alchemy. However, even though a consistent link between Pharaonic and Graeco-Eygptian magic has been reasonably established, at present it is not as evident that such a similar correlation existed within the alchemical corpora. Nevertheless, the Roman Emperor Diocletian (245–313 C.E.) did order the collection and burning of all magical and alchemical books, thus suggesting that both arts had possibly been developed for a considerable period of time prior to the decree. In the end, the quintessential alchemical work of Hermes is the Emerald Tablet, a text that was later translated from Arabic into Latin under the same title, Tabula smaragdina. In brief, the Arabic translation states that: (a) All things were from one; (b) The structure of the microcosm is in accordance with the macrocosm; and (c) The Sun and Moon represent father and mother, respectively.

By the late eighth and early ninth century C.E., late copies of Greek alchemical texts, initially translated into Syriac, appear to have been some of the first works ever translated into Arabic during early Abbasid times. The authorship of early Arabic alchemical texts is obscure until the late ninth and early tenth centuries. Thus, traditionally, the Umayyad prince Khalid ibn Yazid (660–704 C.E.) is credited not only with learning alchemy from a recluse named “Morienus the Greek,” but also with ordering Greek and Coptic writings on alchemy to be translated into Arabic for the first time. Several centuries later, the English monastic scholar Robert of Chester or Robertus Castrenis (fl. 1142–1150 C.E.) translated the Khalid-Morienus work from Arabic to Latin in a treatise entitled Liber de compositione alchimiae (The Book of the Composition of Alchemy). The work is possibly the first book on alchemy translated from Arabic into Latin, and it appears to have been one of the precursors to the great proliferation of alchemical texts translated from Arabic into Latin, which took place in the Ebro valley and, somewhat later, in Toledo in the twelfth and thirteenth centuries. However, like its predecessor, its authenticity has been called into question. Nevertheless, apparently, the work served as one of the first introductions to alchemy in the Latin West.

Influence of Philosophy and Science in Alchemy

Due to the unsystematic manner in which the Greek-Syriac texts were translated into Arabic, errors were prevalent among many of the initial interpretations, and, therefore, had a lasting affect on Western scholarship. In one instance, the Muslim scholar *Jabir ibn Hayyan (c. 721–815 C.E.), known as Geber to the Latin West, appears to have been one of the initiators of the notion of an “assembly of philosophers,” maintaining that Hermes, Pythagoras, Socrates, Aristotle, and Democritus all met at one time to discuss alchemical propositions. It has been suggested that the rationale for Jabir assimilating all of these early Greek philosophers into a single assembly, irrespective of their actual lifetime, is congruent with the idea of unity found in Islam. However, it also appears that the chronological dates of early Greek philosophers were simply not known to early Muslim scholars, which also seems to explain how so many alchemical references were indiscriminately credited to *Plato. Interestingly, the notion of the “assembly of philosophers” later re-emerged in some of the most prominent alchemical works in the Latin West. Translated from Arabic into Latin, the work Turba philosophorum (“Assembly of the Sages”) surprisingly included the pre-Socratic philosophers (i.e., Anaximander, Anaximenes, Anaxagoras, Empedocles, Archelaos, Leucippus, Ecphantus, Pythagoras, and Xenophanes). Therefore, the translator not only included more Greek sources in the text, but clearly elaborated on an error entirely conceived by early Muslim scholarship.

During the late ninth and early tenth century, a number of Greek-Syriac texts dealing with the Greek subject of natural philosophy began to be incorporated into Muslim alchemic commentaries; and, by the twelfth century, these translated annotations would substantially influence the Latin West. One such concept, prevalent among many early Muslim scholars studying tabi’yat (natural philosophy), was the notion that all metals were literally prone to spontaneous growth. Basically, all base metals (e.g., lead) had the ability to “grow” into precious metals (e.g., gold). Thus, in essence, it was only for the alchemists to discover a catalyst that would expedite the process. It is a theme that re-emerged in the De Mineralibus (Book of Minerals) of the thirteenth-century Dominican friar and Scholastic philosopher *Albertus Magnus. In the book, Albertus upheld the hypothesis that a “natural” transmutation occurs between silver and gold because both are “noble” metals. However, Albertus remained doubtful that the process could be duplicated in a laboratory, and concluded that such alchemical claims were made by “deceivers” who preyed on the ignorant. Interestingly, although many early Muslim scholars accepted the idea that metals were living animate objects, which grew like plants or crystallized like minerals, the same scholars were also known to have rejected the alchemic claim of transmutation as being nothing more than deceptive. Thus, eventually, alchemic literature evolved into the realm of philosophical speculation; and soon the art of alchemy, itself, became a metaphor for examining a wide range of considerations focusing on whether or not alchemy was a science and to what degree ethics applied.

Early references to alchemic ethics can be found in the work entitled Kitab al-Hind (The Book of India) by the Muslim scholar *Abu Rayhan al-Biruni (973–1048 C.E.). In one particular chapter, al-Biruni discussed the alchemical work of Nagarjuna (c. 150–250 C.E.), whom he believed to have lived during the eighth century, but who was possibly the Indian Buddhist monk-philosopher who founded the Madhyanika school of Buddhism and who wrote the Rasaratnakara (i.e., a verse treatise on alchemy and metallic medicine). Retelling several gruesome alchemistic stories, in colourful moralistic overtones, al-Biruni rejected alchemy as being a “make-believe science,” and adamantly condemned it on the grounds of its pernicious effects on the ignorant. Another example of moral and ethical speculation can be found in the work of the early Muslim philosopher *Abu Nasr al-Farabi (c. 870–950 C.E.), known to the Latin West as Alfarabius, who was credited for having argued for the validity of maintaining secrecy in the art of alchemy. Al-Farabi maintained that to prevent the collapse of the economic world order, which God had in fact established, one could not divulge the secrets of transmuting base metals into silver and gold. More than four centuries later, the Muslim historian Ibn Khaldun (1332–1406 C.E.) related a somewhat reverse-argument in his seminal work the Muqaddimah (Introduction) by claiming that the alchemic transmutation of silver and gold was not even scientifically obtainable, therefore it was not a matter to be considered seriously, simply because it would defy the laws of God which ensured “the standard of value by which the profits and capital accumulation of human beings are measured.” Interestingly, the Muslim philosopher and physician *Abu Ali ibn Sina (980–c. 1036 C.E.), known as Avicenna to the Latin West, was somewhat ambivalent about the question. He rejected the theory of transmutation, but is known to have praised the alchemists for their technological ability to imitate the properties of silver and gold. Similarly, the Italian Dominican theologian and disciple of Albertus Magnus, *Thomas Aquinas (1225–1274) later concluded in his Summa Theologiae that it was not unlawful to sell alchemical gold as “real gold” so long as it really possessed the same properties as gold: “For nothing prevents art from employing certain natural causes for the production of natural and true effects as Augustine says of things produced by the art of the demons.”

Alchemists at work in the fifteenth century. For the greater part of the medieval period the attempts of alchemists to convert base metal into gold were regarded as legitimate scientific studies. (Ancient Art and Architecture Collection)

Since alchemical texts can be interpreted literally, theoretically, allegorically, mystically, etc., there is no overall consensus that the art of alchemy shared a common origin or was de facto “the precursor to modern chemistry.” Instead, alchemical literature appears to have been in some sense an internal exchange and refinement of unique regional and cultural perspectives on nature, philosophy, religion, etc., which became fundamental for the apprentice to comprehend. However, for an apprentice attempting to penetrate individual perspectives on the art of alchemy, prior to knowledge obtained from the teacher, proved to be increasingly cumbersome, if not impossible, over the centuries for a number of reasons. For example, the majority of writings were frequently disseminated, intentionally, in cipher under a nom de plume to ensure secrecy from the uninitiated and to protect the author from possible abduction or persecution. In addition, epigraphic pseudonyms were commonly assumed by other alchemists simply to add credibility to their own writings. Moreover, following earlier individual perceptions of alchemy, it became increasingly difficult to establish the true identity of any author; there was a whole list of prominent individuals who were frequently identified as alchemists, including the following: Thoth, Moses, Solomon, Mary, Jesus, Hermes, Democritus, Cleopatra, and Zarathustra.

Therefore, the practice of alchemy appears to have evolved into a collective art whose discursive developments far outweighed the minor advancements and contributions made to science and technology. Although the practice of alchemy borrowed from the laboratories of herbalists and physicians and employed materials and equipment used by other artisans, it should be clear that the objective of the alchemists was plain: either to produce or counterfeit precious metals from baser metals, or attain longevity and immortality through the elixir vitae.

See also Magic and the occult; Mineralogy; Translation movements

Bibliography

Biruni, Muhammad ibn Ahmad. Alberuni’s India. Translated by Edward C. Sachau. New York: Norton 1971.

Copenhaver, B.P. Hermetica: The Greek ‘Corpus Hermeticum’ and the Latin ‘Asclepius.’ New York: Cambridge University Press, 1992.

Fowden, Garth. The Egyptian Hermes: A Historical Approach to the Late Pagan Mind. Princeton: Princeton University Press, 1993.

Holmyard, E.J. Alchemy. Baltimore: Penguin, 1968.

Ibn Khaldun. The Muqaddimah. Translated from Arabic by Franz Rosenthal. Princeton: Princeton University Press, 1967.

Levey, Martin. Chemistry and Chemical Technology in Ancient Mesopotamia. New York: Elsevier, 1959.

Magnus, Albertus. De mineralibus. Translated by Dorothy Wyckoff. Oxford: Clarendon Press, 1967.

Montgomery, Scott L. Science in Translation: Movements of Knowledge Through Cultures of Time. Chicago: University of Chicago Press, 2000.

Sivin, Nathan. Chinese Alchemy: Preliminary Studies. Cambridge: Harvard University Press, 1968.

Stavenhagen, Lee. A Testament of Alchemy, Being the Revelations of Morienus, Ancient Adept and Hermit of Jerusalem to Khalid ibn Yazid ibn Mu’awiyya, King of the Arabs, of the Divine Secrets of the Magisterium and Accomplishment of the Alchemical Art. Hanover, NH: University Press of New England for Brandeis University, 1974.

TOD BRABNER

Alfonso, Pedro

Pedro Alfonso (Petrus Alphonsi in Latin), also known as Moses Sephardi, was an outstanding pioneer as a translator, teacher, philosopher, and scientist of the twelfth-century renaissance. Alfonso was one of the most widely read medieval authors.

We know nothing of Alfonso’s birth or early education. Unlike many other medieval scientists, he has left us some autobiographical description, although most of it is in the form of a semi-fictional dialogue between his “Jewish self” and his “Christian self.” In one passage he tells us that he was baptized in 1106 in the northern Spanish kingdom of Aragon, taking his baptismal names from St. Peter and his patron Alfonso I, king of Aragon and of Navarre from 1104 to 1134. After this, Pedro may have lived for a while in Toledo, an important center of translation, served for a time as a teacher in northern France and England, and appears to have been a court physician to the English King Henry I (r. 1100–1135). Of the other details of his life, we know nothing except that he both presented himself and was regarded as a teacher of astronomy. Presumably he died near the middle of the twelfth century.

While Pedro Alfonso clearly regarded himself primarily as a teacher of astronomy, he also had a strong interest in the other physical sciences. He has four major works and a group of minor works, some of whose authorship is still disputed. His two most widely read books were the Disciplina Clericalis (The Secretary’s Art) and the Dialogus Contra Judaeos (Dialog against the Jews). Both exist in numerous manuscripts. Less well known, but of greater interest to historians of science, were the Epistola ad peripateticos (Letter to the Peripatetics) and a set of astronomical tables that he prepared while in England. Common to all these major works are discussions of astronomy, *cosmology, theoretical medicine, and element theory.

There is no question that Alfonso was an adult at the time of his conversion to Christianity and that he was by then already a fairly well-known man of letters having, as Tolan says, “knowledge of Hebrew, of the Bible, and of the Talmud. Alfonsi [sic] also had received an Arab education in letters, science, and philosophy.” Alfonso was one of the earliest scholars who brought Arabic astronomy to Latin scholars. His writings reveal that he was thoroughly familiar with the corpus of Arabic scientific writing, which made up the contemporary scientific curriculum in Muslim Spain. In the preface to his Latin Tables, he wrote “I decided in my mind that I should publish a book on this [i.e., astronomy] and that, by knowledge of [the subject] its usefulness might become known…. This work, sweated over with much labor and brought over from the Arabs, Persians, and Egyptians with extreme industry, I intended to share in a friendly manner with the Latins.”

Furthermore, Pedro Alfonso explicitly offered to teach what he knew to others: sometime in the first quarter of the twelfth century he addressed a “Letter to the Peripatetics of France,” probably intending the students of the schools of Paris as the recipients. After praising the study of grammar, dialectic, arithmetic, and medicine, he encouraged his readers to get to know astronomy “since it is obvious that astronomy itself is more useful, more pleasant, and more worthy than the remaining arts.” He then offered himself as their teacher and incorporated into his letter the preface to his translation and adaptation of the Astronomical Tables.

“Our Teacher”

Throughout the Middle Ages, scholars who wished to know astronomy needed to use astronomical tables adjusted to the latitude of their domicile. While in England, Alfonso reworked *al-Khwarizmi’s ninth-century astronomical tables. While Alfonso’s tables may have been of limited usefulness (they were somewhat muddled), he recalculated the parameters based on his observations of October 1, 1116. In addition, his Dialogus Contra Judaeos often lost sight of its polemical debate as his two personas (the Jewish “Moses” and the Christian “Peter”) shared many discussions of science. This text included diagrams of the Sun’s course around the Earth, and the division of the Earth into seven climatic zones along with (mostly accurate) descriptions of phenomena such as the water cycle. Even though Alfonso uses terminology such as “experimentum,” it would be anachronistic to think of his science as being based in scientific method, for it was more akin to natural philosophy, a kind of scientific reasoning drawing necessary conclusions based on accepted principles rather than the results of experimentation. That Alfonso succeeded as a teacher is clear from De dracone, a minor astronomical text that he produced in 1121. It was clearly written while he was in England, and was translated by Walcher of Malvern, prior of one of the most important early centers of English scientific learning. Walcher called Alfonso “Our Teacher.” On the basis of a study of textual similarities, Burnett (1997) has suggested the possibility that *Adelard of Bath was also taught by Alfonso. There is some question about Alfonso’s knowledge of Latin; for, if fairly late in his career he needed Walcher to turn his teaching into Latin, his skill in that language may well have been limited. However, it was not uncommon in twelfth-century Spain for documents in foreign languages to be worked on by teams of translators. Pedro Alfonso is a crucial figure in the Middle Ages in the transmission to the Latin West of superior Arabic scientific knowledge, especially information pertaining to the study of the stars.

See also Elements and qualities; Medicine, theoretical

Bibliography

Burnett, Charles F. S. The Works of Petrus Alfonsi. Medium aevum. (1997) 66: 42–79.

Jones, Joseph R. and John E. Keller. The Scholar’s Guide. Toronto: Pontifical Institute of Medieval Studies, 1969.

Lacarra, Maria Jesus, editor. Estudios Sobre Pedro Alfonso de Huesca. Huesca: Instituto de Estudios Altoaragonses, 1996.

Neugebauer, Otto. The Astronomical Tables of al Khwarizmi. Translated with Commentaries of the Latin Version. Copenhagen: Munksgaard, 1962.

Tolan, John. Petrus Alfonsi and his Medieval Readers. Gainesville: University Press of Florida, 1993.

MICHAEL C. WEBER

Alfonso X the Wise

Alfonso X, king of Castille, was born in Toledo on July 23, 1221, became king of Castille on June 1, 1252, and died in Seville on April 4, 1284. As a patron of literature and learning, he commissioned a series of translations into Castilian and, later, into Latin, of Arabic astronomical texts, probably as the result of the discovery of new manuscripts in Córdoba and Seville, two cities conquered by his father, Fernando III, in 1236 and 1248 respectively. Alfonso X also sponsored the compilation of original works; these mark the beginning of a new European astronomy which, for the first time, was written not in Latin but in a vernacular language.

Alfonso X or his collaborators set out to compile two great collections of scientific texts. The first was devoted to magic and included the translation of the Picatrix (already available in Latin), four *lapidaries (an index of contents of another ten is also extant) and the Libro de la mágica de los signos. The second collection was astronomical and astrological (Libros del Saber de Astronomía or Astrología). Alfonso also supported the translation of several individual works such as *Ibn al-Haytham’s Cosmology, *al-Battani’s Canons, the treatise on the sine quadrant, two versions of the Alfonsine Tables, *Ptolemy’s Cuadripartito (i.e., the Tetrabiblos) with the commentary of Ali ibn Ridwan, the Libro conplido en los iudizios de las estrellas of Ibn Aben Ragel and the Libro de las Cruzes. Some at least of these independent works could have been conceived as a part of the Libros del Saber, but they are not included in the royal codex of this anthology (MS Villamil 156, in the Library of Madrid University).

The analysis of the previous list shows the existence of a well-structured plan. The king’s ambition was to compile a collection of treatises on astronomical instruments, mainly analogical computers (celestial sphere, spherical and plane astrolabes, universal astrolabes such as the azafea and the universal plate) designed to provide graphical solutions to the problems of spherical astronomy and *astrology (the division of the houses of a horoscope, for example). The purpose of other instruments was time-keeping (cuadrante con cursor, *clepsydra), also necessary to cast a horoscope. A third group is formed by the two treatises on the equatorium, an instrument designed to give graphical solutions to the problem of computing planetary longitudes used in a horoscope. The king ordered that two treatises, one on construction and the other on use, be furnished for each instrument. If an Arabic text was available, a translation was made; otherwise, an original treatise was written. Because treatises on the use of instruments were more common than books dealing with their construction, most of the original books (written mainly by Rabiçag—see below) dealt with the techniques for the fabrication of instruments. This is the origin of the Libros del Saber in which only the first book (Ochava Espera, an updating of ‘Abd al-Rahman al-Sufi’s uranography) is unrelated to astronomical instruments; this work nonetheless has obvious astrological and magical applications.

The computation of planetary longitudes is the main purpose of the tabular works translated (Almanac, Battani’s canons) or compiled (Alfonsine Tables) by the king’s collaborators. Ptolemy’s Cuadripartito, together with a commentary, as well as the Libro conplido and Libro de las Cruzes) provided the reader with the knowledge needed to interpret a horoscope and predict the future. Finally, a collection of magical texts taught how to fabricate talismans and not merely predict the future, but modify it. The basic scheme of the king’s plan is, therefore, clear enough and it is obvious that it had a practical (astrological and magical) purpose: only one work (the translation of Ibn al-Haytham’s Cosmology) falls outside this project and has a theoretical purpose (a description of a physical cosmos) unrelated to astrology.

The Scientific Collaborators of Alfonso X

Alfonso X’s team of collaborators comprised one Muslim convert (Bernardo el Arábigo), four “Spanish” Christians (Fernando of Toledo, Garci Pérez, Guillén Arremón d’Aspa and Juan d’Aspa), four Italians (Giovanni of Cremona, Giovanni of Mesina, Pietro of Regio, and Egidio Tebaldi of Parma), and five Jews. The participation of Bernardo el Arábigo and of the four “Spaniards” had little importance and only one among the latter (Garci Pérez) seems to have been competent as an astronomer. As for the Italians, both Giovanni of Cremona and Giovanni of Mesina participated in the revision of the first translation of the treatise on the açafeha, whilst the other two worked in the retranslations into Latin of the Libro conplido and the Cuadripartito. The arrival at the Castilian chancellery of the group of Italians could be connected to the fact that between 1256 and 1275 King Alfonso was a candidate for the imperial title; this hypothesis might also explain his change of linguistic policy and his interest in preparing Latin translations of texts already translated into Spanish. The Jewish team (Yehudah ben Mosheh, Isaac ben Sid called Rabiçag, Abraham Alfaquín, Samuel ha-Levi and Don Mosheh) was far more important than the other groups and two of its members (Yehudah ben Mosheh and Rabiçag) were particularly relevant: far more productive than the others, they were also exclusively responsable for the Alfonsine Tables. Of these two, Yehudah was mainly a translator while Rabiçag, although he knew Arabic well, concentrated in writing original works, mainly related to the construction of astronomical instruments.

A Typology of Alfonsine Translations

Alfonsine translations vary from literal translations (*Ibn al-Zarqalluh’s treatise on the açafeha, al-Battani’s Canons) to very free adaptations of an Arabic original. Free translations are numerous and often contain interpolations. Such is the case of the Latin version of the Picatrix (derived from a lost previous Castilian translation) where the Alfonsine translator feels free to correct the Arabic original when he considers it obsolete. Alfonso X’s interest in certain astrological matters also impelled his collaborators to add original chapters (e.g., on the division of the houses) to the translation of Qusta ibn Luqa’s treatise on the celestial sphere. In other cases the translator rearranged the materials of his Arabic source: this happens in the Alfonsine Latin translation of Ibn al-Haytham’s Cosmology, in which Abraham Hebraeus has subdivided the materials of the original Arabic text (one book, fifteen chapters) into two books and forty-eight shorter chapters. The order of exposition is also altered: Ibn al-Haytham describes the planetary spheres in ascending order, while the Latin translation uses a descending one. Finally, there are repetitions: Ibn al-Haytham dedicates one chapter to the three superior planets, and another to the two inferior ones; in Abraham’s version there is one chapter on each planet, with a repetition of an identical text for Saturn, Jupiter, and Mars, on the one hand, and for Venus and Mercury on the other. Finally, some texts are adaptations and compilations: the original book written by Rabiçag on the construction of the lámina universal (universal plate) is a mere adaptation of Ibn al-Zarqalluh’s treatise on the construction of a very similar instrument (açafeha). A similar case is that of the treatise on the use of the spherical astrolabe. The lack of an Arabic source on this instrument led the Alfonsine collaborators to adapt the treatise on the use of the planispheric astrolabe by *Ibn al-Samh (d. 1035): the Alfonsine book is divided into one hundred thirty-five chapters and only thirty are independent of the text of Ibn al-Samh. A most peculiar case is that of the IIII Libros de la Ochaua Espera in which books I–III contain the description of each one of the constellations, derived mainly from one Arabic source, al-Sufi. Al-Sufi’s star catalogue represents each constellation in a wheel traced on the recto of each folio of the royal codex, while the corresponding textual description can be found in the verso of the preceding folio and, thus, faces the wheel. The texts of the descriptions are practically the same length, because the codex has been designed for aesthetic impact. Thus al-Sufi’s texts were drastically abbreviated in cases where the constellation has a large number of stars, while they are supplemented with materials from other unidentified sources when the number of stars is small and the author has a blank space to fill in.

The Alfonsine Tables

The Alfonsine Tables are the most important contribution of Alfonsine astronomy. They were used in Europe from c. 1320 to 1551, the year of the publication of the Prutenic Tables computed by Erasmus Reinhold. They had an important influence on the astronomy of the Renaissance. Copernicus used parameters derived from them in his Commentariolus: as well, the tropical Alfonsine year (365 days, 5 hours, 49 minutes, and 16 seconds) is almost the same as the mean tropical year in the De revolutionibus, which became the basis of the Gregorian reform of the *calendar. The work poses important historical problems due to the existence of two different versions. The first is a set of canons or explanatory instructions in Castilian, but without tables, prepared by Rabiçag and Yehudah ben Mosheh between 1263 and 1272. These describe a collection of tables in the Zarqallian tradition: mean motions are sidereal, tropical longitudes can be calculated using trepidation tables, the obliquity of the ecliptic is obtained by means of a Zarqallian model, there are references to Ibn al-Zarqalluh’s correction to the Ptolemaic lunar model, etc. A second set appears in Paris around 1320: these have numerical tables, with headings in Latin, but no canons which can be attributed to Alfonso X. These tables seem unrelated to the aforementioned Castilian canons and are clearly influenced by the zij of al-Battani): mean motions are tropical and most Zarqallian characteristics have disappeared. Many European authors, beginning with the Parisian group formed by *John of Saxony, *Jean de Meurs, and John of Lignières, wrote original canons which were added to the Alfonsine numerical tables. Some scholars conclude that the original Alfonsine Zarqallian tables were the object of a later adaptation probably in Paris, while others believe that the second version of the Tables was prepared by the Alfonsine collaborators themselves, after their translation of al-Battani’s canons.

See also Clocks and timekeeping; Patronage of science; Translation movements; Translation norms and practice

Bibliography

Bossong, Georg. Los Canones de Albateni. Herausgegeben sowie mit Einleitung, Anmerkungen und Glossar versehen. Tübingen: Max Niemeyer Verlag, 1978.

Chabás, José and Bernard R. Goldstein. The Alfonsine Tables of Toledo. Dordrecht: Kluwer, 2003.

Comes, Mercè. Ecuatorios andalusíes. Ibn al-Samh, al-Zarqulluh y Abu-l-S‘alt. Barcelona: Instituto de Cooperación con el Mundo Arabe y Universidad de Barcelona, 1991.

Comes, M., R. Puig and J. Samsó, eds. De Astronomia Alphonsi Regis. Actas del Simposio sobre Astronomía Alfonsí celebrado en Berkeley (Agosto, 1985) y otros trabajos sobre el mismo tema. Barcelona: Instituto “Millás Vallicrosa” de Historia de la Ciencia Arabe, 1987.

Comes, M., H. Mielgo and J. Samsó, eds. “Ochava Espera” y “Astrofísica.” Textos y Estudios sobre las Fuentes Arabes de la Astronomía de Alfonso X. Barcelona: Instituto de Cooperación con el Mundo Arabe e Instituto “Millás Vallicrosa” de Historia de la Ciencia Arabe, 1990.

Hilty, Gerold. El libro conplido en los iudizios de las estrellas. Al-Andalus (1955) 20: 1–74.

Pingree, David. Picatrix. The Latin Version of the Ghayat alhakim. London: The Warburg Institute, 1986.

Poulle, Emmanuel. Les Tables Alphonsines avec les canons de Jean de Saxe. Paris: C.N.R.S., 1984.

Procter, Evelyn S. Alfonso X of Castile Patron of Literature and Learning. Oxford: Clarendon Press, 1951.

Rico y Sinobas, Manuel. Libros del Saber de Astronomía del Rey D. Alfonso X de Castilla, copilados, anotados y comentados. 5 vols. Madrid: Real Academia de Ciencias, 1863–1867.

Samsó, Julio. Islamic Astronomy and Medieval Spain. Aldershot: Variorum Reprints, 1994.

Vernet, Juan, ed. Textos y Estudios sobre Astronomía Española en el Siglo de Alfonso X. Barcelona: Institución “Milà y Fontanals” del C.S.I.C. y Universidad Autónoma de Barcelona, 1981.

JULIO SAMSÓ

Alfred of Sareschel

Alfred of Shareshill or Sareschel, more commonly referred to as Alfredus Anglicus (Alfred the Englishman), probably owes his name to the village of Shareshill, ten miles (16 km) west of Lichfield, and is likely to be the “Magister Alueredus de Sarutehill canonicus Lich.” mentioned in a charter of Ralph Neville, dean of Lichfield from 1214 to 1222 (BL, Harley MS 4799, fol. 62va). Lichfield was the diocese to which Oxford belonged, and the nature and diffusion of Alfred’s writings imply that he was involved in teaching Aristotelian philosophy in the nascent university, along with *Alexander Nequam to whom he dedicates a work. His floruit must have been the late twelfth and early thirteenth century. Alfred continued the program of translating the corpus of texts on Aristotelian natural science set out in order in *al-Farabi’s On the Classification of the Sciences, from the point where *Gerard of Cremona (d. 1187), the Toledan-based translator of texts from Arabic into Latin, left off. Gerard had translated Aristotle’s Physics, On Generation and Corruption, On the Heavens, and completed the Meteorology, Alfred took the texts next in order: On Minerals and On Plants. This strongly suggests that Alfred himself spent some time in *Toledo, a hypothesis strengthened by the fact that several Spanish vernacular words are included in his translations. It was probably here that he studied with a Master Salomon Avenraza, “Israelita celeberrimus et modernorum philosophorum precipuus” (“the most famous Jew and leader of modern philosophers”) (Alfred of Sareshel, Commentary on the “Metheora,” 51). Furthermore, Alfred wrote commentaries on many of these texts on natural science. His commentaries were quoted by Oxford masters lecturing on Aristotle’s natural science in the mid-thirteenth century, such as Adam of Buckfield and “R. de Stanington.”

The works on plants and mineralogy that Alfred of Shareshill translated as part of an Aristotelian corpus were two chapters, on stones and on metals, from Avicenna’s (*Ibn Sina’s) summa of Peripatetic philosophy, the Shifa’ (these became three chapters in Latin), and the On plants of Nicholas of Damascus, which Alfred dedicated to Roger of Hereford. The three chapters on stones and plants were added to Gerard’s translation of the first three books of Aristotle’s Meteorology and Henricus Aristippus’s translation of the fourth book, to form a single text. Alfred wrote commentaries on this composite text, as well as on the On Plants, and refers to his own commentary on On Generation and Corruption. According to a medieval catalog of the manuscripts of Beauvais Cathedral, he also wrote commentaries on Aristotle’s On the Soul, On Sleep, On Death and Life, and On the Heavens.

Alfred’s independent treatise—On the Movement of the Heart (De motu cordis)—was dedicated to Alexander Nequam, probably before c. 1197 when Alexander left Oxford to become a canon of Cirencester. It is concerned with the conditions necessary for life and ensoulment (a topic also covered in his commentary on On Plants), and adopts a strictly Aristotelian view in making the heart rather than the brain the seat of the soul. This work is remarkable for the large number of scientific texts it cites, which include, in addition to the above-mentioned works, Aristotle’s Physics, On Respiration, Metaphysics, and Ethics, Qusta ibn Luqa’s On the Difference between the Spirit and the Soul, Alexander of Aphrodisias’s commentary on the Meteorology, and texts by *Hunayn ibn Ishaq and Ishaq Israeli (*Isaac Judaeus). Alfred’s commentaries on the Meteorology and the On Plants had the same status as the commentaries by Averroes (*Ibn Rushd) on the other books of Aristotle’s natural science among university teachers in Oxford and elsewhere from the mid-thirteenth century onward. He played an important role in the period during which Aristotle was being established as the key authority in natural science in the early universities.

Bibliography

Primary Sources

Alfred of Sareshel, Commentary on the Metheora of Aristotle, ed. J. K. Otte. Leiden: E. J. Brill, 1988.

Nicolas Damascenus, De plantis. Edited by H. J. Drossaart Lulofs and E. L. J. Poortman. North Holland Publishing Co.: Amsterdam, 1989, pp. 465–473.

R. J. Long, “Alfred of Sareshel’s commentary on the pseudo-Aristotelian De plantis: a critical edition.” Mediaeval Studies (1985) 47: 125–167.

Des Alfred von Sareshel (Alfredus Anglicus) Schrift De motu cordis. Edited by C. Baeumker. Beiträge zur Geschichte der Philosophie des Mittelalters, 23. Münster: Aschendorff, 1923.

Secondary Sources

Callus, D.A. Introduction of Aristotelian learning to Oxford. Publications of the British Academy (1943) 29: 229–281.

Southern, R.W. Robert Grosseteste: the growth of an English mind in medieval Europe, 2nd edn. Oxford: Clarendon Press, 1992, pp. 90–92.

CHARLES BURNETT

Algebra

Defined as the science of determining unknown quantities in mathematical relations or equations, algebra has been studied by almost every culture, although in markedly different ways. Its appearance before the Renaissance would be foreign to modern readers; the symbolic language that we associate with algebra is a sixteenth-century invention. In ancient and medieval times algebraic expressions were written rhetorically, i.e., in words rather than symbols. Methods and goals differed as well: some relied on geometrical reasoning and others on arithmetic; some accepted approximation techniques while others looked for closed-form solutions. In China, for instance, polynomial equations were solved using a method—relying on the binomial theorem—that determines successive decimal places of the solution, whereas the Babylonians, Indians, and Muslims used procedures that led directly to the solution, as we learn today in high school. Greek mathematicians were especially interested in geometric proofs of what we now call algebraic identities, but in medieval India, as in ancient Babylon, the focus was on the steps that led to a numerical solution. Often these steps were given in verse, partly for ease of memorization. As early as Aryabhata’s Aryabhatiya (499 C.E.), we find instructions for solving problems that can be reduced to quadratic equations (ax² + bx + c = 0). Similar instructions may be found in Brahmagupta’s Brahmasphutasiddhanta (628 C.E.) and in later, more systematic works such as Bhaskara II’s twelfth-century Bijaganita. Thus the form of Indian algebra differed dramatically from its Greek counterpart, and the stage was set for a synthesis in medieval Islam.

Early Islamic science was influenced heavily by Indian sources. A case can be made for at least some Hindu origin in the most important algebraic text of the medieval period, *Muhammad ibn Musa al-Khwarizmi’s al-Jabr wa’al-Muqabalah. The two terms in the title refer to, respectively, moving a subtracted quantity on one side of an equation to the other side, and combining like terms on opposite sides of an equation. The phrase came to mean the entire science of algebra; in fact, al-Jabr is the origin of our word “algebra.” The first part of al-Khwarizmi’s book is a collection of algorithms to solve various types of quadratic equation (indeed, al-Khwarizmi’s name is the origin of the word “algorithm”). Because the existence of negative numbers was not yet recognized, al-Khwarizmi needed to approach, say, ax² + bx + c differently from ax² + bx = c; altogether he classified six types of equations, five of them quadratic. Although geometrical explanations of his methods are present, the work is mostly arithmetical in character. The second part of al-Jabr wa’al-Muqabalah deals with the science of measuring areas and volumes; the third and final part consists of solutions to problems of the disposition of inheritances under Islamic law.

The influence of al-Jabr wa’al-Muqabalah was dramatic. It immediately spawned a number of successors and commentaries, among them Abu Kamil’s Algebra (900 C.E.). This work, not surprisingly very much in al-Khwarizmi’s style, is innovative particularly for its general statements of algebraic rules (such as $\sqrt{a} + \sqrt{b} = \sqrt{a} + 2 \sqrt{a b + b}$ ), as well as its treatment of irrational quantities as numbers rather than the Greek treatment as geometric magnitudes. (It also contains the rudiments of what was to become linear algebra.) Al-Khwarizmi’s Algebra, meanwhile, became widely used as a textbook, and was to become a major impetus for the study of algebra in Europe after its translation into Latin in the twelfth century.

Al-Khwarizmi was a member of the House of Wisdom, a research institute founded by caliph al-Ma’mun in the early ninth century. One of the House of Wisdom’s most important activities was the translation into Arabic of many of the most important texts of Greek mathematics, including those of *Euclid, *Archimedes, and Apollonius. These translations propagated Greek geometric and logical methods widely, and their impact was felt in algebra as well. For instance, *Thabit ibn Qurra (836–901 C.E.), one of the translators of Euclid’s Elements, wrote Discourse on the Establishment of the Correctness of Algebraic Problems, in which he sets out to demonstrate the rules for solving quadratic equations. His main concern is for logical validity, and he achieves it by geometric deductions using propositions from Book II of the Elements.

However, this geometrization was not to last long; the quantities at the heart of algebra were increasingly being seen as numbers rather than geometric magnitudes. This trend came to fruition in the work of al-Karaji (1000 C.E.). His book The Marvellous contains the first set of rules to manipulate expressions involving terms xⁿ with arbitrary exponents; of course, only powers up to x³ can be represented geometrically. He developed algebraic procedures not by proving them from the Elements, but rather by making an analogy with arithmetic: for instance, the expression 3x² + 5x + 8 is analogous to the number 358, and arithmetic operations applied to numbers can equally well apply to the corresponding polynomials. However, al-Karaji was unable to take certain vital steps, due to the lack of a concept of negative numbers. This prevented him from being able to perform the operations needed to divide polynomials. This shortcoming was addressed in the early twelfth century by the Iraqi Jewish scholar al-Samaw’al Ibn Yahya al-Maghribi, who at age nineteen wrote a systematization of algebra called The Dazzling Book on Calculation, in which we find a proper theory of negative quantities. Al-Samaw’al used it effectively, extending al-Karaji’s approach to make possible not only polynomial division, but also the extraction of the square root of a polynomial. Curiously, however, when al-Samaw’al deals with quadratic equations later in the book, he returns to geometric demonstrations. Also found in The Dazzling are examples of recursive reasoning and a preservation of al-Karaji’s computation of the binomial coefficients (now known as Pascal’s triangle).

Geometry, however, plays a vital role in the next great Arab contribution to algebra. Having dealt so long with quadratic equations, it is natural to ask how one might solve a cubic (in modern form, ax³ + bx² + cx + d = 0). Just as with quadratic equations, the lack of a concept of negative numbers broke the consideration of the cubic into a number of cases. Although attempts were made to solve cubics as early as the ninth century, only four of the fourteen types were solved before *‘Umar al-Khayyam (1048–1131 C.E., known to the West as Omar Khayyam, author of the epic poem The Rubaiyat). Al-Khayyam’s Algebra solves all fourteen types geometrically in a manner similar to his predecessors, by demonstrating that certain line segments in diagrams in which various conic sections such as circles, parabolas, and hyperbolas intersect satisfy the relation set out in the equation. He seems to have failed in an attempt to find a solution more recognizable to us, one which is calculated directly from the coefficients in the equation.

Less than a century later, Sharaf al-Din al-Tusi’s On the Equations (1170 C.E.) took al-Khayyam’s work on cubics in a new direction. It opens with a discussion of cubics using conic sections, similar to the method in al-Khayyam. However, the second half of the book contains a startlingly modern analysis of the existence of solutions to certain cubics. Representing the equation in the form f(x) = k, he considers the possibilities for the maximum value of f(x), and determines the ranges of values of x for which f(x) increases or decreases. While the mathematics of al-Tusi’s method can be verified using differential calculus, the path that he might have taken to arrive at his conclusions remains controversial.

Europe

There is very little to say about algebra, or indeed mathematics of any sort, in early medieval Europe. Interest in the subject finally began to develop in 1145, when the first two parts of al-Khwarizmi’s Algebra were translated into Latin—the first part by Robert of Chester (and again, later, by *Gerard of Cremona), and the second part (in an expanded edition by *Abraham bar Hiyya) by Plato of Tivoli. The first original contributions to algebra in Europe are found in the works of Leonardo of Pisa (1180?–1240? C.E.), also known as *Fibonacci. His best-known work, the Liber abaci (1202; revised 1228), contains an exposition of Hindu-Arabic arithmetic and uses algebra systematically to solve a variety of problems. Having traveled widely, Fibonacci was influenced greatly by both Greek and Arabic works; we find traces of the methods of al-Khwarizmi and al-Karaji within the pages, of his work, and many of the problems are Arabic in origin. Fibonacci handles problems related to quadratic equations, commercial interests, and number theory; he also delves into recreational mathematics, including a problem that leads to the famous Fibonacci sequence. Later, in his Flos (1225), he analyzes a cubic equation found in al-Khayyam’s Algebra (x³ + 2x² + 10x = 20), demonstrates that the solution is not one of the types of irrational magnitude found in Book X of Euclid’s Elements, and gives an approximate solution accurate to the equivalent of about ten decimal places. Finally, in his Liber quadratorum (also 1225), Fibonacci solves expertly the system of indeterminate equations x² + 5 = y² and x² - 5 = z² in the manner of Diophantus. Even taking into account Fibonacci’s reliance on his Greek and Arabic forebears, there is no doubt that he was the most creative algebraist in medieval Europe.

Fibonacci’s contemporary *Jordanus de Nemore, most widely known for his work in mechanics, also wrote the algebraic treatise De numeris datis. This book, written in the style of Euclid’s Data, was intended to be used in the practice of the first half of the paired ancient Greek techniques of analysis and synthesis; the propositions are in the form “if x, y… are given, then z is given.” However, unlike the Data, its contents were intended to be used for algebraic rather than geometric purposes. It has been suggested that Jordanus here anticipated François Viète, sometimes called the father of symbolic algebra, in applying analysis to the solution of equations.

Although the books by Fibonacci and Jordanus contained much creative mathematics, they seem to have stirred only a little interest in the European scholarly community, and the algebraic tradition that followed them was not nearly as lively as it was in Islam. Through the fourteenth century solutions of cubic and even some quartic equations were sought, but substantial progress on these and other algebraic problems did not occur until the late fifteenth and sixteenth centuries, when the birth of symbolism changed the face of algebra forever.

See also Arithmetic; Commercial arithmetic

Bibliography

Berggren, J. L. Episodes in the Mathematics of Medieval Islam. New York: Springer-Verlag, 1986.

Franci, R. and L. Toti Rigatelli. “Fourteenth-century Italian algebra.” In Mathematics from Manuscript to Print 1300–1600. Edited by Cynthia Hay. Oxford: Clarendon Press, 1988.

Hughes, Barnabas, ed. Jordanus de Nemore, De numeris datis: A Critical Edition and Translation. Berkeley: University of California Press, 1981.

Kasir, Daoud S., ed. The Algebra of Omar Khayyam. New York: Teacher’s College, Columbia University, 1931.

Mahoney, Michael S. “Mathematics.” In Science in the Middle Ages. Edited by David C. Lindberg. Chicago: University of Chicago Press, 1978.

Martzloff, Jean-Claude. A History of Chinese Mathematics. Berlin: Springer-Verlag, 1997.

Rashed, Roshdi. “Algebra.” In Encyclopedia of the History of Arabic Science. 2 vols. Edited by Roshdi Rashed. London: Routledge, 1996.

Rosen, Frederic, ed. The Algebra of Mohammed ben Musa. London: Oriental Translation Fund, 1831. Reprinted by Elibron Classics, 2002.

Sigler, Laurence, ed. Fibonacci’s Liber abaci: A Translation into Modern English of Leonardo Pisano’s Book of Calculation. New York: Springer-Verlag, 2002.

Van Egmond, Warren. The algebra of Master Dardi of Pisa. Historia Mathematica (1983) 10: 399–421.

GLEN VAN BRUMMELEN

Almanacs

Although its ultimate origin remains unknown, the word almanac appears as almanac in a text attributed to *Abraham Ibn Ezra (c. 1089–1167), only extant in Latin, and in the Arabic astronomical literature as manakh, in various texts associated with Ibn al-Banna’ (d. 1321), an astronomer from Marrakesh who used this term to refer to “the ephemerides of the Sun and the Moon.” Later, the term’s semantic range increased and it was understood as a set of tables, whether accompanied or not by a text explaining their use, giving the daily (or at intervals of a few days) true positions in longitude of the Sun, the Moon, and the five planets for a period of time of different duration for each celestial body. These periods of recurrence, or cycles, were fixed at an integer number of years, after which the planet returns to its initial position, very nearly, thus giving the almanac a “perpetual” use. The planetary periods, usually called goal-year periods, were already known to Babylonian astronomers and were used for predicting lunar and planetary phenomena. In the Almagest IX. 3, *Ptolemy (second century C.E.) gives the values for such periods. See Table One (below), where N is the number of solar years spanning the same time as an integer number (very nearly) of revolutions in longitude (R), and corresponding to an integer number of returns in anomaly (A), i.e., returns of the planet with respect to the position of the Sun.

TABLE ONE

Planet	N	R	A

Saturn	59y + 1;45d	2 rev. + 1;43°	57
Jupiter	71y − 4;54d	6 rev. − 4;50°	65
Mars	79y + 3;13d	42 rev. + 3;10°	37
Venus	8y − 2;18d	8 rev. − 2;15°	5
Mercury	46y + 1; 2d	46 rev. + 1°	145

TABLE TWO

The almanacs differ from other sets of tables in that the entries found in the almanacs give directly the positions of the celestial bodies and need no further computation, contrary to what is required with what are called “auxiliary astronomical tables” which are far more common and follow the pattern of the tables in Ptolemy’s Almagest.

The oldest work of this kind compiled in the Iberian peninsula is known as the Almanac of Azarquiel (*Ibn al-Zarqalluh), but the extant copies of it do not include the word almanac. This set of tables was composed by Azarquiel, a leading astronomer in eleventh-century *Toledo, and consists of canons and tables. A Castilian version of the tables translated for *Alfonso X (1221–1284) also survives. The Almanac of Azarquiel uses Ptolemaic models and parameters, and seems to derive from a similar work by an Alexandrian astronomer, referred to as Awmatiyus, Armeniut, or Humeniz, otherwise unknown. The Almanac of Azarquiel is based on almost the same periods as those mentioned by Ptolemy, and its entries were computed with the data in the Toledan Tables, a set of tables (zij) compiled in Toledo by a group of astronomers, including Azarquiel, led by *Sa‘id al-Andalusi. The almanac provides the true daily positions of the Sun for four years from September 1, 1088 (beginning of year 1400, era of Alexander), and the five planets (in sidereal coordinates), as well as the mean positions of the Moon (longitude, anomaly, and node), and contains many more tables than those in other almanacs.

What has been traditionally called the Almanac of Tortosa is a perpetual almanac, consisting of a text and tables beginning in 1307. This designation was coined when the only known copy of it was a Latin version made in Tortosa, now in Catalonia, from an archetype in Arabic. This designation is no longer appropriate, for various copies in Latin, Catalan, Castilian, Portuguese, and Hebrew have recently been identified. The Arabic archetype, however, has not been found. Some of the characteristics of the Almanac of 1307 are listed below.

The Jewish-Provençal astronomer and translator Jacob ben Makhir Ibn Tibbon (c. 1236–1304), also called *Profatius Judaeus, is the author of an Almanach perpetuum compiled for the meridian of Montpellier in southern France. The tables for the daily positions of the Sun begin on March 1, 1301, and those for the planets on various days in March 1300 (see Table Two). Jacob ben Makhir’s Almanach also contains tables for the computation of eclipses and several tables for purposes of interpolation. The longitudes tabulated in the Almanach are tropical and were calculated according to the Toledan Tables.

The astronomical genre of almanacs expanded greatly in the fourteenth century, and more so in the fifteenth century. We shall only mention a few of these works. John of Lignières, an astronomer active in Paris in the 1320s and 1340s, is the author of an almanac only very recently described by historians of astronomy and uniquely preserved in an incomplete copy. This almanac follows the pattern put in place by his predecessors. A contemporary of John of Lignères, *John of Saxony, also working in Paris, compiled an almanac of a different kind. It lists the true positions of the two luminaries and the planets, distributed in nine tables, covering the period 1336–1380. The almanac of John of Saxony is not organized according to the goal-year periods used by his predecessors, and no increments are given for each planet after these cycles, as is the case with all perpetual almanacs. There is evidence of various almanacs compiled in England, but no names are associated with them. In the Iberian peninsula, Pere Gilbert and Dalmau Ses Planes, two astronomers in the service of King Pere III of Catalonia (IV of Aragon), wrote a text called Tables and Almanac, partially preserved in Latin in a unique manuscript lacking the tables. The introduction explains that the tables were valid for a period spanning from 1360 to 1433, and that the tabulated longitudes were tropical. Ferrand Martines, from Seville, compiled an almanac preceded by a text in Castilian in fifteen chapters and consisting of tables adapted for 1391 from those in the Almanac of 1307.

Many almanacs were compiled during the fifteenth century, and among them stands out the Almanach Perpetuum associated with *Abraham Zacuto (1452–1515), the most celebrated astronomer in the Iberian Peninsula of his time. Zacuto produced the bulk of his astronomical work in Salamanca, although not at the university (as has often been said), until he left Spain for Portugal when the Jews were expelled from Spain in 1492. Zacuto’s principal work is a set of astronomical tables called Ha-hibbur ha-gadol (The Great Composition), composed in 1478. The Almanach Perpetuum, on which Zacuto’s fame rests, consists of a set of canons by Joseph Vizinus and a great number of astronomical tables, almost all drawn from the Hibbur. The Almanach Perpetuum was first printed in Leiria, Portugal, in 1496, probably without the intervention of Zacuto himself, and was reprinted several times, not always mentioning the author’s name.

Table Two summarizes such features as the length of the cycle, the frequency of the entries (“1y, 1d” means that two tables are presented, one at intervals of one year, and one at intervals of one day), and the precision in several almanacs.

Bibliography

Boffito, J. and C. Melzi d’Eril. Almanach Dantis Aligherii sive Profhacii Judaei Montispessulani Almanach Perpetuum ad annum 1300 inchoatum. Florence, 1908.

Chabás, J. 1996. “El almanaque perpetuo de Ferrand Martines (1391).” Archives internationales d’histoire des sciences, 46: 261–308.

Chabás, J. and B. R. Goldstein. Astronomy in the Iberian Peninsula: Abraham Zacut and the Transition from Manuscript to Print. Transactions of the American Philosophical Society, 90.2. Philadelphia, 2000.

Millás, J. M. Estudios sobre Azarquiel. Madrid-Granada, 1943–1950.

JOSÉ CHABÁS

Anatomy

In late medieval Latin the word anatomia, also spelled anothomia, had three principal meanings. It referred simultaneously to the structure of human or animal bodies, to the medical discipline devoted to the study of this structure, and to the practice of opening or eviscerating bodies. The last was used not only for the purposes of medical instruction and study (the practice we call dissection) but also in order to determine cause of death (the practice we call autopsy) and to preserve human corpses through techniques of embalming that involved evisceration. Of these three related practices, the earliest and most common was embalming; thus it is no coincidence that the only extensive study of human anatomy through dissection, before the late medieval era, took place in Hellenistic Egypt, where techniques of mummification were highly developed.

After the third century B.C.E., however, human dissection fell into disuse, as the culture of ancient Greeks and Romans, as well as of medieval Muslims, discouraged the mutilation of the human body after death. Thus the anatomical teaching of the most influential ancient Greek writers on anatomy and physiology, such as Aristotle, in the fourth century B.C.E., and *Galen in the second century C.E., relied instead on the dissection of animals. The treatment of human anatomy in the works of the most important medieval Arabic authors from the late ninth through twelfth centuries, including *Abu Bakr Muhammad ibn Zakariyya al-Razi (Rhazes), *Ibn Sina (Avicenna), and *Ibn Rushd (Averroes), was even less oriented toward observation of opened bodies; they drew for the most part on the descriptions of earlier Greek writers, supplemented by casual observations made in the course of medical and surgical practice. As a result, their discussions of human anatomy were relatively brief, intended for the most part to elucidate the nature and causes of disease.

The first signs of what was to become one of the distinguishing features of Western Christian medicine—its strong interest in the study of human anatomy, and its practice of dissection in this connection—are traceable to twelfth-century *Salerno, in southern Italy, the most important early center of medical study in Europe before 1200. Building on the work of their Greek and Arabic predecessors, several Salernitan masters wrote short, independent treatises on anatomy, one of which described the systematic dissection of a pig. This southern Italian orientation toward anatomy as basic to medical study and practice was ratified by *Emperor Frederick II in a decree of 1241, which required knowledge of anatomy on the part of all those seeking a license to practice medicine in the Kingdom of Naples. Frederick did not specify that this knowledge should be based on the dissection of human bodies, although it is worth noting that contemporaries attributed to him an experiment that involved killing two men and opening their bodies to study the process of digestion. Although the story of this experiment is probably apocryphal, it does suggest that the idea of opening and inspecting human corpses in the interests of advancing medical and physiological knowledge was in the air.

It was only in the late thirteenth century, however, in north-central Italy, that the study of anatomy based on human dissection was established as a permanent element in Western medical culture. This new practice had its roots in several contemporary developments. Thanks to the work of *Taddeo Alderotti, the years around 1300 saw the establishment in Bologna of a university medical curriculum that focused on the works of Galen and his followers and presupposed Aristotelian ideas about the functioning of animal (including human) bodies. Alderotti and his contemporaries looked in particular to two works attributed erroneously to Galen, although of Galenic inspiration: De interioribus (On Things Inside) and De juvamentis membrorum (On the Uses of the Members). Taddeo’s interest in anatomy—he lamented that he had never seen the opening of a pregnant woman, suggesting that he had witnessed the dissection of other human bodies—was certainly reinforced by the elaboration of *surgery as a learned discipline at the hands of writers such as *Teodorico Borgognoni and Guglielmo of Saliceto. The study of anatomy based on dissection seems to have become a regular part of the medical curriculum in Bologna in the generation after Alderotti and was codified in an influential textbook, the Anothomia of Taddeo’s student *Mondino de’ Liuzzi, completed c. 1316. Over the course of the fourteenth century, this study spread to other Italian universities and medical corporations (primarily colleges of physicians and surgeons), including those in Perugia, Florence, Padua, and Venice, as well as to the university of Montpellier, in southern France.

Another development that facilitated the adoption of anatomical dissection in late medieval Italy was the practice of using autopsy to determine cause of death in criminal trials and to study epidemic diseases that posed a threat to public health. Autopsies of this sort seem also to have been pioneered initially in Bologna and other nearby cities. Equally important was the increasing use of evisceration to embalm the bodies of popes, holy men and women, and eventually civic leaders and rulers, whose corpses might be placed on public display. It was relatively straightforward to examine the viscera of people who had been embalmed to see if they had died of natural causes, or if their corpses showed signs of supernatural intervention or foul play.

As this last practice makes clear, there was nothing intrinsically degrading about having one’s body opened or intrinsically un-Christian or impious about dissection. Indeed, medieval Christianity—a religion organized around the mutilated body of the crucified Christ and the corporeal relics of the Christian martyrs—contrasted markedly with Judaism, Greco-Roman paganism, and Islam in rejecting the idea of corpse pollution and the overriding importance of bodily integrity after death. Pope Boniface VIII’s famous decree Detestande feritatis (1297), prohibited the dismembering and boiling of human corpses in order to reduce them to bones for easy transportation, but his rulings targeted funerary customs (including embalming by evisceration) rather than the nascent practices of autopsy and dissection. Nonetheless, the decree had a chilling effect on the spread of dissection in northern Europe, where the practice was widely understood as prohibited or as requiring a special ecclesiastical license. It is in part for this reason that the practice of autopsy and the study of anatomy based on dissection were slow to be adopted outside the Mediterranean basin, where they did not begin to make serious inroads until the late fifteenth century.

This fact may help to account for the flowering of anatomical illustration in fourteenth- and fifteenth-century France and Germany. *Henri de Mondeville, for example, who had studied surgery in Bologna, created a series of anatomical images for use in his teaching at the university of Montpellier, to substitute for the dissected cadaver. A generation later, Guido of Vigevano, also trained in Italy, commissioned elaborate illustrations for his own treatise on anatomy (1345)—based heavily on Mondino’s Anothomia—which he addressed to the King of France.

Wherever the teaching of anatomy was based, at least in part, on the practice of dissection, universities, and medical corporations struggled with the limited supply of cadavers. While few Italians seem to have viewed the opening of the body as sacrilegious, it shamed and dishonored dead person and his or her family when performed in public, in front of an audience of unrelated men. It is for this reason that formal dissections, unlike autopsies, were typically carried out on the corpses of executed criminals. Because executions were relatively rare before the sixteenth century, this meant that cadavers—especially female cadavers—were in very short supply. As a result, although many university statutes called for at least one dissection a year by the end of the fifteenth century, the practice seems to have been infrequent, prompting petitions and protests from teachers and students in medical faculties. This situation was remedied in part by the increasing currency of autopsies, typically performed in domestic spaces at the request of the family, and what came to be called “private” dissections, attended by one or more medical masters and a small number of students, which were performed on private citizens and people who had died in *hospitals for the poor. It is worth noting that physicians and professors of medicine rarely carried out their own dissections, employing surgeons for this purpose.

The relative infrequency of dissections reflected in part the fact that they were ancillary to the study of anatomy, intended to supplement the university lectures and learned texts that were the principal sources of knowledge about the human body and its structure. Until the early sixteenth century, in fact, anatomy was primarily a text-based discipline, studied above all through Greek and Arabic treatises, principally the third book of Ibn Sina’s Canon, which discussed human diseases and their treatments according to the organs affected, ordered spatially from head to foot. (This organization contrasted with that of Mondino’s Anothomia, written specifically to accompany dissections, which was divided according to the order in which the parts of the body were opened, treating sequentially the organs of the quickly putrefying abdomen, followed by those of the chest and the head.) Dissections helped students understand and commit to memory their textbooks, but they were not for the most part intended to serve as independent sources of information or to create new knowledge. This situation began to change dramatically in the years around 1500, when learned medical men, inspired in part by the humanist recovery of Galen’s lost text, De anatomicis administrationibus (On Anatomical Procedures), began to treat anatomy as an arena for research as well as teaching and practice. In the process, they began to compare their own observations with those recorded in ancient and medieval texts and to criticize these on the basis of their own experience; in this way, anatomy began to assume a quasi-autonomous status, as a source of natural philosophical knowledge concerning the human body, which it had not enjoyed before.

The new enthusiasm for dissection affected not only medical students and teaching masters but also artists such as Leonardo da Vinci and Michelangelo, who saw it as fundamental to the naturalistic portrayal of the human body. Although these new developments belong properly to the Renaissance and to the sixteenth century, however, they were by no means independent of the medieval tradition. Both the revival of Western interest in anatomy as a medical subfield and the institutionalization of anatomical practices of autopsy and human dissection were above all products of the medieval Western Christian world.

See also Bartolomeo da Varignana; Henri de Mondeville; Liuzzi, Mondino de’; Medicine, practical; Medicine, theoretical

Bibliography

Primary Sources

Corner, George. Anatomical texts of the Earlier Middle Ages: A Study in the Transmission of Culture, with a Revised Latin Text of Anatomia Cophonis and Translations of Four Texts. Washington: Carnegie Institution of Washington, 1927.

Mondino de’ Liuzzi. Anothomia di Mondino de’ Liuzzi da Bologna, XIV secolo. Edited by Piero P. Giorgi and Gian Franco Pasini. Bologna: Istituto per la Storia dell’Università di Bologna, 1992.

Wickersheimer, Ernest. L’ ‘Anatomie’ de Guido de Vigevano, médecin de la reine Jeanne de Bourgogne (1345). Archiv für Geschichte der Medizin (1913) 7: 2–25.

Wolf-Heidegger, Gerhard and Anna Maria Cetto. Die anatomisches Sektion in bildlicher Darstellung. Basel: S. Karger, 1967.

Secondary Sources

Alston, Mary Niven. The Attitude of the Church toward Dissection before 1500. Bulletin of the History of Medicine (1944) 16: 221–238.

French, Roger K. Dissection and Vivisection in the European Renaissance. Aldershot: Ashgate, 1999.

Herrlinger, Robert. History of Medical Illustration, from Antiquity to A.D. 1600. Translated by Graham Fulton-Smith. London, Pitman Medical, 1970.

Mondino de’ Liuzzi, Anothomia, trans. Michael McVaugh. In A Source Book of Medieval Science. Edited by Edward Grant. Cambridge: Harvard University Press, 1974. (Partial translation.)

Park, Katharine. The Criminal and the Saintly Body: Autopsy and Dissection in Renaissance Italy. Renaissance Quarterly (1994) 47: 1–33.

Park, Katharine. The Life of the Corpse: Division and Dissection in Late Medieval Europe. Journal of the History of Medicine and Allied Sciences (1994) 50: 111–132.

Savage-Smith, Emilie. Attitudes toward Dissection in Medieval Islam. Journal of the History of Medicine (1994) 50: 67–110.

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

KATHARINE PARK

Andalusi, Sa‘id al-

Sa‘id al-Andalusi was a religious scholar, judge, and patron of astronomy, born in Almería, Spain, in 1029. He moved to *Toledo in 1046, where he studied astronomy. He became friendly with the king, al-Ma’mun (reigned 1037–1064) who used Sa‘id to attract astronomers to his court, possibly in conscious emulation of his namesake the Abbasid caliph al-Ma’mun, famous for his encouragement of translations of Greek scientific works. Sa‘id wrote what amounts to a history of science viewed through the prism of the Arabic scientific movement, titled Kitab Tabaqat al-‘Umam (Book of the Categories of Nations).

In his account of Indian science, he introduces the Sindhind astronomical system, later adopted by Muslim scientists including *al-Khwarizmi, the bias of which is the long-term cyclical nature of celestial movements. He also gives an account of Indian arithmetic, which he calls hisab al-ghubar (dust board calculations), and of the invention of chess. His account of the Greeks is surprisingly detailed, but he concentrates particularly on Aristotle (“the first to separate the art of proof… and to provide it with its syllogistic type of argument”) and *Ptolemy, whose theoretical treatise the Almagest was so complete that no one since has even criticized it, although al-Nayrizi had clarified some of its points and *al-Battani had made it more accessible.

In a general chapter on Arab science, which he begins by noting the lack of interest that astronomy held for the ancient kings of Himyar, he praises the caliph al-Ma’mun for his efforts in promoting science, describes his contacts with the Byzantine emperors, his hiring of translators, and his encouraging his subjects to read the translated books: “As a result of his efforts, a scientific movement was firmly established during his reign.” With the decline of the caliphate, which Sa‘id ascribes to the influence of “women and Turks,” came the neglect of science.

In a chapter on science in the Arab east, Sa‘id elaborates on al-Ma’mun’s particular love of astronomy, charging astronomers, once they were familiar with the Almagest, to construct the equipment of the kind that Ptolemy and the ancient Greeks had used, creating an observatory at Shamasiyah, near Damascus. The observations made there resulted in a collection of tables called al-Rasd al-Ma’muni (Observations of al-Ma’mun). The rest of the chapter describes the contributions to philosophy and logic by *al-Kindi and then *al-Farabi, who supplied the analytical method lacking in the works of the former. There is considerable detail on the compositions of astronomical tables, in particular by al-Battani, the leader in the Islamic world “in rectifying celestial observations and examining stellar movements.”

In a long chapter on science in al-Andalus (Islamic Spain), he praises al-Kirmani, a Cordoban who had studied geometry and astronomy in the east and then settled in Saragossa where he introduced the astronomical works of the Banu Musa. Al-Kirmani was a practicing physician and surgeon and was known for medical experimentation, but not for observational astronomy. Sa‘id says that he learned his information on al-Kirmani from Abu’l-Fadl ibn Hasdai, another member of the group of scientists and philosopher in the court of the Banu Hud—an important piece of information because the scientific library of Banu Hud ended up in Toledo when their kingdom was conquered in the early twelfth century. Sa‘id’s statement attests to the ongoing contact between scientists of the two courts.

Sa‘id’s most important colleague or disciple in Toledo was the astronomer *Ibn al-Zarqalluh, the principal author of the Toledan Tables, which in Latin translation became the most influential astronomical tables in Europe until supplanted by the Alfonsine Tables of *Alfonso X the Wise. The Toledan Tables in general reflect the Sindhind tradition that had been predominant in Andalusi astronomy from the time of Maslama al-Majriti (*Maslama of Madrid) (d. 1007) and his school. A study of the numerical parameters of the tables reveals a mélange of sources, including the Sindhind, Ptolemy, al-Khwarizmi, Maslama and his school, and al-Battani.

Oddly, Sa‘id does not mention the work on the preparation of these tables, no doubt because the Tabaqat was written in 1068, and Sa‘id died in 1070, just when the Tables were nearing completion. The original Arabic version of the Tables has been lost, but in the canons of the first Latin translation, attributed to *John of Seville, it is stated that “Abensahet (Ibn Sa‘id) the judge of king Maymon of Toledo composed these tables, along with his disciple Arzachel (al-Zarqalluh) and others, but Arzachel handled the instruments and studied the positions.” This account became the standard one: the fourteenth-century Toledan Jewish historian Isaac Israeli wrote in his Yesod ha-‘Olam that Sa‘id had directed the work of twelve astronomers, mainly Muslims but also including some Jews.

See also Aristotelianism; Astronomy, Islamic; Astronomy, Latin; Planetary tables; South-central Asian science

Bibliography

Sa‘id al-Andalusi. Kitab Tabaqat al-‘Umam. L. Cheikho, ed. Beirut: Imprimerie Catholique, 1912.

———. Science in the Medieval World: Book of the Categories of Nations. A. S. Salem and A. Kumar, eds. Austin: University of Texas Press, 1991.

Samsó, Julio. Las ciencias de los antiguos en al-Andalus. Madrid: Mapfre, 1992.

THOMAS F. GLICK

Aquinas, Thomas

Born near Naples in either 1224 or 1225 and expected by his family to spend his life as a Benedictine monk at Monte Cassino, Thomas Aquinas was instead attracted to the newly established Order of Preachers (Dominicans), founded early in the century by St. Dominic. As a young Dominican Aquinas was sent to Paris to study with *Albertus Magnus and went with him in 1248 as the latter founded a new Dominican house of studies in Cologne. He returned to Paris in 1252 to lecture on the Sentences of *Peter Lombard. In 1256 Aquinas became Master of Theology at the University of Paris. He returned to Italy in 1259 (teaching in Naples, Orvieto, and Rome), and then went back again to Paris, where he taught from 1268 to 1272. He returned to Naples in 1272, and died on March 7, 1274, at Fossanova, south of Rome, on his way to the Council of Lyon.

No doubt under the inspiration of Albertus Magnus, who sought to make Aristotle “intelligible to the Latins,” Aquinas wrote extensive commentaries on Aristotle’s books in the natural sciences. He also incorporated his knowledge of Aristotelian thought in his more famous works: Summa theologiae and Summa contra gentiles. The commentaries on Aristotle, especially on Physics and De Anima, and his own early work, The Principles of Nature, as well as important sections of On the Power of God and On Truth, manifest Aquinas’s lively interest in fundamental questions of natural philosophy. Evidence of the importance Aquinas placed on a correct understanding of natural philosophy is the fact that his major commentaries on Aristotle were undertaken during his intellectually mature years.

Science and Faith

As a theologian and philosopher, Aquinas was especially concerned with questions involving the relationship between faith and reason. In the midst of debates about the role of Greek learning, especially the heritage of Aristotle in the context of religious belief, Aquinas sought to use the insights of that learning to help to understand what was believed. In this enterprise he was influenced by Muslim and Jewish predecessors, such as *Ibn Sina (Avicenna), *Ibn Rushd (Averroes), and *Maimonides, as well as by his teacher, Albertus.

In the tradition of Aristotle, Aquinas viewed science as sure and certain knowledge of a specific subject, achieved by the discovery of a necessary nexus between cause and effect. For the natural sciences, this meant an understanding of all four causes: formal, final, efficient, and material. Committed to the principles of Aristotelian metaphysics and natural science, Aquinas recognized that explanations of the natural world must employ the notions of form and matter, substance and accident, and act and potency. Following the analysis of science set forth in Aristotle’s Posterior Analytics, Aquinas thought of scientific knowledge as including both theoretical and practical domains: from metaphysics and natural science to ethics and politics.

Since, for Aquinas, God is the author of all truth, the truths discovered by reason, including truths about nature, cannot in principle contradict the truths disclosed by God in Scripture. Conflicts, when they do arise, must be the result of an improper use of reason or a misunderstanding of faith, or both. Furthermore, he thought that specific truths about God, such as that He exists, is one, and that He is the creator, are discoverable by reason alone. One of his famous arguments for the existence of God proceeds from the reality of motion to the existence of an unmoved mover, Who is God. Since faith is an illumination of the intellect, there can be no radical disjunction between faith and reason. As he famously remarked: Grace does not abolish nature; it perfects nature. Faith presupposes and thus needs that knowledge of reality which reason provides.

In the very first question of the Summa theologiae, Aquinas argued that sacra doctrina (which includes both Scripture and theology) is truly a science, although, unlike all other sciences, it takes its first principles from God’s own knowledge (as revealed in Scripture). Thus sacra doctrina has an inherently intelligible content even though the recognition of its truth depends on faith.

Throughout his career Aquinas sought to delineate the appropriate domains of theology, on the one hand, and the natural sciences and philosophy, on the other. He also sought to make clear the differences between metaphysics and natural philosophy, the latter being a more general science of nature than any one of the special empirical sciences. As such, natural philosophy, what Aristotle called physics, concerns itself with topics such as nature, change, and time. Although his ultimate concern was theological, Aquinas recognized the appropriate autonomy of the natural sciences—as well as of all the sciences based on reason alone.

Aquinas had no doubts that human beings are able to come to know the world, themselves, and (to some extent) God. Such knowledge is of two kinds: (1) Self-evident truths which are apprehended by a kind of intellectual intuition (including general notions such as the law of non-contradiction and the first principles proper to a given science, such as definitions of lines and points in geometry, or of motion in physics), and (2) Scientific knowledge, properly speaking, which is the result of demonstrations. Without the first, self-evident truths, there is no possibility to achieve the second. Scientific knowledge is of universals, not particulars: of what it means to be a bee, for example, not of an individual bee. Although scientific knowledge itself is the result of a deductive syllogism, it depends on sense experience. For Aquinas, all knowledge begins with sense experience. The human intellect has the ability to abstract from the particulars of sense experience to discover universals.

Motion and Change

Throughout his commentary on Aristotle’s Physics, Aquinas defended and made his own Aristotle’s understanding of nature and motion. The eight books of the Physics set forth general principles of the philosophy of nature which are necessary for detailed studies of celestial and terrestrial realities. Aquinas did not reduce all of motion or change to local motion. He defined motion (mutatio) in the broadest sense as the “act of the potential insofar as it is potential.” Motion is a reality that can be identified neither with mere actuality (for the actual is no longer in motion) nor with mere potentiality (for the potential is not yet in motion). Motion or change is understood in four analogical senses. Substantial change is the most fundamental; it is the change from one kind of natural unit to another (e.g., the coming into existence of a new individual member of a particular species). There are three kinds of accidental changes: changes with respect to sensible qualities are called alterations; changes with respect to quantity are augmentation or dimunition; changes with respect to place are locomotion. All substantial changes are instantaneous, although most are preceded by accidental changes, which involve time.

Any form of atomism, which reduces change to the mere rearrangement of fundamental elements (a kind of locomotion), must be rejected as rendering unintelligible both natural things and change.

Aquinas accepted Aristotle’s distinction between natural and violent motion: for the former the source of the motion is intrinsic to the body, for the latter it is extrinsic.

At times, Aquinas rejected some of Averroes’s interpretations of Aristotelian physics: for example, Averroes claimed that motion in a void is impossible, and that Aristotle’s principle that everything that is moved is moved by another required that every motion have a conjoined mover. Aquinas also thought that almost all substantial changes can be accounted for by causes in nature, and that there was no need to appeal, as Avicenna did, to a supernatural “giver of forms” to account for the appearance of new substances.

Thomas Aquinas and Albertus Magnus advance to meet Dante and Beatrice in Heaven. Seated in a semicircle in the foreground are ten doctors of the church, including three mitred bishops, Gratianus, Peter Lombard, and Isidore of Seville. This illustration is taken from a copy of Dante’s The Divine Comedy made for Alfonso V, King of Aragon (1416–1458) and Naples (as Alfonso I, 1442–1458). (Topham/The British Library/HIP)

Mathematics and Physics

Aquinas was especially insightful in distinguishing between mathematics and the natural sciences. Early in his career, in writing a commentary on *Boethius’s On the Trinity, he argued that there is an important difference between what each discipline studies. The natural sciences have as their proper area of investigation that which exists in motion or is capable of motion: mobile being (ens mobile). As he remarked, such entities depend on matter for their existence and for their being understood: that is, the natural sciences, although leaving behind particular sensible bodies (this horse or that plant, for example), do not leave behind in their explanation all references to material things. As he put it: the natural scientist abstracts from individual sensible matter, but not from common sensible matter (from this flesh and these bones, when speaking of animals, but not from flesh and bones, taken in a universal sense). The mathematician, on the other hand, abstracts from any reference to material being and considers quantities as such: continuous (in geometry) and discontinuous (in arithmetic). Aquinas thought that quantity, as an accident, does not exist separately from the material substance in which it inheres; nevertheless, the human intellect can leave behind all other sensible features of physical things and consider quantity as such. Arithmetic and geometry are both sciences rooted in what exists, but they consider the real world in terms of categories abstracted from that world. Mathematics does not provide a deeper explanation of reality than the natural sciences do; nor does mathematics provide the true principles for all scientific inquiry.

Particularly important for the history of science is Aquinas’s account of what he calls “intermediate sciences,” which employ mathematical principles to study physical reality. Following Aristotle, Aquinas cited examples such as harmonics and optics in which principles drawn from arithmetic, in the first case, and geometry, in the second, result in sciences different from either the natural sciences or mathematics. Aquinas also thought that mathematical principles can be applied to motion: the resulting mathematical physics is an “intermediate science.”

Aquinas was aware of the differences between Aristotelian cosmology and Ptolemaic astronomy, even though many in the Middle Ages conflated the two. The former seeks to discover the nature of the heavens in terms of causes; the latter, with its use of geometric entities such as epicycles, deferents, and equants, offers a mathematical description of observed phenomena in the heavens.

Creation and the Natural Sciences

Aquinas addressed the topic of creation in a magisterial way four times, and each time he noted that it is important to distinguish between creation and change; or as he would say: creatio non est mutatio (creation is not a change). The natural sciences study the world of changing things, and a self-evident principle of such a world is that something cannot come from nothing: all change requires an underlying material reality. Creation, however, is a concept in metaphysics and theology; it is a topic on which the natural sciences are not themselves competent to comment. Aquinas thought that “to create” means to be the complete cause of all that is. Creation refers to a metaphysical dependence in the order of being: were God not causing all that is, no things would exist. Thomas thought that the science of metaphysics is able to demonstrate that all things depend on God as the cause of their existence. As he wrote in his commentary on the Sentences of Peter Lombard: “Not only does faith hold that there is creation, but reason also demonstrates it.”

Aquinas distinguished between the origin of the universe and the beginning of the universe. Although he thought that reason alone can demonstrate that the world is created, that is, has an origin, he did not think that reason can conclude whether or not the world is temporally finite. Here he set himself apart from some Muslim and Christian thinkers who thought that, on the basis of what reason tells us, one could indeed conclude that the world must have a temporal beginning. Following the tradition of the Church Fathers and the decree of the Fourth Lateran Council (1215), he accepted as a matter of faith that the world is temporally finite; nevertheless, he argued that a created, eternal world would involve no logical contradictions. He pointed to the limits of the natural sciences: in principle, they cannot conclude whether or not the world has a temporal beginning. He specifically rejected Aristotle’s claim that it is demonstrably true that the world is eternal. He also warned believers to avoid using faulty scientific arguments which purport to show the temporal beginning of the world.

Although recognizing that God possesses an infinite power to produce beings ex nihilo, Aquinas did not think that such absolute power eliminates real secondary causes operating in nature: causes which it is the function of the natural sciences to discover. Aquinas did not think that one must choose between affirming God’s complete causality of all that is and the existence of other causes—a dilemma which vexed both mutakallimun and Averroes. Only by understanding divine transcendence, and that God is a cause in a way quite different from the way creatures are causes, was Aquinas able to defend the view that both God and creatures are the complete causes of what occurs in the world. Aquinas, thus, was able to affirm both a robust notion of divine agency and a natural order susceptible to scientific understanding in terms of causes discoverable in that order.

Biology and Psychology

Questions of the origin, development, and nature of human beings were part of Aquinas’s larger concern about understanding nature. He accepted Aristotle’s comment that the developing human embryo first lives the life of a plant, then that of an animal, and finally becomes human. Unlike Albert the Great, Aquinas thought that embryogenesis involves a series of substantial changes, with each rational soul’s being created immediately by God only when the embryo possesses the appropriate biological complexity to have such a soul as his or her substantial form. Each living being has a soul, which is the source of the being’s characteristic activity. Aquinas rejected the arguments of some of his contemporaries that a human being has three souls—vegetative, sensitive, and rational. He was always alert to defend the “unity of substantial form,” that is, that each substance has only one informing principle which makes it the one thing which it is.

Aquinas is not a dualist. He did not think that a human being is the combination of two things: body and soul (or, more generally, matter and form). A human being is one thing, understood in terms of the unity of two principles, one material, the other spiritual. Aquinas’s analysis of the human soul is part of his explanation of living things, which is itself part of his even broader understanding of the distinction between form and matter, the co-principles of all physical reality. That the rational soul is the informing principle of each human being follows from his view that each individual substance, inanimate and animate, must have an informing principle, and that the differences among informing principles are correlative to the differences among existing substances. Soul is not something added to, or which falls inside, or is united to a physical thing. Soul is what makes a living being the kind of living thing it is, and a human soul makes one a human being. The incorporeality of the human intellect means that human beings are of a very special sort, irreducible to physical things or sentient animals. In commenting on Aristotle’s De Anima, Aquinas rejected Averroes’s contention that there is a single “agent intellect” for all human beings; he locates an active power to come to know the world within each human being.

See also Albertus Magnus; Aristotelianism; Condemnation of 1277; Ibn Rushd; Ibn Sina; Lombard, Peter; Maimonides; Nature: diverse medieval interpretations; Reason; Religion and science; Scholasticism; Universities

Bibliography

Primary Texts

Aquinas, Thomas. Commentary on the “Posterior Analytics” of Aristotle (trans. by F.R. Larcher). Albany, NY: Magi Books, 1970.

———. Commentary on Aristotle’s “De Anima” (trans. by Kenelm Foster and Silvester Humphries). Notre Dame: Dumb Ox Books, 1994.

———. Commentary on Aristotle’s “Physics” (trans. by Richard J. Blackwell, Richard J. Spath, and W. Edmund Thirlkel). Notre Dame: Dumb Ox Books, 1999.

Baldner, Steven E. and William E. Carroll. Aquinas on Creation: “Writings on the ‘Sentences’ of Peter Lombard” 2.1.1. Translation, Introduction, and Notes. Toronto: Pontifical Institute of Mediaeval Studies Press, 1997.

Bobik, Joseph (trans. and ed.). Aquinas on Matter and Form and the Elements. A Translation and Interpretation of the “De Principiis Naturae” and the “De Mixtione Elementorum” of Thomas Aquinas. Notre Dame: University of Notre Dame Press, 1998.

Maurer, Armand (trans. and ed.). Thomas Aquinas: The Division and Methods of the Sciences. Questions V and VI of His Commentary on the “De Trinitate” of Boethius. Toronto: Pontifical Institute of Mediaeval Studies Press, 1986.

Secondary Sourcss

Davies, Brian. The Thought of Thomas Aquinas. Oxford: Clarendon Press, 1992.

Elders, Leo. The Philosophy of Nature of Saint Thomas Aquinas: Nature, The Universe, Man. New York: Peter Lang, 1997.

Jenkins, John. Knowledge and Faith in Thomas Aquinas. New York: Cambridge University Press, 1997.

Kretzmann, Norman and Eleonore Stump (eds.). The Cambridge Companion to Aquinas. New York: Cambridge University Press, 1993.

Stump, Eleonore. Aquinas. London: Routledge, 2003.

Torrell, Jean-Pierre. Saint Thomas Aquinas, vol. 1, The Person and His Work; Vol. 2, Spiritual Master (trans. by Robert Royal). Washington, D.C.: The Catholic University of America Press, 1996.

Weisheipl, James A. Friar Thomas D’Aquino: His Life, Thought, and Works. New York: Doubleday, 1974.

———. Nature and Motion in the Middle Ages (edited by William E. Carroll). Washington, D.C.: The Catholic University of America Press, 1985.

Wippel, John. The Metaphysical Thought of Thomas Aquinas. Washington, D.C.: The Catholic University of America Press, 2000.

WILLIAM E. CARROLL

Archimedes

Through the works of Archimedes (d. 212 B.C.E.) and the commentaries on them by Eutocius the mathematicians of the Arabic-Islamic world, and later those of the Latin world, were introduced to such varied matters as an advanced form of the principle of exhaustion, methods of solving cubic equations, solutions of geometrical problems by neusis (verging), and hydrostatic theory. Short biographies of Archimedes circulated at least as early as that of *Vincent of Beauvais (d. c. 1256). They relied principally on the account by Valerius Maximus (first century C.E.) of Archimedes’ death at the taking of Syracuse by the Roman general Marcellus: that he had hindered the Roman victory by constructing machines, and that he was killed after he had told a Roman soldier to go away from the mathematical diagram that he had drawn in the dust. The only mathematical work mentioned is the Measurement of a Circle.

At least two of Archimedes’ major works were translated into Arabic: the Sphere and Cylinder and the Measurement of a Circle. The first of the two books of the Sphere and Cylinder is largely about determining the surface area or volume of a sphere (or a segment thereof) by applying exhaustion procedures to the figure formed by rotating a polygon inscribed in, or circumscribed round, a great circle on the sphere. Much of Book II is on cutting a sphere with a plane so that the areas (or volumes) of the segments are in a given ratio. In the Measurement of a Circle the area of a circle is approximated by considering inscribed and circumscribed polygons. *Nasir al-Din al-Tusi (d. 1274 C.E.), who made a tahrir (redaction) of the text, reports two translations of the Sphere and Cylinder, one by *Hunayn ibn Ishaq and one corrected by *Thabit ibn Qurra. An almost complete text (in MS Istanbul, Fatih 3414) corresponds well enough to al-Tusi’s description of the text corrected by Thabit. In the Fatih manuscript, however, the translation is attributed to Qusta ibn Luqa, so perhaps we may speak of the Qusta-Thabit translation. We learn that the translation was made from Syriac, for the translator into Arabic complains that the Syriac translator has left out some definitions and other preliminary matter. To make this omission good, the scribe added a fragment from another translation.

Also translated into Arabic was Eutocius’s sixth-century commentary on the Sphere and Cylinder; a translation apparently by Ishaq ibn Hunayn was known to al-Tusi. This work was particularly important in transmitting to the Arab world numerous Greek solutions to what a modern mathematician might call cubic equations.

The Measurement of a Circle was translated from Arabic into Latin twice in the twelfth century, once probably by Plato of Tivoli and once by *Gerard of Cremona. There were at least a dozen reworkings of the latter, most of them with Gerard’s enunciations but supplied with new proofs. In some there are discussions of such matters as the meaning of the length of a curved line. Of the Sphere and Cylinder there is only a fragment in Latin, apparently translated by Gerard, consisting of six enunciations taken from the prefaces to the two books.

Material from both the Sphere and Cylinder and Measurement of a Circle was incorporated in the treatise usually known by its Latin title Verba filiorum or Liber trium fratrum, written by the three sons of Musa ibn Shakir. The book was translated into Latin by Gerard of Cremona and was later the subject of a tahrir by al-Tusi. In Latin Archimedes’ ideas were also transmitted by the De curvis superficiebus, a text apparently translated from the Greek. This, too, was sometimes expanded or commented on. Archimedes’ influence is clear to see on *Thomas Bradwardine (early fourteenth century) in his Geometria speculativa and on the anonymous fifteenth-century author of the De inquisicione capacitatis figurarum.

The Sphere and Cylinder was translated into Hebrew by Qalonymus ben Qalonymus (early fourteenth century, Provence) from an Arabic text apparently translated by Qusta—so perhaps our Qusta-Thabit translation. Most of Book I of Eutocius’s commentary was also translated, probably by the same translator. Further research will be required before we know how influential these translations were among medieval Jewish mathematicians. We may note that the Latin and Hebrew translations imply the availability of Archimedes manuscripts in Arabic.

Archimedean results on areas and volumes were also transmitted in handbooks, of which one type went under the name Practica geometrie. Of these perhaps the best known is that of Leonardo of Pisa (*Fibonacci), which has the peculiarity of containing passages copied verbatim from the Verba filiorum.

Indirect Transmission

Archimedes was also influential through indirect transmission: through collections of results sometimes attributed to him, but not part of the Greek corpus. An example is the Liber Archimedis de insidentibus in humidum (the book of Archimedes on [things] floating in water). This is probably not a genuine work, but it contains the Principle of Archimedes and treats Archimedean problems such as determining the proportion of substances in an alloy. There are several collections of geometrical propositions usually attributed to Archimedes that appear to be of Greek origin but not directly by him. Thus one such collection, included by Heath in his translation of Archimedes’ works under the title Book of Lemmas, mentions Archimedes by name. This text is known in the redaction of the eleventh-century mathematician Abu ’l-Hasan Ali ibn Ahmad al-Nasawi, which was later the subject of a tahrir by al-Tusi. Another collection is attributed in one manuscript to Archimedes and in another to a certain Aqatun. A third collection, On Tangent Circles and a fourth, a treatment of the regular heptagon, are each attributed to Archimedes in the one known manuscript. Sometimes the same result appears in several collections, often in slightly different forms. An example is an elegant theorem attributed to Archimedes by *Abu al-Rayhan al-Biruni in his Istikhraj al-autar (The Determination of Chords) and used by *Ptolemy (second century C.E.) in the Almagest in the determination of chords: if AB and BC are chords in a circle and AB is the longer, and if the perpendicular ED from the mid-point E of arc ABC to AB is drawn, then AD = DB + BC. There are various presentations of this in the Istikhraj, in the Book of Lemmas, in On Tangent Circles, and in the treatise on the regular heptagon.

Archimedean ideas contained in these collections sometimes found their way into Latin. Thus a construction of the regular heptagon similar to that ascribed to Archimedes is in a fragment translated by Gerard of Cremona and later taken almost word-for-word into the Liber de triangulis once thought to be by *Jordanus de Nemore. Again, al-Biruni says in the Istikhraj—and presumably with good reason—that Archimedes enunciated the theorem that we now call “Hero’s formula” for the area of a triangle. A proof of this result is to be found in the Verba filiorum; and another proof, in two Latin versions, was claimed to be from the Arabic.

In 1269 *William of Moerbeke translated almost all of Archimedes (and also Eutocius’s commentary on the Sphere and Cylinder) direct from Greek. The translation is so literal that it was used to help establish the Greek text. William was a Flemish Dominican, at one time confessor of Pope Clement IV. He is most famous for his translations of Aristotle from Greek. *Witelo, the Polish writer on optics, was a close friend and dedicated his Perspectiva to him. Not surprisingly, Witelo was one of the first to use the material provided by the new translations—his treatment of ratios, inter alia the notion of the denominatio of a ratio, owed something to Eutocius’s commentary on the Sphere and Cylinder.

The Measurement of a Circle (under the title De quadratura circuli) and the Liber de curvis superficiebus were explicitly cited by the thirteenth-century Gerard of Brussels—although without giving an author in either case—in his Liber de motu (Book on Motion), which in turn had some influence on the fourteenth-century masters of Oxford and Paris. The Moerbeke translations were used too: witness *Nicole Oresme’s use of the Spirals in his De configurationibus qualitatum et motuum (On the Configurations of Qualities and Motions); Henry of Hesse’s references to the Floating Bodies in his Questiones super perspectivam (Questions on General Optics); material taken from Eutocius on the duplication of the cube in the De arte mensurandi (On the Art of Measurement) by *Jean de Meurs; and many other examples.

In 1450 Jacobus Cremonensis made a new translation of Archimedes’ works (almost complete) from the Greek at the behest of Pope Nicholas V, who sent a copy to Nicholas of Cusa (d. 1464). Whether the new translation was completely independent of Moerbeke’s has yet to be investigated. Some printed editions of the sixteenth century were based on Moerbeke and other medieval material: these include the first two printed works of Archimedes, the Quadrature of the Parabola and the Measurement of a Circle, printed by Gaurico in 1503 from the Moerbeke translation. *Regiomontanus may be seen as a bridge between the medieval and the modern mathematical world. He copied one of the reworkings of Gerard’s translation of the Measurement of a Circle and owned copies of the Verba filiorum, but he also copied Jacobus’s new translations, making numerous emendations to them. He intended to reproduce them as part of his project to print the ancient classics of mathematics, but was prevented by his untimely death.

Many writings have been attributed to Archimedes. A book on water-clocks is ascribed to him, but without certainty. That he concerned himself with mechanical contrivances is clear (the machines he is supposed to have made to defend Syracuse are not meant), for Cicero describes his celestial globe and another, more complex, instrument. Whether they contained anything new we do not know. Again, according to ancient testimony Archimedes had written on catoptrics (on the reflection of light), and it has even been suggested that he is partly responsible for the pseudo-Euclidean Catoptrics, but we can only speculate about this. Much of Archimedes’ enormous achievement must remain hidden.

See also Clepsydra; Optics and catoptrics

Bibliography

Clagett, M. Archimedes in the Middle Ages. Vol. I Madison: University of Wisconsin Press, 1964; vols. II–V. Philadelphia: The American Philosophical Society, 1976–1984.

Folkerts M., and R. Lorch. “Some Geometrical Theorems Attributed to Archimedes and their Appearance in the West.” In Archimede—Mito, Tradizione, Scienza…, ed. Corrado Dollo, Nuncius, Studi e Testi IV, Florence 1992, pp. 61–79. Repr. in R. Lorch, Arabic Mathematical Sciences: Instruments, Texts, Transmission. Aldershot: Variorum, 1995.

Heath T.L. [translator]. The Works of Archimedes. New York: Dover Press, 1955.

Knorr, W.R. Textual Studies in Ancient and Medieval Geometry. Boston, Basel, Berlin: Birkhauser, 1989.

Lorch, R. The Arabic Transmission of Archimedes’ Sphere and Cylinder and Eutocius’ Commentary. Zeitschrift für Geschichte der Arabisch-Islamischen Wissenschaften (1989) 5: 94–114. Repr. in R. Lorch, Arabic Mathematical Sciences: Instruments, Texts, Transmission (op. cit.).

RICHARD LORCH

Aristotelianism

In Nicomachean Ethics VI 3–5 Aristotle distinguishes theoretical “science” from the practical “arts” and “prudence.” In the Aristotelian tradition before the Latin Middle Ages the theoretical “sciences” rather than the practical disciplines in Aristotle’s encyclopedia were stressed, and within the theoretical disciplines the systematic presentation of “true and certain” knowledge rather than the inductive search for its principles.

The edition of Aristotle’s works made by Andronicus of Rhodes (fl. c. 70–c. 50 B.C.E.) established the knowledge of a comprehensive, structured body of demonstrated conclusions as Aristotle’s ideal of science. The works of Alexander of Aphrodisias (fl. c. 193–217), the first great commentator on Aristotle, complemented this view of the Philosopher’s scientific corpus. The Neoplatonic movement attempted to harmonize the thought of Plato and Aristotle as the two great representatives of the Greek tradition. The tradition of commentary on Aristotle as an introduction to the higher wisdom of Plato was represented at Athens by the Elementatio theologica and the Elementatio physica of Proclus (c. 410–485), which exhibit all forms of substance as deriving from a single first principle, the Platonic One.

Alexandrian exegesis of Aristotle’s text, following Ammonius Hermeae, a pagan (fl. c. 500), was more independent. John Philoponus (fl. c. 529), a Christian follower of Ammonius, even contested various Aristotelian notions. His introduction of the Judaeo-Christian idea of creation into philosophy rendered Proclus’ entire system questionable. These Alexandrian developments determined, in large measure, the approach to Aristotle’s philosophy in the Byzantine world. Plato and Aristotle were regarded as representatives of “Hellenic philosophy,” as part of a pagan tradition, generally opposed to “our [Christian] philosophy.” The interest of Christian theologians in Aristotle was mostly limited to the parts of his logic necessary in theology. After the fall of Constantinople to the Crusaders in 1204 the necessity of answering the challenge of an increasingly sophisticated Latin theology led to the composition of comprehensive compendia of Aristotelian doctrine.

Arabic Aristotelianism

By the ninth century practically the entire corpus of Aristotle’s works, together with the Greek commentators on them, had been made available in Arabic. Aristotle’s classification of the natural sciences supplied the structure for an encyclopedia in which classical authors such as Hippocrates and *Galen, *Euclid, and *Ptolemy also found a place. But Muslim thinkers generally opposed studies concerned with their own way of life, called the “Arabic or traditional sciences” (the Qur’an, traditions, kalam or dialectical theology, and the like) to the “Greek or rational sciences” associated for the most part with Aristotle’s name. Kalam’s task was to supply the faithful with logical proofs for their belief.

*Al-Farabi (d. 950) attempted to fit the “traditional sciences of the Arabs” into the Aristotelian division of the sciences. The doctrine of God was taken up under the theoretical science of metaphysics, whereas kalam was regarded as a part of politics, with the function of defending the articles of faith. About a century later, Avicenna (*Ibn Sina) undertook to reform kalam in accordance with the Aristotelian theory of demonstrative science and understood kalam, not as a part of politics, but rather as metaphysics. Averroes (*Ibn Rushd), writing in Muslim Spain, also confronted the theologians with Aristotle’s idea of demonstrative science, stressing the truth and certainty of Aristotle’s presentation of theoretical science.

Jewish and Medieval Latin Aristotelianism

Medieval Judaism also had need of Aristotelian science and the logic which went with it. Where conflicts between philosophy and the Jewish faith appeared, some thinkers—of whom *Moses Maimonides (1135–1204) is the best example—held that only when the philosophical and theological doctrines have been clearly defined can one ask how the two realms are related. But an increasingly critical evaluation of Aristotle’s doctrines in the light of the Jewish faith appeared in the fourteenth century.

The works of Aristotle were made available in the Latin West in four clearly distinguishable stages. The first stage opened in the sixth century with translations by *Boethius of Aristotle’s treatises on logic, along with some notions transmitted by Cicero (106–43 B.C.E.). But the monastic teacher of the times knew little of Greek philosophy and science, and less of Aristotle.

With the rise of the towns new schools appeared and with them a new type of teacher. This new teacher—*Peter Abelard (1079–1142) is the best known—slowly pieced together the original fabric of the Aristotelian logic with the exception of the theory of demonstration as it is found in the Analytica posteriora. But because Boethius in his De hebdomadibus had described the organization of scientific knowledge much as Aristotle had done, twelfth-century authors often sought to develop a general theory of scientific method from it. Gilbert of Poitiers (c. 1075–1154), for example, maintained that first principles can be established for all the liberal arts and in the same way for theology itself. Nicholas of Amiens (fl. c. 1190) in his Ars fidei catholicae attempted to present theological doctrine in accordance with Euclid’s geometrical model.

The function of the masters was no longer simply that of transmitting traditional biblical wisdom. The “School of Chartres” confronted the Bible and the Church Fathers with the Timaeus of Plato, and Alain de Lille sought to work Platonic notions into Christian theology, employing the methodology of the newly translated Liber de causis. The translators of the period made immense additions to these sources, challenging the masters further: for geometry and optics Euclid, for astronomy Ptolemy, for medicine Hippocrates and Galen, and above all the works of Aristotle, together with his Muslim and Jewish commentators.

The consequent condemnation in 1210 and 1215 of Aristotle’s libri naturales at Paris was followed by an intense effort to axiomatize the quadrivial sciences. The attempt was most successful in the science of optics, a science subalternate to geometry. But attention was also turned to Aristotle’s theory of science directly. *Robert Grosseteste (c. 1168–1253) commented on Aristotle’s Analytica posteriora and explained that “science” means true and certain knowledge derived by syllogistic demonstration from first principles. Accordingly, the theologians undertook to transform their discipline into an Aristotelian science. In his Summa aurea, William of Auxerre (1140/50–1231) proposed taking the articles of faith as the principles of theological demonstration, on the basis of which Catholic theology could be presented as a structured body of strictly demonstrated conclusions. This lead was followed in particular by the Dominican theologians of the early part of the thirteenth century.

The Aristotelian encyclopedia provided the framework not only for theology, but also for the new philosophical, medical, astrological, and natural sciences, both those of ancient Greece and those of past and contemporary Islam and Judaism. There is a manuscript at Barcelona, in the Archives of the Crown of Aragon, which contains a manual or guidebook for students in the arts faculty in Paris. This text, which was apparently based on early thirteenth-century practice, was composed about 1230–1240 by an unknown master of the faculty for the benefit of students having to prepare for examinations. It reveals very clearly the role which the Aristotelian encyclopedia played in mastering the ancient legacy.

For the author of the guide-book the arts are no longer simply the seven liberal arts of the trivium and *quadrivium; they comprise rather all the philosophical and scientific disciplines newly recovered at his time. The author divides his subject into three branches: rational, natural, and practical or moral philosophy. Under rational philosophy he takes up the subjects of the trivium, assigning to grammar the works of Priscian and Donatus, to rhetoric Cicero’s De inventione, and to dialectic Aristotle’s Organon together with the Isagoge of Porphyry and the logical treatises of Boethius. Natural philosophy is divided into metaphysics, mathematics, and physics. For metaphysics the standard texts are the hardly known Metaphysica of Aristotle and the pseudo-Aristotelian Liber de causis. Under mathematics the author takes up the subjects of the quadrivium, but assigns to some of its branches works which were unknown in the earlier Middle Ages. To astronomy he assigns *Ptolemy’s Almagest, to geometry *Euclid’s Elements, to arithmetic Boethius’ Institutio arithmetica, and to music Boethius’ Institutio musica. Then are included the works at that time ascribed to Aristotle on natural philosophy: Physica, dealing with the general principles of physical change; De caelo, dealing with the eternal motion of the celestial bodies; De generatione et corruptione, dealing with the four sublunary elements which explain generation and corruption; Meteora, dealing with a great variety of natural phenomena; De plantis, De animalibus, De anima, Parva naturalia, and De motu cordis, which deal with the whole range of animate nature. But for moral philosophy the author’s assignment of texts to the different branches is less clear. He assigns the Ethica of Aristotle to the treatment of the life of the soul in itself. But the author does not yet know of Aristotle’s Oeconomica and Politica and fills the gap with Cicero’s De officiis and Roman and canon law. This students’ guide marks a definite stage in the evolution of the medieval arts faculty, the final stage in the formation of a new, urban type of school. Although the author attempts to assign theology a place among the practical disciplines, his concern is rather with the Aristotelian system of the natural sciences. The Aristotelian classification supplied the framework for the vast amount of new scientific material which the translators of the late twelfth and early thirteenth centuries had made available.

By about 1240/1250 the Latins had at their disposal the complete body of Aristotelian doctrine together with Averroes’ commentaries. Institutionally, the Aristotelian paradigm for science was established on March 19, 1255, when Aristotle’s works were prescribed for the lectures in the Paris arts faculty. Working within this paradigm, the Latins made, in the course of the next two centuries, enormous progress not only in mathematics and the physical sciences, but also in the Aristotelian practical philosophy, following new translations of the Ethics and Politics. *Albertus Magnus (c. 1200–1280) was among the first to turn his attention to the complete Aristotelian encyclopedia. His paraphrases of all of the fundamental works in Aristotle’s encyclopedia prepared the way for the vast commentatory literature through which the Middle Ages assimilated Aristotelian science.

More importantly, the Aristotelian system of the sciences was decisive for the formation of the medieval university. The arts faculty became what we might call a philosophical faculty, with a tendency to develop a teaching independent of the theological faculty. This development was bound to arouse a growing rivalry between the two faculties. The conflict had broken out at least as early as the students’ guide. It concerned at first moral philosophy, but far more profound than such particular differences was the implicit distinction between theological and philosophical discourse to which our master of arts here appealed. Medieval exegesis had been concerned with the Bible. The task of the exegete was not the discovery of new truths, but rather the unveiling of the truth concealed in the words of the sacred text. In the twelfth century, as discrepancies among his authorities became increasingly obtrusive, Scholastic teachers, working in the tradition of the concordia discordantium, made the epoch-making decision not to try to separate—as the Byzantines and Muslims before them had done—their own religious disciplines from the profane sciences inherited from the ancients. They attempted rather to situate theological teaching within the Aristotelian classification of the sciences.

The prescription of the Aristotelian philosophy as the basis of instruction in the arts faculty brought with it for the masters the obligation of interpreting the texts they had sought after. Their commentaries on the works of Aristotle open a new epoch in the history of medieval exegesis. In Paris *Siger of Brabant (c. 1240–c. 1284) explained their purpose: “We seek what the philosophers meant in this matter, their intention rather than the truth, because we proceed philosophically.” Siger and his fellow masters were the first to want to interpret philosophical texts “philosophically,” that is, by abstracting from the question of the truth of the teaching. Their task was not—like that of the theologians—the unveiling of a truth already possessed, but hidden; it was rather the discussion of the opinion of a most distinguished colleague. Siger gave the following rule for the interpretation of Aristotle: “It should be noted by those who undertake to comment upon the books of the Philosopher that his opinion is not to be concealed, even though it be contrary to the truth.” The interpreter of Aristotle’s text, having abandoned the notion of truth possessed for the notion of truth to be sought, could approach the text of the Philosopher in a critical, questioning way. Behind this revolution lay no doubt the de facto conflicts between Aristotle’s teachings and the doctrines of faith. The masters of arts were confronted with an important literature opposing various interpretations of Aristotle. In the face of such opposition it was difficult to maintain that Aristotle had spoken the whole truth.

The theologians had traditionally attempted to solve problems arising out of divergent authorities by seeking a standpoint from which all the relevant texts could be brought into harmony. But in the thirteenth century the newly translated philosophical and scientific sources rendered questionable the simple concordances which the twelfth century had made between authorities limited to the Latin ecclesiastical tradition. In this new situation some rejected the new literature and attempted by ecclesiastical condemnations to prevent its being read; still other theologians, like Albertus Magnus, showed themselves receptive to the new sources and tried in a new and very subtle way to continue the clerical enterprise of a concordia discordantium.

Influence on Aquinas

The Aristotelian paradigm was taken up by many theologians, most prominently by *Thomas Aquinas (1225–1274). At this period the theologians were faced with the same problem as that which confronted the masters of arts, the systematic presentation of a body of traditional knowledge. Thomas sought to establish a concord between revealed doctrine and Aristotle’s conclusions. While revealed Christian doctrines could not be proved, their acceptance was thought to be able to be shown at least reasonable, because congruent with the basic philosophical conclusions which Aristotle was thought to have demonstrated. Thomas maintained that God had revealed not only strictly supernatural truths, but also some truths which are philosophically demonstrable. For example, God revealed his existence, for otherwise but few men would have attained certain knowledge of this truth. Nevertheless, Thomas argued, God’s existence can be also rationally demonstrated on the basis of the principles of the philosophers and is that very being which the Christian by revelation knows as God.

The concord between philosophy and revelation which Thomas intended involved not only the demonstration of rationally accessible truths, but also the discovery of natural analogies to transcendent truths. It was in dealing with the Aristotelian astronomy that Thomas encountered a type of discourse different from that between dissenting theological authorities. The translators from Arabic and Greek had made available two far more advanced, but mutually opposed, discussions of the problem of celestial motion: the Almagest of Ptolemy and Aristotle’s De caelo. While the professional astronomers of the period adopted Ptolemy’s theory of eccentrics and epicycles and paid little attention to Aristotle’s theory of homocentric spheres, the theologians were very disturbed by the contradiction between Ptolemy’s mathematical astronomy which claimed to save the phenomena and Aristotle’s physical theory which was presented as a deduction from first principles. To the argument that Ptolemy’s hypotheses are supported by experience, Thomas rejoined that the experimental verification of an hypothesis does not necessarily demonstrate the hypothesis.

Although Thomas thus formulated explicitly one of the most important principles in the theory of science, he employed it to render harmless the objections to his theological interpretation of Aristotle’s astronomy—in the hope that some day a way might be found to make Aristotle’s theory agree with experience. His appeal to the principle that verification does not demonstrate a hypothesis meant only that his conception of the concordance between philosophy and revelation need not be disturbed by the contrary data of experience. Armed with Thomas’s principle, this clerical world-view was able to maintain itself and disappeared only with the new astronomical discoveries of the sixteenth and seventeenth centuries.

Other anomalies in the Aristotelian paradigm appeared even in the thirteenth century. About the year 1250, as Averroes’ real position on the immortality of the human soul became known, the Latins came increasingly to distinguish between the teaching of Aristotle and that of Averroes. And in the year 1277 the Bishop of Paris condemned two hundred nineteen propositions, of which the majority represented Aristotelian positions, condemned because they entailed consequences contrary to revealed doctrine. The masters of arts regarded their work as philosophy, but it was meant to include the vast legacy they had inherited from antiquity—a legacy which embraced logic and mathematics, mechanics and astronomy, ethics and political theory. The “philosophical procedure” made it possible for the masters of arts to criticize Aristotle’s idea of science and to ask the new logical and mathematical questions with which *William of Ockham (c. 1285–c. 1347), Walter Burley (c. 1275–c. 1346), and the Merton school led philosophy in the early fourteenth century into new paths.

No longer simply the gateway to theology, the arts faculty became an institution on an equal footing with the faculties of law, medicine, and theology. Aided by the Aristotelian idea that the individual sciences are autonomous in their own realm, philosophers such as *John Buridan (c. 1295–c. 1358) were able to develop theories in physics which were independent of Aristotle’s treatment, while mathematicians such as *Nicole Oresme (c. 1320–1382) turned to areas which Aristotle had neglected. Oresme was able to fuse Mertonian mathematics with the Parisian physics of Buridan in the late fourteenth century, while Paul of Venice (c. 1370–1429) and others in Padua in the fifteenth century were able to bring these developments together with the Averroist attitude to form the secular Aristotelianism of the sixteenth-century Italian universities.

A fourth stage of the Aristotelian tradition appeared in the fifteenth century. This period can be said to have begun in the year 1438 with the arrival Georgius Gemistus Pletho (c. 1360–1452) at the Council of Florence. Pletho charged the Latins with misunderstanding Aristotle’s teaching because they had been misled by Averroes to believe that Aristotle’s works contained a demonstrative summary of scientific truth. The character of the new era became more philological than philosophical. New editions and vernacular translations of the Greek and Latin classics and new philosophical options—Platonism, Epicureanism, and Stoicism—began to appear. A last wave of editions, translations, and commentaries on the works of Aristotle began in the fifteenth century and lasted until about the middle of the seventeenth. But new sources, new scientific interests, new classes of students, new geographical divisions led such groups of scholars to attend to the various parts of philosophy without reference to Aristotle’s organization of science.

See also Condemnation of 1277; Scientia; Translation movements; Universities

Bibliography

Callus, Daniel. Introduction of Aristotelian Learning to Oxford. Proceedings of the British Academy (1943) 29: 229–281.

Dreyer, M. More mathematicorum: Rezeption und Transformation der antiken Gestalten wissenschaftlichen Wissens !m 12. Jahrhundert. [Beiträge zur Geschichte der Philosophie und Theologie des Mittelalters NF 47] Münster: Aschendorff, 1996.

Gottschalk, H.B. “Aristotelian Philosophy in the Roman World from the time of Cicero to the end of the second century AD.” In Aufstieg und Niedergang der römischen Welt (ANRW): Geschichte und Kultur Rms im Spiegel der neueren Forschung. 2 volumes. Berlin: W. de Gruyter, 1987. II. 36.2, 1079–1174.

Grabmann, M. “Eine für Examinazwecke abgefasste Quästionensammlung der Pariser Artistenfakultät aus der ersten Hälfte des XIII. Jahrhunderts.” In Mittelalterliches geistesleben. 3 volumes. München: Hueber 1926–1956. vol. 2, pp. 183–199.

Hisette, R. Enquête sur les 219 articles condamnés à Paris le 7 mars 1277. Louvain: Nauwelaerts, 1977.

Kennedy, E.S. Late Medieval Planetary Theory. Isis (1966) 57: 365–378.

Krafft, F. Physikalische Realität oder mathematische Hypothese? Philosophia naturalis (1973) 14: 243–275.

Lang, A. Die Entfaltung des apologetischen Problems in der Scholastik des Mittelalters. Freiburg: i.Br: Herder, 1962.

———. Die theologische Prinzipienlehre der mittelalterlichen Scholastik. Freiburg: i.Br.: Herder, 1964.

Lohr, C. H. “The Medieval Interpretation of Aristotle.” In The Cambridge History of Late Medieval Philosophy. New York: Cambridge University Press, 1982.

———. Medieval Latin Aristotle Commentaries. Traditio (1967) 23: 314–413; (1968) 24: 149–245; (1970) 26: 135–215; (1971) 27: 251–351; (1972) 28: 281–396; (1973) 29: 93–197; (1974) 30: 119–144; and Bulletin de philosophie médiévale (1972) 14: 116–126.

———. Latin Aristotle Commentaries: II. Renaissance Authors. Florence: L.S. Olschki, 1988; III. Index initiorum et finium. Florence: L.S. Olschki, 1995; IV. Bibliography of Secondary Literature. Florence: L.S. Olschki, 2005.

Moraux, P. Der Aristotelismus bei den Griechen von Andronikos bis Alexander von Aphrodisias. 2 volumes. Berlin: De Gruyter, 1973–1984.

Peters, F. E. Aristoteles arabus. The oriental translations and commentaries of the Aristotelian Corpus. Leiden: E.J. Brill, 1968.

Podskalsky, G. Theologie und Philosophle in Byzanz. Munich: Beck, 1977.

Sorabji, R., ed. Aristotle Transformed: The Ancient Commentators and Their Influence. London: Duckworth, 1990.

Van Steenberghen, F. Aristotle in the West; the origins of Latin Aristotelianism. Translated by Leonard Johnston. Louvain: Nauwelaerts, 1970.

———. Maître Siger de Brabant. Louvain: Publications universitaires, 1977.

CHARLES H. LOHR

Arithmetic

The story of the growth of arithmetic from the ancient inheritance to the wealth passed on to the Renaissance is dramatic and passes through several cultures. The most groundbreaking achievement was the evolution of a positional number system, in which the position of a digit within a number determines its value according to powers (usually) of ten (e.g., in 3,285, the “2” refers to hundreds). Its extension to include decimal fractions and the procedures that were made possible by its adoption transformed the abilities of all who calculated, with an effect comparable to the modern invention of the electronic computer. Roughly speaking, this began in India, was transmitted to Islam, and then to the Latin West. (Although Chinese mathematics included many of the concepts discussed here from an early stage, it does not play a large role in the transmission of ideas.) By the Renaissance arithmetic was a powerful tool, prepared to meet the computational challenges of both science and commerce.

India

Unlike the geometrically- and logically-minded Greeks, Indian mathematicians emphasized computation; they readily accepted irrational quantities and zero as numbers and incorporated them easily into their arithmetic. Mathematics in India divides into two disciplines, patiganita (the “mathematics of algorithms,” or arithmetic) and bijaganita (the “mathematics of seeds,” or *algebra). Although this distinction is not yet found in Aryabhata’s mathematical and astronomical work Aryabhatiya (499 C.E.), it is present in Brahmagupta’s Brahmasphutasiddhanta (The Opening of the Universe, 628 C.E.) and afterward. We also find a progression in the notion of positional arithmetic from a mere hint in Aryabhata to a fully formed theory in Brahmagupta. Although Brahmagupta did not extend his system to include decimal fractions, he conceived such innovations as the beginnings of the system for notating fractions that we use today (numerator over denominator), and rules for handling zero and negative numbers. One of India’s greatest works was the Bhaskara II’s Lilavati (twelfth century), which became the most popular textbook on arithmetic and spawned numerous commentaries. Among the topics found in Indian treatises on arithmetic are the rule of three (essentially the solution to a/b = c/x), useful to merchants dealing with weights and measures; the solution of linear equations by the method of false position; the solution of linear indeterminate equations (kuttaka, or pulverizer), useful for calendrical work; and combinatorial problems.

Islam

Before the Indian presence began to be felt in the late eighth century, Islamic calculators relied primarily on finger reckoning. This primitive but surprisingly useful tool did not disappear immediately with the rise of Hindu methods; in fact, the two most important works on finger reckoning are by Abu’l-Wafa’ (late tenth century) and al-Karaji (early eleventh century, who also introduced Pascal’s triangle of binomial coefficients to Islam). However, it faded away gradually as the new methods proved their worth. Perhaps the earliest exposition of the new arithmetic was *Muhammed al-Khwarizmi’s early ninth-century Kitab hisab al-‘adad al-hindi (Book on Calculation with Hindu Numerals); it is now lost in Arabic, but it was to play a vital role in Europe through Latin translation. Although al-Khwarizmi used the Hindu system he did not extend it to fractions, instead still relying on the ancient representations using sums of unit fractions. As with many of his successors, al-Khwarizmi’s procedures for the basic arithmetic operations (addition, subtraction, multiplication, division) were designed to be used on a dust board, which was compact and on which figures could be easily erased and replaced. Dust board arithmetic had staying power; it is found, for instance, in works by Kushyar ibn Labban in the late tenth century and by the famous astronomer *Nasir al-Din al-Tusi almost three centuries later. However, it was gradually replaced by algorithms performed with pen and paper. The earliest text to describe these new methods was *al-Uqlidisi’s Arithmetic, written in Baghdad in 945 C.E.; in it the author argues for pen-and-paper techniques so that arithmeticists could be distinguished from the dust board-wielding astrologers. Also within its pages is an early appearance of decimal fractions, although a systematic treatment would not come until the twelfth century with al-Samaw’al. A complete mastery of pen-and-paper arithmetic with a positional number system, including decimal fractions, may be seen in the early fifteenth-century Iranian astronomer Jamshid al-Kashi’s Miftah al-hisab (The Calculator’s Key). Used as a textbook for centuries, this book contained all the arithmetic needed for astronomy, surveying, commerce, and architecture.

Concurrent with these developments, astronomers were using a full-fledged positional numeration system, with base 60, that dates back to the Babylonians. Authors of arithmetic texts such as Kushyar and al-Kashi described computational procedures for the so-called “astronomers’ arithmetic” that were analogous to their decimal counterparts. Since the “digits” in this system range from zero to 59, the process of multiplication required the use of tables listing the products of all whole numbers up to 59 x 59. However, the great eleventh-century scholar *al-Biruni once remarked that many of his predecessors cheated by converting base 60 numbers into whole decimal numbers, then multiplying, then converting back.

Much Muslim work in arithmetic was inspired by Greek ideas; this included results on amicable numbers and sums of sequences, including squares and cubes. We also find explorations of binomial coefficients, and related algorithms for computing the nth root of a given number, at least as early as *‘Umar al-Khayyam (around 1100 C.E.; known to the West as Omar Khayyam), and later in al-Samaw’al and al-Kashi. In the latter’s Calculator’s Key there is a truly impressive calculation of $5 \sqrt{44, 240, 899, 506, 197}$ , using an algorithm designed with the aid of the binomial theorem.

Europe

The main source for arithmetic in early medieval Europe was Nicomachus’s Introduction to Arithmetic, through a paraphrased translation by *Boethius in the early sixth century. As one of the subjects in the *quadrivium, arithmetic was part of what it meant to be educated; Charlemagne even ordained its instruction, although over time it was subject to neglect. Although the available techniques were crude, they sufficed for the requirements of the day—especially the determination of the date of Easter, and probably numerology and divination. The science of the *computus relied mostly on Roman numerals, finger reckoning, and the abacus, although textual evidence for the latter begins only in the late tenth century. At this time *Gerbert of Aurillac reintroduced mathematics in school and popularized a variant of the Roman abacus which used Hindu-Arabic numeration, although he did not include a symbol for zero and his calculation methods were not very effective. It is possible that he learned decimal numeration from contacts with Muslim science during his studies in Barcelona.

It was not until the twelfth century that needs arose requiring substantial improvement. The introduction of mathematical astronomy through translations into Latin of works by al-Khwarizmi, *al-Battani, and *Ptolemy placed higher demands on arithmetic than it could handle. Fortunately, the translation of al-Khwarizmi’s Arithmetic by *Adelard of Bath contained sections on the base 60 astronomers’ system as well as on Hindu-Arabic decimal numeration. Al-Khwarizmi’s dust board computations transformed the practice of arithmetic; the abacus was soon supplanted by so-called “algorismus” texts propagating the new methods. Indeed, it is probable that the word “algorithm” arose from the Latinization of his name within these texts. The two most influential algorismus works in the thirteenth century were Alexander de Villadieu’s Carmen de algorismo, used extensively for calendar calculations; and *John of Sacrobosco’s Algorismus vulgaris, which became a leading university text on the subject.

The switch from dust board to pen-and-paper calculations is due mainly to Leonardo of Pisa, known as *Fibonacci. His Liber abaci (1202; in Italy at this time the word “abaco” had come to mean computation in general) promoted the use of Hindu-Arabic numerals, including zero, but did not yet use decimal fractions. Although Fibonacci learned to compute on Gerbert’s abacus using Hindu-Arabic numerals, the Liber abaci owes a large debt to Arabic sources. The advanced number theory in his other works was not really appreciated in his own time, but the Liber abaci did originate the Italian tradition of “abbacus” arithmetic of the fourteenth and fifteenth centuries. The abacus methods were essentially the same as those taught in schools today, and were inspired by commercial interests.

Hindu-Arabic arithmetic did not have a smooth reception in Italy; it was actually banned in Florence in 1299 and in several places early in the fourteenth century, presumably due to the possibility of fraud. However, its benefits in trade made it inevitable. Although ordinary Europeans would not become familiar with it until the seventeenth century, positional decimal arithmetic flourished in science and especially in business by the fifteenth century.

See also Algebra; Arabic numerals; Commercial arithmetic; Translation norms and practice

Bibliography

Al-Khwarizmi, Muhammed. Mohammed ibn Musa Alchwarizmi’s Algorismus. Das früheste Lehrbuch zum Rechnen mit indischen Ziffern. Nach der einzigen (lateinischen) Handschrift (Cambridge Un. Lib. Ms. Ii. 6. 5) in Faksimile mit Transkription und Kommentar herausgegeben. Aalen: Zeller, 1963.

Al-Uqlidisi, Abu l-Hasan. The Arithmetic of al-Uqlidisi. Translated by Ahmad S. Saidan. Boston: Reidel, 1978.

Berggren, J. L. Episodes in the Mathematics of Medieval Islam. New York: Springer-Verlag, 1986.

———. “Medieval Arithmetic: Arabic Texts and European Motivations.” In Word, Image, Number. Communication in the Middle Ages. Edited by John J. Contreni and Santa Casciani. Florence: SISMEL—Edizioni del Galluzzo, 2002, pp. 351–365.

Contreni, John J. and Santa Casciani, eds. Word, Image, Number. Communication in the Middle Ages. Florence: SISMEL—Edizioni del Galluzzo, 2002.

Evans, Gillian. From Abacus to Algorism: Theory and Practice in Medieval Arithmetic. British Journal for the History of Science (1977) 10: 114–131.

Kushyar ibn Labban. Principles of Hindu Reckoning. Translated by Martin Levey and Marvin Petruck. Madison/Milwaukee: University of Wisconsin Press, 1965.

Mahoney, Michael S. “Mathematics.” In Science in the Middle Ages. Edited by David C. Lindberg. Chicago: University of Chicago Press, 1978.

Sigler, Laurence, ed. Fibonacci’s Liber abaci: A Translation into Modern English of Leonardo Pisano’s Book of Calculation. New York: Springer-Verlag, 2002.

Van Egmond, Warren. “Abbacus arithmetic.” In Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences. Edited by Ivor Grattan-Guinness. London/New York: Routledge, 1994. Vol. 1.

GLEN VAN BRUMMELEN

Arms and Armor

Iron ores are very widespread and may be reduced by heating with carbon (as charcoal) in small furnaces. The non-metallic elements in the ore form slag, which liquefies at around 1200°C, and runs away from the solid iron, leaving it as a lump or bloom, porous in form and containing much entrapped slag. Repeated heating and forging are necessary to expel most of the slag and consolidate the bloom.

If the bloom was left in the hearth for some time, then parts of it might absorb some carbon, and form steel. Steel is harder and stronger than iron. So the product of the bloomery might well be a heterogeneous lump, parts of which would be of higher carbon content than others. Early smiths would have found that some samples of “iron” were twice as hard as others, but whether they could be deliberately produced was another matter. A more efficient way of proceeding could be to make an artefact of iron, and then convert part of it to steel. This might be done by forge-welding a steel edge to an iron back, or by case-carburizing the edge (heating the iron in contact with carbon).

Many medieval smiths, and indeed Celtic and Roman smiths before them, attempted to overcome the difficulty of carburizing iron uniformly by treating only very small pieces, of which several could then be piled together, and forged into a blade.

The technique known as pattern-welding (sometimes called “false Damascus” or “twisted Damascus”) grew out of piling as a means of making long blades from many small pieces of metal with varied compositions. Pieces of iron and steel were twisted as they were welded together, and then the surface ground and etched with fruit acids to reveal a pattern. The pattern visible on the surface may have contributed to their popularity, being reminiscent in appearance to blades made of true “Damascus steel.” From about the third to the tenth century pattern-welded swords were common in Western Europe, but after about 1000 C.E. their occurrence diminishes, presumably because larger pieces of steel became available.

The relatively high cost of steel meant that smiths would often make swords and other weapons by forge-welding a steel edge, or edges, onto an iron body, thus making a scarce material go further. After fabrication, the red-hot blade could be quenched (plunged red-hot into cold water) to harden it. The process is a difficult one to manipulate, however, as the hardness is accompanied by embrittlement.

The Roman army was based on legionaries who were armed with javelins and swords and were armored by metal helmets and shirts of mail (interlinked rings), scale armor (small plates of metal fastened to a cloth backing) or lamellar armor. Lamellar armor can be traced back to the Assyrians and consists of small plates laced to each other (but not to the underlying garment) for maximum flexibility. It was to remain in use outside Europe throughout Central Asia, China, and Japan.

Effective at close quarters, the legionary armies proved unable to defend the frontiers of the Roman Empire successfully. A faster-moving army was required, and the elite of the army became the armored cavalry. A Near-Eastern influence, from Iran, on the use of cavalry has been suggested. Rock-carvings at Naqsh-i-Rustem, from the third to the fifth century C.E., show the Sassanid kings on horseback charging their enemies with lances, but without shields or stirrups. A graffito from Dura Europos shows a mailed cavalryman on a mailed horse also charging with a lance, and without stirrups or shield. Some writers have suggested that the adoption of the stirrup was of profound importance in enabling cavalry to fight as shocktroops, rather than mounted archers or scouts, by seating the warrior firmly. Certainly it improved the efficiency of cavalry considerably, but so did the invention of horseshoes (also perhaps from this period) which enormously extended the useful life of the horse.

It is also possible that armored lancers might have been practical even without stirrups if saddles could be gripped for leverage. Roman saddles show four “horns” which may have been grasped to steady the rider, as an alternative to stirrups, but of course, the left arm could not then manipulate a shield as well as reins.

The last Western Emperor was deposed in 476 and the old empire was succeeded by various Germanic kingdoms. Most of their armies still apparently consisted of foot-soldiers, but mailed cavalry continued to become steadily more important. The Franks in Gaul under Charles Martel seem to have been the first to use large numbers of mailed cavalry as their principal weapon. They certainly used stirrups by this time, but it may have been their organization which made the crucial difference. In 755 Pepin III changed the date of the muster from March to May, so that there would be enough grass for the horses to eat. The bulk of the Frankish army was mounted, costly though this was. The price of the equipment of a mailed horseman totaled as much as twenty-three oxen, according to Verbruggen. This enormous sum was justified by their complete supremacy on the battlefield.

In Western Europe any man who fought on horseback was known from the tenth century onward as a knight, whatever his precise social status. He had to be a fulltime soldier because the cost of his equipment, and the training required to use it effectively, left little time for any economic activity. If he could not be paid in cash, he would have to be paid in land. Many knights were not landowners of course, but they formed a social class which lived on the work of others who cultivated the land on their behalf.

Mail Armor

Throughout the early Middle Ages, the mail shirt was the principal body defense for those warriors fortunate enough to be able to afford it. Its adaptability, however, meant that it was frequently repaired and reused, so that very little has survived intact from this period. The links, made of lengths of strip or drawn wire, were formed into rings and then linked together. Each link is attached to four others, except of course, at the edges, where the garment ends. The links are then closed by riveting. An economy of effort may be made by closing half the links by hammer-welding, so that only alternate rows need to be riveted. Most medieval European mail shirts consist of all-riveted links; this arrangement is less common but still found in Oriental mail.

A series of boat-burials at Vendel in Sweden, Valsgarde, and elsewhere from the seventh to the ninth century have yielded samples of mail with rectangular reinforcing pieces of plate. This innovation might be ascribed to an Eastern influence. Certainly, Vikings employed the rivers of Russia to trade to the Black and Caspian seas as well as setting up the Kingdom of Kiev (864 C.E.), from which the nucleus of medieval Russia grew. Russian armor of the Middle Ages was a mixture of mail, scale, and lamellar not dissimilar to that depicted in Byzantine images of soldiers. Although sometimes reinforced with pieces of plate, mail remained the principal form of body armor in the Islamic world, as late as the Ottoman Empire, and in India, as well as Russia, until armor itself went out of use.

Carolingian manuscripts of the ninth and tenth centuries show mounted warriors wearing mail shirts extending from the elbow to the knee, and conical helmets. The armor for knights and also protection for their horses was extended steadily. By the eleventh century mail shirts are shown reaching down to the wrist, and separate leggings of mail to complete the protection of the limbs appear by the twelfth century, as do hoods of mail like balaclavas over the head and neck. Horses acquired some mail also, although cloth wrappers hide its extent in illustrations. Knights on the winning side could feel very safe, unless they were unhorsed. At the battle of Lincoln (1217) just three were killed, at Falkirk (1297) only one, although many lost their horses.

While the body defense made entirely of mail had reached a peak of completeness by the thirteenth century, some of its limitations were becoming apparent. Crossbows were growing in power, and while mail was generally a good defense against slashing weapons, always in conjunction with a quilted undergarment (gambeson), it was less effective against the points of arrows which were retained rather than deflected by its links.

Missile Weapons and Infantry

Despite the great effectiveness of knights, infantry that could withstand a charge of knights was not unknown. However, by the early fourteenth century, given favorable local circumstances, knights were being defeated by foot-soldiers in Flanders, Switzerland, and Scotland. The citizens of Ghent, Bruges, and Ypres are shown in contemporary illustrations as being armored from head to knee and carrying spiked maces (“goedendags”) as well as pikes and crossbows. The pikes were set against the ground and used to stop a charge of knights. Then for hand-to-hand combat, heavy two-handed weapons which would reach up to a man in the saddle were needed. The goedendags of the Flemings, the halberds of the Swiss and the battleaxes of the Scots all belonged in this category.

In 1291 the farmers and herdsmen of Switzerland asserted their independence from Rudolph of Hapsburg. The terrain did not favor knights at the best of times, and the Swiss infantry won the battle of Morgarten (1315) against Austrian forces. They organized themselves into squares of pikemen which were eventually able to take the offensive against armies in the field and won famous victories over Charles the Bold at Grandson and Morat in 1476, and at Nancy in 1477.

In England, Edward I recruited large numbers of Welsh archers, and used them on the battlefield in thousands rather than in hundreds notably after Gerald of Wales had earlier described how during the siege of Abergavenny in 1182, Welsh arrows pierced an oak door four inches (10 cm) thick. Edward II failed to coordinate the use of his knights and archers, and lost the battle of Bannockburn (1314) to Scots pikemen. Edward III maintained his grandfather’s faith in archers, recruiting even more of them, and making his knights dismount and fight on foot beside them. Such was the army that he took to France and used to win the Battle of Crecy (1346).

Miniature illustration of the Battle of Crecy from the Chronique of Jean Froissart (c. 1347–c. 1405). English longbows on the right face French crossbows. (Corbis/Bettmann)

Crossbows

The earliest crossbows were simply heavy bows fixed to a stock, with a trigger release which enabled it to be spanned with both hands, both feet being placed on the bow. Simply making a bow thicker does not make it more powerful. It may be more difficult to bend into a curve, but it still has to bend and straighten again quickly and without cracking. So overall the stiffness must be increased, rather than the thickness. One way of achieving this is by making a “compound” bow. Horn or whalebone (which resist compression) are placed on the inside, and animal sinew (which resists extension) on the outside, of a wooden bow, and the whole assembly glued together with fish glue and rendered waterproof with a skin covering.

As early as 1139 the crossbow had become such a dangerous weapon to knights that its use was banned by the Second Lateran Council in 1139. To span these stronger bows, a stirrup was added to the stock in the twelfth century, and a belt with a hook could be worn by the operator to enable his upper body as well as his arms to take part in drawing the bow. By the fourteenth century a belt such as this, improved by incorporating a pulley (“Samson’s belt”) or a “goat’s foot” lever might be used. By the fifteenth century a windlass with a system of pulleys, or a cranequin (a rack and pinion gear) were needed to span the powerful steel crossbows then in use.

Plate Armor

The threat from crossbows meant that mail was regularly reinforced by some sort of rigid body defense from at least the thirteenth century. Several large plates of metal, or sometimes hardened leather (“cuir bouilli”) would be formed as a defense to be worn on top of the hauberk, or a coat-of-plates. This would indeed protect the knight from missile weapons, but at the cost of extra weight.

So the combination of mail and plate steadily developed into a “harness” or suit of armor made up of articulated plates designed to cover the entire body except for the armpits and bottom, which had to remain protected by gussets of mail. This started to emerge in its final form in fourteenth-century Lombardy, and was fully developed by about 1400, when it remained in use for more than two hundred years. It required the production of large pieces of plate, made of steel of acceptable quality. A plate of armor which weighs between 5½ and 10 pounds (2.5–4.5 kg) will require billets of metal of 22 pounds (10 kg) or more and their production from a bloomery is difficult. However, during the fourteenth century in Italy, bloomeries had become large enough to make the production of such large plates possible, while their operators developed sufficient skill to prevent the furnace overheating and producing liquid “cast iron.”

As a result, European armor starts to differ fundamentally in design from those forms of armor used in other parts of the world, namely Islam, India, China, and Japan. All of those cultures continued to use armor made up of a large number of small plates or rings joined together to form a flexible garment, rather than a rigid exoskeleton.

Asiatic Swords

“Damascus steel” swords were the famous blades with a “watered-silk” or “damask” pattern on their surfaces, made from a very high-carbon steel (wootz) formed by melting iron with carbonaceous material in a sealed crucible over several days until it wholly or partially melted into a cake of steel, and was then allowed to cool extremely slowly. These cakes were exported to centers of arms manufacture (such as Damascus) where they were carefully forged, with some difficulty, into sword blades. Since the melting-point of steel falls with increasing carbon content, a lower temperature than usual has to be employed to forge a harder blade of higher carbon content than usual (around 1.2–1.6 percent). This forging broke up network of iron carbide crystals left over from the casting, reducing brittleness, and producing the characteristic pattern (“watered silk”) on the surface of the blade. The blade so formed needed no further heat treatment to harden it, nor did any amount of sharpening ever remove the edge.

However it has become clear, that wootz was only a small part, albeit a special part, of a crucible steel industry, active throughout the Middle East. Crucible steel that was not as slowly and carefully cooled would have a similar chemical composition to wootz, but without its surface pattern. Crucible steel weapons were expensive, and probably reserved for a tiny minority. But the vast topic of Indian arms and armor is still largely unexamined in any detail. Until the eighteenth century, Indian warriors wore body defenses of mail, sometimes reinforced with small plates, and fought with sword bow and spear like medieval Europeans, but without employing the shock tactics of knights.

Bibliography

Blair, Claude. European Armour. London: Batsford 1958, reprinted 1972.

Boccia, Lionello. Armi e Armature Lombarde. Milan: Electa, 1980.

Elgood, Robert. Islamic Arms and Armour. London: Scolar Press, 1979.

ffoulkes, Charles. The Armourer and his Craft. New York: Dover, 1988.

Oakeshott, R.E. The Sword in the Age of Chivalry. Guildford: Lutterworth, 1964.

Robinson, H. Russell. Oriental Armour. London: Jenkins, 1967.

Sewter, E.R.A. The Alexiad of Anna Comnena. Harmondsworth: Penguin, 1969.

Smith, Cyril Stanley. A History of Metallography. Cambridge: MIT Press, 1988.

Strickland, Matthew and Robert Hardy. The Great War Bow. Stroud: Sutton, 2005.

Thomas, Bruno and Ortwin Gamber. Katalog der Leibrüstkammer. I. Vienna: Schroll, 1976.

Thordeman, Bengt. Armour from the Battle of Wisby, 1361. 2 vols. Stockholm: 1939–1940. Reprinted in one volume: Chivalry Bookshelf, 2001.

Trapp, Oswald Graf, and J.G. Mann. The Armoury of the Castle of Churburg. Udine: Magnus, 1995.

Verbruggen, J.F. The Art of Warfare in Western Europe during the Middle Ages. Woodbridge: Boydell. 1997.

Williams, Alan. The Knight and the Blast Furnace. Leiden: E.J. Brill, 2003.

ALAN WILLIAMS

Arnau de Vilanova

Arnau de Vilanova’s early life and education are not known with certainty. The agreed date of his birth is c. 1240 but the place, somewhere in the Crown of Aragon, is still a subject of debate. In the 1260s he was studying medicine at Montpellier, where he earned his degree. He married Agnès Blasi and established himself in Valencia. In 1281 Arnau moved to Barcelona to serve King Pere III as his personal physician. Despite this move and his many later travels, Arnau and his family kept strong personal and economic links with Valencia throughout their lives. After the death of Pere in 1285, Arnau became royal physician to the king’s sons; first to Alfons II, and after his death in 1290 to his brother and successor Jaume II and to his youngest brother Frederic III, who become king of Sicily in 1296. As was the case with many of his colleagues at the royal courts, Arnau’s activities went far beyond the strictly medical. A personal friend of the monarchs, he served them informally as a political and spiritual adviser and at a more formal level as representative of the Crown in some diplomatic negotiations. His role at the royal court was not an impediment to his development as a teacher and author of medical works at the medical school of Montpellier, to which he was attached from 1289 to 1301. The value of his presence at the Studium was recognized in 1309 by the papal bull that regulated its medical syllabus. In Montpellier, the flourishing of Arnau’s medical production paralleled his growing interest in spiritual matters in line with the reformist views of certain Franciscans groups. Some historians have made an effort to show the crossing of boundaries in Arnau’s interests between divine illumination and reason, between the religious and the medical; others have been readier to defend the independent development of both enterprises. By 1300 Arnau had already finished a number of religious works of a didactic nature (addressed to the Aragonese royal family), biblical exegeses, anti-Jewish apologetics, and prophetic and reform writings. Thereafter he did not occupy his chair at the medical school, instead devoting the bulk of his energies to diffusing his eschatological views and to defending himself in various conflicts with elements within the Church. However, he did not abandon his medical activities, and continued his service as physician to the Aragonese royal family and at the papal court, first to Pope Boniface VIII and later to his successor Benedict XI. After Benedict’s death in 1304, Clement V took Peter’s chair. The new pope was an old friend of Arnau and more sympathetic to his ideas than his predecessors. Consequently 1305 marked the beginning of a period of relative calm in Arnau’s life. Enjoying the patronage of the pope as well as that of the kings of Aragon and Sicily, Arnau envisaged the possibility of realizing his proposals for the social and religious reform of Christendom. The ideals of poverty, charity, and the need to preach evangelical truth to the poor led Arnau during these years to write a number of religious works in the vernacular that reflected and reinforced the ideals and practices of various groups of lay spirituals. However, the patronage of the king of Aragon that had been so important to Arnau, providing him with protection and a means for achieving his goals, was soon to be withdrawn. In 1309, the disclosure and prophetic interpretation of the dreams of the two monarchs, Jaume II and Frederic, to the papal curia in Avignon, caused the former to break with Arnau. Despite his indiscretion, Arnau kept the support of the younger brother, Frederic, who was the recipient in 1310 of the Informació espiritual per al rey Frederic, in which Arnau set out the guidelines to the perfect Christian king. Traveling by sea in the service of this monarch, Arnau died off the coast of Genoa in 1311.

Medical Writings

Despite his religious interests and their public impact, Arnau was regarded by his contemporaries principally as a physician. And it was as a physician that he was able to build his influential connections at the royal and papal courts. About his actual healing activities there is not much information, although his success and his patrons’ appreciation of his application of the art are well documented. Further information about Arnau’s medical thought can be obtained from the wide number of medical writings that he produced and that are extant in manuscript form or in sixteenth-century printed editions (Lyons, 1504, 1509, 1520, 1532; Venice, 1505, 1527; Basel, 1585).

Unfortunately there is no list of Arnau’s medical works equivalent to that of his spiritual works, which he prepared himself in 1305. Neither do his medical writings contain references to dates and places of composition that might help to establish a genuine Arnaudian corpus and an accurate chronology. Manuscript tradition, cross-references, theoretical consistency, data from archival material, and the inventory of his possessions made after his death are the main tools that allow us to draw Arnau’s professional profile. From the early 1280s to his death, Arnau touched on almost all medical genres and subjects: commentaries on medical authorities, monographs on particular diseases in the form of *consilia or epistles, aphorisms, medical compendia, and pharmacological treatises. He made translations too. Arnau confessed that he knew no Greek, but he mastered Arabic. In 1282, while staying in Barcelona, he translated several medical treatises from Arabic into Latin: the De viribus cordis of *Ibn Sina (Avicenna), De rigore by *Galen, and De medicinis simplicibus, a pharmacological work by Abu-Salt.

Arnau’s main written production must surely be dated to 1290–1300, when he held his position as master at the Montpellier medical school. Before this period Arnau seems to have composed only a short treatise (Tractatus de amore heroico, composed before 1285) devoted to a single disease, love-sickness, a kind of mental alteration, and an epistle (De reprobacione nigromantice ficcionis, c. 1276–1281 or c. 1286–1288) condemning necromantic practices and arguing that those who believed that they had mastered the devil were in fact insane.

The first work produced by Arnau at Montpellier, De intentione medicorum, laid the ground for his medical epistemology. What is medicine, *scientia or ars? What are the nature and the aim of medical knowledge? What role must be performed by the university physician? And accordingly, what training will best suit him for this role? All these questions were contained in this programmatic text where Arnau explored the limits between medical and philosophical knowledge and proposed a duality of objectives and two levels of epistemological evaluation. The physician, according to Arnau, is an artifex sensualis et operativus and thus, at least rhetorically, his theoretical interests must be limited by their practical usefulness. This stance, which Michael McVaugh has called “medical instrumentalism,” allowed Arnau to establish an intermediary space between an idea of medicine as science that would fulfil itself in theoretical speculation and an anti-intellectual empiricism. Arnau identified the first position with medical Averroism, against which he confessed that he wrote several works: De intentione medicorum; the Epistola de dosi tyriacalium (c. 1290–1299) on the effect of antidotes designed to refute the De tyriaca of *Ibn Rushd (Averroes); De considerationibus operis medicine sive de flebotomia (c. 1298–1300) on phlebotomy; and the Aphorismi de gradibus, a pharmacological work composed between 1295 and 1300. Historiography has highlighted Arnau’s supposed anti-intellectualism and connected it with his religious views. However, this link has been based mostly on the erroneous ascription to Arnau of the work Breviarium practice. In fact, Arnau’s position on medieval empirics, as stated in his De consideracionibus and elsewhere, is by no means a positive one.

The polemical tone employed by Arnau in some of his medical writings reflected a tense intellectual and professional environment at Montpellier where Arnau was strongly involved. Like other masters at Paris, Bologna, and Montpellier, Arnau was responsible for developing at the medical school a wider intellectual framework that overshadowed the one focused in the canonical texts of the so-called *Articella collection. The change, termed by García Ballester as the introduction of “the new Galen” to medical teaching and research, involved revaluations of more than thirty works of Galen and also revisiting Arabic works, which previous generations had not done. This no doubt helped to pose new questions and to offer new answers, both at a theoretical and a practical level. The rhetorical aspect of this movement is clear—it gave to university medicine a more convincing presentation within the academia and outside—but there is evidence of actual changes in diagnosis, prognosis, and therapy as a result of this new reading of Galenic works. Arnau’s pedagogical impetus extended not only to his classroom expositions but also to other works devoted to a wider audience and composed with an aphoristic structure to make them easy to memorize: Medicationis parabole, dedicated in 1300 to King Philip IV of France; Aphorismi particulares; Aphorismi extravagantes. The pedagogical intention is also clear in Arnau’s last complete work, the Speculum medicine, a compendium composed as an introduction to the principles of medicine following the scheme of the Isagoge of Johannitius (*Hunayn ibn Ishaq). There is debate about its date of composition. For some, it must be the product of Arnau’s final activities at Montpellier in 1300–1301; for others, archival evidence suggests 1305–1308 as a more probable date range. Since the Speculum, according to Arnau, was composed as the theoretical part of medicine, it has been assumed that the unfinished De parte operativa was the practical sequel of Arnau’s projected summa.

Pedagogical concerns of another sort inspired some of Arnau’s practical writings: regimens of health (Regimen sanitatis ad regem aragonum, c. 1305–1308 and Regimen Almarie, c. 1309–1310), and consilia aimed not only at giving therapeutic advice but also at teaching certain regulations in the lifestyles of those to whom he addressed the works.

Historiography has traditionally adorned Arnau de Vilanova with features common to other heterodox figures in the history of science and medicine. As a supposed rebel against medical *Scholasticism, Arnau’s clinical common sense and lust for empirical findings have been contrasted with the inane subtleties of his academic contemporaries. Yet the magical and the alchemical, too, have often been associated with Arnau. In both cases, however, the picture is highly distorted. In his theoretical and practical medical writings, Arnau was much like other university physicians in using the tools provided by scholasticism: the authority of the ancients, a logical apparatus based on Aristotelian principles, and recourse to experience in a variable degree. It is true that he wrote about the value of divine illumination in obtaining medical knowledge, and that he used some magical and alchemical concepts in his medical thinking. It is also true that he distrusted medical speculation and natural-philosophical intrusions into health matters. Nevertheless, Arnau was not the master of the arcane secrets of nature in the service of an alchemical dream any more than he was the avant-garde scientist molded by the patterns of experimental medicine.

A painstaking critical edition of the Arnaudian medical corpus accompanied by historical studies has been under way since 1975 and is establishing the foundation for a more balanced understanding of his thought.

See also Alchemy; John of Saint-Amand; “Latin Averroists”; Medicine, practical; Medicine, theoretical; Patronage of science; Pharmaceutic handbooks; Regimen sanitatis; Religion and science; Translation movements; Translation norms and practice; Universities

Bibliography

Primary Sources

García Ballester, Luis and Michael McVaugh and Juan A. Paniagua, general editors. Arnaldi de Vilanova Opera Medica Omnia. Granada/Barcelona: Universitat de Barcelona, 1975–.

Secondary Sources

Batllori, Miquel. Arnau de Vilanova i l’arnaldisme. Valencia: Tres I Quatre, 1994.

García Ballester, Luis. Arnau de Vilanova (c. 1240–1311) y la Reforma de los Estudios Médicos en Montpellier (1309): El Hipócrates latino y la introducción del nuevo Galeno. Dynamis (1982) 2: 119–146.

———. Galen and Galenism. Theory and medical practice from Antiquity to the European Renaissance. Aldershot: Ashgate, 2003.

Giralt, Sebastià. “Decus Arnaldi. Estudis entorn dels escrits de medicina pràctica, l’ocultisme i la pervivència del corpus atribuït a Arnau de Vilanova.” PhD. Dissertation, Universitat Autònoma de Barcelona, Barcelona, 2002.

McVaugh, Michael. Medicine before the Plague. Practitioners and Their Patients in the Crown of Aragon, 1285-1345. New York: Cambridge University Press, 1993.

Mensa i Valls, J. and S. Giralt. Bibliografía Arnaldiana (1994–2003). Arxiu de Textos Catalans Antics (2003) 22: 665–734.

Paniagua, Juan A. Studia Arnaldiana. Trabajos en torno a la obra médica de Arnau de Vilanova, c. 1240-1311. Barcelona: Uriach, 1994.

Perarnau, Josep, ed. Actes de la I Trobada Internacional d’Estudis sobre Arnau de Vilanova. Barcelona, Institut d’Estudis Catalans, 1995 (2 vols.).

Ziegler, Joseph. Medicine and Religion c. 1300. The case of Arnau de Vilanova. Oxford: Clarendon Press, 1998.

FERNANDO SALMÓN

Articella

Articella—an Italian word meaning “little art”—is one of many titles given to a collection of texts of Greek and Arabic origin that served as the basis of nearly all medical teaching in Europe from the twelfth to the sixteenth centuries. The collection was put together in *Salerno in the early twelfth century, and was adopted as the fundamental textbook of university medical education in the thirteenth century. The collection continued to be widely read and commented on in universities and was printed in at least sixteen editions between 1476 and 1534. As the introductory text to medicine, the Articella supplied the conceptual framework within which medicine was studied in the late Middle Ages.

The Articella was put together for the purpose of teaching medicine in a classroom setting. Initially, it comprised five texts: the Isagoge of Johannitius, the Aphorisms and Prognostics of *Hippocrates, the Urines of the Byzantine physician Theophilus Protospatharius, and the Pulses of Philaretus. By the middle of the twelfth century *Galen’s Tegni had been added to the collection, creating a core of six texts.

These texts provide a systematic outline of Galenic medical theory together with the basics of Hippocratic medical practice. For the most part, the texts are short, introductory works written in summary fashion, containing easily memorized statements of fundamental medical concepts. The Isagoge is a short compendium that proceeds by division and definition to give a schematic overview of Galenic medicine in the form of brief summaries. Although attributed to an author named Johannitius, the text is an abridgement of a work by *Hunayn ibn Ishaq as an introduction to Galenic medicine. The Tegni (or Techne) was Galen’s own summary of the medical system he had developed in the course of his practice and had expounded in his other medical writings.

The Aphorisms—probably the most famous medical text of the Middle Ages—is a collection of terse statements that encapsulate the wisdom of the medical art. The aphorisms are loosely grouped into topics dealing with purging and diet, sleep patterns, environmental factors of sickness, age-related illness, diagnosis from urine samples, spasms and epilepsy, women’s ailments, prognosis and therapy, and identification of the stages of illness. The Prognostics—the companion text to the Aphorisms—tells the physician how to recognize acute illnesses, especially their past, present, and future states, and how to treat such ailments.

Pulses is a work of Byzantine origin which defines the function of the pulse and then describes it under ten categories, including dimension, type, consistency, and beat. Its companion text, Urines, categorizes urine in terms of its color, consistency, sediment, and odor, and then relates these characteristics to changes taking place in various parts of the body.

These two texts introduced students to the chief diagnostic tools of medieval medicine, and were being read by scholars in Salerno soon after 1100. By the middle of the century *Bartholomaeus of Salerno had commented on the entire collection, and by the end of the century all six texts had been commented on once again by *Maurus of Salerno. The commentaries marked a shift in interest among Salernitan masters from their traditional concern with practical medicine toward a new fascination with medical theory. In their commentaries they sought to establish a philosophical framework for medicine in which detailed theoretical explanations were given for the workings of the human body. Drawing on Aristotle’s natural philosophy, the Salernitan masters offered explanations of health and disease in terms of human beings’ relationships to the natural world.

The method of teaching medicine by commenting on the Articella was adopted at other centers of learning as well. For example, by the end of the twelfth century, the collection had been commented on in the schools of Chartres. In this process of dissemination, the collection was developed to suit different intellectual and pedagogical needs. The earliest changes involved supplementing the collection with works on practical medicine, such as the De regimine acutorum morborum of Hippocrates and *Gilles de Corbeil’s verses on Pulses and Urines. A more substantial alteration was made when five Arabic texts on medical theory were added, namely, the Viaticum of Isaac (Ibn al-Jazzar) and four works by *Isaac Judaeus: the Universal Diets, the Particular Diets, a treatise on fevers, and a treatise on urines. This expanded Articella was recommended to medical students in Paris in the 1180s, and by the 1240s it had been commented on by *Petrus Hispanus in Siena and by Cardinalis in Montpellier. It was subsequently adopted as the basis of the medical curriculum in the universities of Paris (1270–1274), Naples (1278), and Salerno (1280).

University masters of medicine continued to develop the Articella in new ways. In particular, they drew on Galen’s commentaries on the Aphorisms, the Prognostics, De regimine acutorum morborum, and Haly Ridwan’s commentary on Galen’s Tegni to develop more definitive interpretations of the Articella. These authoritative commentaries provided masters with models of exposition in which logical analysis and sophisticated tools of exegesis were used to create a philosophically more rigorous framework for medicine.

A fundamental change occurred in the middle of the thirteenth century when masters made these commentaries the primary object of their teaching. This shift in focus from text to commentary dramatically expanded the scope of university medical education. Accordingly, from the 1260s onwards, the Articella became a much bigger textbook, including not only the texts of the Aphorisms, Prognostics, De regimine acutorum morborum, and the Tegni, but also their respective commentaries.

This new version of the collection was being taught in Bologna by the end of the thirteenth century by *Taddeo Alderotti and *Mondino de’ Liuzzi, and it was soon incorporated into the statutes of the medical faculties at Montpellier (1309) and Paris (1331). It also provided the basis of the medical curriculum at the new universities of central Europe, including Vienna (1389), Erfurt (1412), and Tübingen (1497).

The Articella presented a new view of medicine in which medical theory was grounded in authoritative texts and taught by means of textual exegesis. Originally a fairly flexible group of texts, in the context of the new universities the Articella took on a more elaborate and stable form as the centerpiece of a medical curriculum in which Galen was the ultimate authority.

See also Aristotelianism; Cathedral schools; Constantine the African; Gerard of Cremona; Medicine, practical; Medicine, theoretical; Monte Cassino; Nequam, Alexander; Nicholas of Salerno; Scholasticism; Universities

Bibliography

Arrizabalaga, Jon. The Articella in the Early Press, c. 1476–1534. Cambridge: Cambridge Wellcome Unit for the History of Medicine, 1998.

Beccaria, Augusto. “Sulle trace di un antico canone latino di Ippocrate e di Galeno.” Italia medioevale e umanistica (1959) 2: 1–56; (1961) 4: 1–73; (1971) 14: 1-23.

Kristeller, Paul O. “Bartholomaeus, Musandinus and Maurus of Salerno and other Early Commentators on the Articella, with a Tentative List of Texts and Manuscripts.” Italia medioevale e umanistica (1976) 19:57-87. Revised Italian edition in his Studi sulla Scuola medica salernitana. Naples: Istituto italiano per gli studi filosofici, 1986.

O’Boyle, Cornelius. The Art of Medicine: Medical Teaching at the University of Paris, 1250-1400. Leiden: Brill, 1998.

Pesenti, Tiziana. “Arti et medicina: la formazione del curriculum medico.” In Luoghi e metodi di insegnamento nell’Italia medioevale (secoli XII-XIV). Edited by L. Gargan and O. Limone. Galatina: Congedo, 1989.

———. “Articella dagli incunabula ai manoscritti: origini e vicende di un titolo.” In Mercurius in trivio: studi di bibliografia e di Biblioteconomia per Alfredo Serrai nel 60o compleanno (20 novembre 1992). Edited by M. Cochetti. Rome: Bulzoni, 1993.

Saffron, Morris H. Maurus of Salerno, Twelfth-Century ‘Optimus Physicus,’ with his Commentary on the Prognostics of Hippocrates. Philadelphia: American Philosophical Society, 1972.

CORNELIUS O’BOYLE

Artillery and Firearms

Gunpowder was first used as projectile propellant in thirteenth-century China. Between the tenth and twelfth centuries a wide variety of powder-based incendiary and explosive devices were developed by the Chinese, including bombs, grenades, rockets, land and sea mines, and flame-throwers, on the basis of the experience acquired with fireworks in civilian contexts.

True guns appeared later, as a development of the fire-lance. This flame-throwing device, closely related to the rocket, consisted of a tube socketed to a wooden shaft into which low-nitrate, slow-burning black powder was tightly packed, with solid debris and other chemicals intermixed, in order to cast a jet of sparkling fire, scattershot and toxic fumes on the enemy for several minutes. The substitution of the original bamboo cane by a metal barrel, and the use of high nitrate, explosive black powder, plus one single, bore-filling projectile, gave birth to the first gun. A bronze handgun dating to 1288 was found in the Manchurian province of Heilungchiang. The oldest representation of a firearm, the sculpture of a demon carrying a shooting gun, dated between 1250 and 1280, decorates one of the Buddist cave-temples at Ta-tsu in Szechuan province. Early Chinese guns, cast in bronze or iron, were muzzle-loaders of medium and small size, with a typical bulbous thickening of the explosive chamber, and a blunderbuss-like muzzle.

The first unquestionable European references to guns are noticed a few decades later. The illuminators of Walter de Milimete’s treatise De notabilibus, sapientiis et prudentiis regum (Concerning the Majesty, Wisdom and Prudence of Kings), dated 1326, depicted the oldest representation of a gun. Milimete’s gun, a vase-shaped artifact shooting a big crossbow bolt, looks close to early Chinese guns. A gun similar to Milimete’s, although bigger, illustrates another contemporary English manuscript containing the work Secretis secretorum Aristotelis (The Secrets of Secrets of Aristotle). Also in 1326, the acquisition of iron pellets and metal cannons was ordered for the defense of Florence.

Wandering artisans looking for the jobs offered by the uncertain market of war quickly spread gun technology thoughout Western Europe. But how guns made their way from China to Europe is unclear. Competing theories identify either the Mongols or the Arabs as responsible for the *technological diffusion. The conquest of China, completed in 1276, put all the available knowledge on black powder weaponry in Mongol hands, who made use of it in their campaigns in Eastern Europe, the Middle East, and India. Some Europeans, including fellow friars of the Franciscan *Roger Bacon, who first described the explosive mixture in Latin Christendom, could have acquired first-hand knowledge of guns on their trips to the Mongol khans.

The Arabs were also aware of the new technology. Hasan al-Rammah’s treatise Kitab al-furusiya wa’lmunasab al-harbiya (Treatise on Horsemanship and Stratagems of War), written by 1280, describes gunpowder recipes of clear Chinese filiation, and the fire-lance. Historical sources point to the Muslims as responsible for the introduction of guns in the Iberian Peninsula. In 1331, the Nasrid army besieging Elche made use of “iron pellets that were shot with fire.” Guns are recorded in Mamluk Egypt in the 1360s.

Early guns were muzzle-loaders of medium and small size, cast in iron or bronze, that shot quarrels and lead and iron balls, making use of small amounts of gunpowder relative to the projectile’s weight. These were low-power weapons, fairly inaccurate and slow to reload, that could only be used as anti-personnel weapons from secure positions in close-range fighting. But they were cheap, in comparison to the available projectile-throwing engines.

The static nature of siege and naval warfare provided the niche for the establishment and further development of early guns. Among the oldest references to their use, are the sieges of Cividale (1331), Cambrai (1339), Quesnoy (1340), and Stirling (1341). In 1337, an English cog had aboard “a certain iron instrument for firing quarrels and lead pellets, with powder, for the defense of the ship.” Efficient gun use in ship-to-ship combat is reported in an Aragonese-Castilian engagement fought in 1359 in Barcelonan waters.

Early firearms were given long-lasting names like guns, cannons, and bombards. But they also received specific names that carry significant information on their relative size (the Italian distinction between schioppi and the larger vasi), their appearance (French pots de fer, iron pots), the sound they produced (English “crakys of war,” Castillian truenos, thunderclaps), and even their resemblance to regard to traditional weaponry (Catalan ballestes del tro, thunder crossbows). But guns were still far from being a serious rival to the powerful and accurate crossbows of the day. The biggest siege engine, the counterweight trebuchet, was simply beyond their reach.

The Age of the Bombard

The first firearm capable of tearing down castles and city walls, the bombard, appeared in the early 1370s. Bombard development relied on the blacksmiths’ wrought-iron techniques, and the adoption of round stone shot, used for centuries as projectiles by *catapults and trebuchets. Forged iron allowed the construction of bigger guns, overcoming the checks posed by deficient cast-iron techniques and the high costs of casting bronze. And stone shot, of much lower density than lead and iron shot, did not cause primitive guns to break.

To produce the barrel of the gun, previously forged and heated iron bars were welded together around a wooden cylinder by means of hammering. White-hot forged iron hoops were placed along the barrel afterwards, which, in cooling, contracted, lending additional strength to the gun. The bombard was completed by the attachment of the chamber, of less diameter and thicker walls, to the barrel’s end opposite to the muzzle. In some bombards, the hoop and stave wrought-iron dual structure was forged around a cast iron core. Bombards grew astoundingly in size in a few decades. The ones at the siege of Saint-Sauveur-le-Vicomte (1375) fired stone balls of about 100 pounds (45 kg), whereas the Austrian von Steyr bombard, forged by 1420, fired stones of over 1,500 pounds (700 kg). The success of the iron bombards stimulated the casting of expensive but more reliable giant bronze bombards, a challenge to the bellfounders’ skills, that had the chamber and the barrel, of equal external diameter, bolted together.

To absorb the enormous recoil produced by each shot, bombards were placed on cumbersome wooden frames reinforced with ropes and backed by thick wooden wedges dug into the earth. Sometimes the barrels were simply spiked to the earth. Bombards, as early guns, still used only small amounts of gunpowder per shot. To inflict damage they had to be placed close to the bombarded ramparts, considering the great resistance offered by the inertial mass of the projectile. Bombards fell thus into the range of the defenders’ crossbows, longbows, small firearms, and sorties, and their positions had to be protected by wooden screens, lifted in the moment of fire, palisades, gabions, earthworks and trenches. Giant bombards played a major role in the conduct of key sieges, such as those of Balaguer (1413), Harfleur (1415), Orléans (1429), Naples (1442), and Constantinople (1453). The monster guns were given individualized names such as La plus du monde, Luxembourg, or The King’s Daughter.

The success of the bombards made the number of guns involved in siege trains increase, as bombardments grew in intensity, producing a sharp increase in gunpowder consumption. Only ten guns took part in the siege of Calais by the English in 1346–1347, whereas by 1410 Christine de Pizan stated in her Livre des faicts d’armes et de chevalerie (Book on the Feasts of Arms and Chivalry, an adapted translation of Flavius Vegetius Renatus’s Epitoma rei militaris) that the siege of a stronghold defended by six hundred well-armed combatants should imply the use of two hundred forty-eight guns—forty-two shooting stones of 200 pounds (90 kg) or more—with an overall gunpowder consumption estimated at 30,000 pounds (13,600 kg). The development of saltpeter farming techniques, first reported in Frankfurt in 1388, made the success of the new artillery possible. The dependence on imported Eastern saltpeter was reduced, gunpowder production increased, and prices decreased sharply.

By the mid-fifteenth century, bombards were achieving perfection in design, but constituted a technological dead end in the evolution of artillery, which had already shifted to the development of smaller but powerful and versatile guns, and improved handguns. Small and medium-sized guns started their development in parallel to big bombards, as reflected in the proliferation of gunports for the defense of castles and city walls in the 1380s, and the irruption of firearms in European battlefields, as in Bevershoutsveld (1382), Aljubarrota (1385), and Castagnaro (1387).

The new trend was connected with the increasing use of corned powder, of greater ballistic performance than the flour-like powder used in primitive guns and big bombards. Granulated powder is mentioned in the oldest section of the Feuerwerkbuch (Firework Book), written in Germany by 1380, but its general diffusion was delayed until the 1420s because of the challenge posed to available guns by their highly explosive nature. Looking for the highest muzzle velocities then possible and increasing rates of fire, guns tended to grow in length, and breech-loaders with multiple chambers per barrel flourished. A wide variety of guns, designed to match specific commitments in combat, were developed. They were named after birds of prey (falcons), venemous reptiles (rattlesnakes), and mystical beasts (basilisks), as a recognition of their death-dealing swiftness.

Permanent artillery services developed by the powers involved in the final phases of the Hundred Years War became centers of innovation. The forgers, founders, carpenters, cartwrights, horse- and ox-herders, and sappers under the command of artillery masters did not disband after the end of each military campaign. Continuous exercise of gunnery fostered the introduction of improvements in gun design. These included mobile gun carriages (four-wheeled and two-wheeled), aiming mechanisms (perforated curved bars for fixing barrel elevations by means of safety bolts; trunnions), and hoisting devices (rings, “dolphins”). By the late 1440s the adoption of cast iron shot promoted standardization of guns around determined projectile weights. The new guns used specific gunpowders with different granule size and/or different proportions of saltpeter (the bigger the piece, the bigger the granule size and the smaller the saltpeter content). Bigger powder charges were used in relation to projectiles, obtaining higher muzzle velocities for smaller but denser projectiles. The big bombard was substituted by the battery of smaller but more efficient guns.

The expulsion of the English from Normandy and Gascony betwen 1449 and 1453 by the artillery train commanded by the brothers Gaspar and Jean Bureau forced the adoption of the new French guns and organizational techniques by their foes. The compact and mobile muzzle-loader, smooth-bore, cast-bronze gun, shooting cast-iron balls, provided with trunnions and mounted in two-wheeled, tailed wooden gun carriages, was the finest outcome of the French artillery service. Its design, with walls narrowing from the chamber to the muzzle, as gas pressures propelling the projectile decreased inside the barrel, reflected almost full mastery of the art of smoothbore gunnery by the 1490s. Gun design remained stable for centuries. The artillery train used by King Charles VIII of France in his 1494 speedy campaign for the crown of Naples was equipped with cannons similar to those used in European warfare up to the nineteenth century.

Cannons forced radical changes in military architecture. Medieval walled towns and castles, that withstood the bombard’s slow rate of fire by means of temporary reinforcements, were easily destroyed by the new artillery batteries. New fortifications able to resist cannonade and to use the new artillery in active defense were desperately sought. Multiple solutions were devised, from the erection of fortified earthen defenses (boulevards) to permanent low-level artillery platforms surrounding medieval fortifications, massive artillery towers, or low-profile artillery fortresses, which featured common traits such as round forms, scarped, thick walls, and wide, defensive dry ditches. But the future lay in the angle bastion, first reported in Italy in the mid-fifteenth century, whose design maximized the capability of flanking fire for inflicting damage on assailants.

Handguns underwent a parallel development, from short iron or bronze muzzle-loader guns, socketed to a wooden tiller or fastened to it by means of metal straps, to the arquebus, which began to diffuse in the 1470s. The arquebus incorporated improvements developed from the 1410s, like longer wrought iron barrels, wooden buttstocks, flash pan for priming powder, and the matchlock, a further refinement of the crude serpentine fire mechanism depicted in an Austrian manuscript dated 1411. Arquebusiers were capable of aiming without the help of an assistant in charge of putting fire to the touchhole, as in the case of early handguns. Nevertheless, because of smoothbore ballistics, arquebuses were still inaccurate weapons. More accurately rifled firearms, with spiral grooves cut along the bore to put spin on the bullet, first reported in Nuremberg in the 1490s, remained out of military use because ramming the tight-fitting bullet down the barrel imposed an unbearable delay in the already slow loading process.

Effective development of artillery and firearms on the battlefield derived from their tactical use. Close-range volley fire, able to stop a charge of cavalry or pikemen, made up for the lack of individual marksmanship. But gunners and handgunners were easily cut to pieces by enemy assault while reloading, so they had to fight under cover of either fortified positions or formations of pike-men. The wagon laager (wagenburg), a mobile fortress used by the Bohemian Hussites in their 1419–1434 wars, provided a successful and long-lasting solution and was introduced into the Ottoman army by the Hungarians. Earthworks and trenches made firepower victorious against frontal assault in Castillon (1453) and Cerignola (1503). Nevertheless, fixed positions were an easy target for enemy field artillery and subsequent cavalry charges, as happened in Ravenna (1512). Battlefield tactics of the sixteenth century, characterized by the coordinated action of field artillery, pikemen, arquebusiers, and cavalry, emerged as a response to the benefits and drawbacks of the available artillery and firearms technology.

Gun use in naval warfare increased in the 1370s. Contemporary chronicles refer to their use in the battles of La Rochelle (1372), Saint-Malo (1379), and Dunkirk (1387). Improvements in gun design fostered the adoption of firearms by military and merchant ships by the mid-fifteenth century. Breech-loader swivel guns shooting small stone balls or lead pellets, and bigger stone-shooting bombards, each one provided with multiple removable chambers, were placed by the dozens on round ships and galleys. Standardization was purposely sought. In 1447 Burgundian galleys defeated an Egyptian fleet off the Anatolian coast by rapid fire of their stern guns, fed with the interchangeable chambers of the rest of the guns, unable to fire. The bigger guns concentrated atop the round ship’s lower flushdeck, and on the prow of the galleys. Numbers increased as the century progressed. The Holy Ghost of the Tower had two guns aboard in 1416. Six years later, it had six guns, plus twelve chambers. In 1497, the Sovereign had one hundred forty-one guns with four hundred nineteen chambers.

Cast-bronze cannon were incorporated into ships’ arsenals by 1500, but stone shot remained in use and crossbows were not completely superseded by arquebuses until the mid-sixteenth century. Wrought-iron guns remained in service well into the century, as evidence found in the 1545 Mary Rose shipwreck proves. Stone-shot bronze guns known as perriers are also documented in sixteenth-century naval and land warfare. Mediterranean galleys easily placed big guns aboard, close to the waterline—typically one main centerline bow gun flanked by smaller pieces. Artillery duels resulted in sinkings, and naval warfare gradually changed its nature. But galleys could not deploy big guns along their sides, which were occupied by oarsmen. The adoption of gun-ports allowed round ships of new design, the carracks, to place plenty of guns on the lower decks of their broadsides. Galleys were soon widely surpassed in heavy ordnance by sailing ships, although further refinements in their design was required to guarantee stability, as the surprising sinking of the Mary Rose demonstrated. The refined offspring of the heavily armed round ships of the early 1500s, first galleons, then ships of the line, ruled naval warfare up to the nineteenth century. The maintenance of Portuguese supremacy in the Indian Ocean, in spite of the incursions of Ottoman galley fleets, inaugurated the new era.

See also Albertus Magnus; Alchemy; Arms and armor; Metallurgy; Navigation; Shipbuilding; Transportation; Travel and exploration

Bibliography

Buchanan, Brenda J., ed. Gunpowder: The History of an International Technology. Bath: Bath University Press, 1996.

Chase, Kenneth. Firearms. A Global History to 1700. New York: Cambridge University Press, 2003.

DeVries, Kelly. Medieval Military Technology. Peterborough, Ontario: Broadview Press Ltd., 1992.

———. Guns and Men in Medieval Europe, 1200-1500. Studies in Military History and Technology. Padstow, Cornwall: Variorum Collected Studies Series, 2002.

Guilmartin, John Francis. Gunpowder & Galleys. Changing Technology & Mediterranean Warfare at Sea in the 16th Century. New York: Cambridge University Press, 1974 [revised edition, Annapolis: Naval Institute Press, 2003].

Hall, Bert S. Weapons and Warfare in Renaissance Europe. Gunpowder, Technology, and Tactics. Baltimore: Johns Hopkins University Press, 1997.

Needham, Josep et al. Science and Civilisation in China. Volume V. Chemistry and Chemical Technology. Part 7: The Gunpowder Epic. New York: Cambidge University Press, 1986.

Partington, James Riddick. A History of Greek Fire and Gunpowder. Cambridge: W. Heffer & Sons, 1960 [new edition, with a new introduction by Bert S. Hall, Baltimore: Johns Hopkins University Press, 1999].

Rogers, Clifford J., ed. The Military Revolution Debate. Readings on the Military Transformation of Early Modern Europe. Boulder: Westview Press, 1995.

Smith, Robert D. and Ruth Rhynas Brown. Bombards. Mons Meg and her Sisters. Dorset: Royal Armouries Monograph 1, 1989.

LUIS PABLO MARTINEZ

Astrolabes and Quadrants

The astrolabe is a two-dimensional representation of the three-dimensional celestial sphere, a model of the universe that one can hold in one’s hand. The representation is achieved by a mathematical procedure known as stereographic projection. There is a “celestial” part, consisting of a cutout frame known as a rete, with star-pointers for various bright stars and a ring for the ecliptic, or path of the Sun against the background of the stars. Then there is a terrestrial part, comprising a set of plates for different latitudes, with markings for the local horizon and altitude circles up to the zenith and azimuth circles around the horizon. The rete is placed on top of the appropriate plate, and the ensemble fits in a hollowed-out frame known as the mater. On the back of the mater is the alidade, a viewer for measuring the altitude of any celestial body, as well as scales for finding the position of the Sun from the date, for measuring shadows, and often more besides.

The configuration of the heavens relative to the horizon of a given locality is determined by the instantaneous altitude of the Sun or any star above that horizon. Having measured the altitude of the Sun or any star with the alidade and altitude scale on the back of the astrolabe, one sets the marker for the celestial body on the rete on top of the appropriate altitude circle on the plate: the instrument then shows the instantaneous configuration of the heavens relative to the local horizon. If one rotates the rete over one of the plates one can simulate the apparent daily rotation of the Sun or of the starry heavens above the horizon of the observer; the passage of time between two positions of the rete is measured by the rotation of the rete (360° correspond to twenty-four hours). In addition, one can investigate the position of the ecliptic relative to the local horizon and meridian, configurations of prime importance in *astrology. The astrolabe is thus a multifunctional analogue computer.

The astrolabe is a Greek invention that was inherited by the Muslims in the eighth century and much developed by them over the centuries. (Here we consider only standard astrolabes.) The astrolabe became known to Europeans in Islamic Spain in the tenth century only in its simplest form. Thus the Europeans essentially had to develop technical improvements to astrolabe design for themselves, as well as artistic details on the retes and thrones; this accounts for the very different appearance of medieval Islamic and European instruments. Occasional transfers of knowledge and skills and artistic design between the two cultural regions are attested.

Close to one hundred fifty brass European astrolabes survive from the period before c. 1500, and it was clearly the most popular instrument of the Middle Ages. For some we still do not know even a rough provenance and cannot suggest a reliable dating. Furthermore, some of the most historically important pieces have been dubbed fake by would-be specialists who did not understand them, or by medievalists confronted with their first instrument. There is no incontrovertible evidence that any of the purportedly fake medieval astrolabes ever actually existed.

Early Surviving Examples

The earliest known astrolabe with Latin inscriptions dates from the tenth century, and is now preserved in Paris. The rete is simple and barely decorated: it bears no resemblance to tenth-century Eastern or Western Islamic retes. The piece is rather crudely made (judging it by the standards of, say, tenth-century Islamic astrolabes), and the numbers are in a Latin alphanumerical notation inspired by the Western Arabic notation. The star-positions are not particularly accurate and the maker left out the star-names. The most important plate is for 41°30’ and is labeled “Roma et Francia,” the former perhaps an indication of a Greco-Roman tradition of astrolabe making, about which we otherwise know nothing, and the latter referring to Catalonia as the land of the Franks. The Latin names of the zodiacal signs in the later (thirteenth- or fourteenth-century) inscriptions on the ecliptic ring show Catalan influence. (This remarkable piece was first published by Marcel Destombes, the leading French instrument specialist, in 1962 as the oldest surviving European astrolabe, and was immediately labeled a fake by experts in Latin manuscripts who had never looked at any astrolabes.)

The distinctive form of rete design (a Y- or V-shaped frame inside the ecliptic ring) that is found in manuscripts of *Chaucer’s Treatise on the Astrolabe is attested on several surviving pieces. However, other English pieces display a different design with a single quatrefoil and some zoomorphic star-pointers. All of these are preceded temporally by the monumental Sloane astrolabe in the British Museum, London, England, with an imposing diameter of 18.3 inches (46.5 cm) and a complex arrangement of three quatrefoils, two trefoils, and a half-quatrefoil at each end of both perpendicular axes. Since this piece is datable c. 1300, it symbolizes how little we know about the introduction of the astrolabe to England. Clearly it came from continental Europe, and it is surely significant that we find the V-shaped rete on a Catalan astrolabe from c. 1300.

An astrolabe from fourteenth-century Picardy has all numbers marked in an ingenious cipher notation that was developed by Cistercian monks in the thirteenth century, proving that these ciphers were used on material objects as well as in manuscripts for listing, foliation, dates, and concordances. A later inscription on the instrument dated 1522 shows that it was given by Pascasius Berselius, a Humanist monk of Liège, to Hardianus Amerotius, his teacher of Greek in Louvain. The latter wrote one of the first histories of number notations, but did not realize that the monastic ciphers on his own astrolabe were based on an ancient Greek prototype.

The magnificent painting of St. Jerome in his Study associated with Jan van Eyck (d. 1441) shows the back of an astrolabe among a group of objects with symbolic significance. The piece is unusual in that there is no solar/calendrical scale, and the numbers in the scale are in a distinctive hand, also the throne is of a very early design. An Italian astrolabe from c. 1300 with a diameter of 2.4 inches (6 cm) with the same features on the back survives in Oxford. The scales on the astrolabe in the painting suggest that the original from which it was copied was even smaller; in any case, the artist drew it with a diameter of 0.8 inches (2 cm), larger than the saint’s face.

Astrolabe design varied considerably in the major centers of instrumentation in Europe, and although no workshops or schools can be identified before c. 1425, by that time we know of instrument centers at least in Vienna and Paris. Since most medieval European astrolabes are unsigned, and very few are dated, it is pure speculation to suggest that there must have been workshops in cultural centers such as Montpellier, London or Milan, already before the appearance of the above schools.

However, we can identify designs and trends that can be associated with various regions. Also, regional influence on Latin names for the months and zodiacal signs, or names in vernaculars, offer clues to provenance, sometimes more than the latitudes and localities chosen for the plates. There was a tradition inherited from antiquity of representing the latitudes of the seven climates, roughly, 16°, 24°, 30°, 36°, 41°, 45°, and 48°, which tells us little about the provenance. But the presence of a plate with additional markings for, say, 52°, suggests an interest in London. And the presence of a plate for 32°, Jerusalem, reflects a wish to go on a pilgrimage or crusade, although we have no instruments that were clearly taken that far. A plate for, say, 30° marked “Babylonie” (Cairo) or 36° marked “Affrica” (Tunisia) is a reminder of the tradition of the climates.

We have no dated pieces from before the fourteenth century. It is instructive to look at some of the earliest pieces that are both signed or dedicated and dated or datable:

A German quatrefoil astrolabe now in Kraków was made for Ludolf de Scicte, treasurer of the Cathedral at Einbeck. Archival evidence yields the period of his tenure of this position as 1322–1342. The quatrefoil design on this, the earliest known German astrolabe, is second in complexity only to the London Sloane astrolabe mentioned above.

Thirteenth-century miniature depicting three scientists, one of whom is using an astrolabe to observe the sky. (Bettmann/Corbis)

An astrolabe now in Boston is dated Barcelona, 1375, and signed by Petrus Raimundus from Aragon. Further research is necessary to clarify the relationship of the maker to Pedro IV (1336–1387), ruler of the Crown of Aragon, well known for his astronomical, astrological, and cartographic interests.

An English astrolabe of the Chaucer type now in London is signed “Blakenei me fecit Anno Do’ 1342.” The name recalls towns in Gloucestershire and Lincolnshire. One set of markings is finished for latitude 52° and the other unfinished for 51°, which tells us little, not least because at the time the latitude of London had already been carefully measured as 51°34’ (accurately 51°30’). Some other fourteenth-century English astrolabes have a plate for London at 51°34’.

An astrolabe in a German private collection with an unusual appearance bears a signature by Antonio de Pacent and the date 1420. The plates are labeled for different latitudes but their markings are all for latitude 45°, so that one might think that the piece could work only in the Po Valley. However, the star positions have been totally confused (ecliptic coordinates used equatorially), which explains the strange appearance of the rete. The ensemble is useless for any practical purposes.

It is fortunate that so many surviving astrolabes can be “read” in this way, once we can decode their “language.” Perhaps the most colorful example is a quatrefoil astrolabe with inscriptions in Hebrew, Latin, and Arabic. It was constructed c. 1300, probably in *Toledo. The bare instrument was made by a Jewish craftsman who left scratches in Hebrew alphanumerical script for the latitudes of each of the plates. The quatrefoil design of the rete is European, with strong mudéjar influence. The inscriptions on the rete and the plates are in a scholastic Latin, with very distorted Arabic names for the stars, and some regional peculiarities that could eventually localize the engraver (a Tironian 9-like the abbreviation for cum-, con-, and -us, here used for a hard c, k, and q, as in ON9E for onq/ke, from Arabic ‘unuq). But the back was never completed by the Christian, and the piece fell into the hands of a Muslim Arab, who put his name, Mas’ud, on the shackle of the throne. He also had plans to emigrate to more hospitable climes: he replaced one of the plates with one of his own, serving Algiers and Mecca. He seems to have been at least partly successful for we have an Ibn Mas’ud born in Tlemcen at the right time, but his astrolabe ended up in northern France by the sixteenth century, as attested by a final set of numbers around the rim. It surfaced in Lorraine in the 1990s, and is now in a private collection.

Numerous manuscripts exist of treatises in Latin or the vernaculars on the construction and/or use of the astrolabe. They are of interest for transmission of textual knowledge and linguistic aspects but tell us little about the instruments themselves. For example, the star-names that we find on medieval astrolabes are often quite different from those we find in star-lists in medieval manuscripts. The manuscripts seldom give lists of latitudes for engraving on plates. Rarely do we find illustrations of retes, which would help in investigations of instruments and regional schools. No corpus of such illustrations has been gathered. One example must suffice:

The Brussels miniature of the monk Heinrich Suso and Sapientia shows an astrolabe of typical French design, which is “safely” datable to c. 1400. However, the same design is illustrated in a medieval French astrolabe treatise, now in Berlin, which is dated 1276.

Of particular interest are texts by people who actually made astrolabes. The best example is Jean Fusoris of Paris c. 1425. Some two dozen astrolabes that can be associated with his atelier survive. Although they are neither signed nor dated, all incorporate an error that is also found in his star-catalog.

Renaissance astrolabes appear almost, as it were, out of the blue, and all those known from Elizabethan England and sixteenth-century Flanders are now carefully described. However, they often cannot be properly understood without the medieval connection, Islamic or European. The astrolabe depicted in the intarsia of the studiolo in the palace of the Archduke Frederico at Urbino built in 1476 was copied from a Renaissance Italian astrolabe with a distinctive rete design. One such astrolabe, dated Urbino 1462, was stolen from a museum in Moulins in 1977. Its design was copied in turn from a medieval Italian astrolabe, and one with this same design datable c. 1400 survives in Florence. The design can be traced to Marrakesh c. 1200.

An astrolabe dedicated in 1462 by *Johannes Regiomontanus to his patron, Cardinal Bessarion, shows the transition from Gothic script to Antiqua as well as from Latinized Arabic star-names to Latin ones. The back is embellished by an Italian angel (Gabriel) bearing good news on a scroll: the dedication to Bessarion is a masterpiece of Renaissance Latin, with clever plays of words and numbers. Hidden in the text, for Bessarion to enjoy, is a reference to the four-hundredth anniversary of a splendid Byzantine astrolabe dated 1062, now preserved in Brescia, which Bessarion surely brought to Italy from Constantinople along with all his manuscripts. A text by Georg Hartmann of Nuremberg dated 1527 mentions a feature of all the astrolabes that Regiomontanus made which he had seen, and which we find on this astrolabe. This and another ten mid- and late-fifteenth-century German astrolabes from the same or related workshops all identified in the late 1980s bear witness to Italian influence and their design provides the model for Hartmann’s prolific workshop half a century later.

The magnificent astrolabes of the Arsenius brothers in sixteenth-century Louvain have a cluster of pointers for the stars of the Plough. This proves that they owe something to a medieval French tradition, for the seven stars are included in Jean Fusoris’ astrolabe treatise and feature on the instruments that can be associated with his atelier.

The serious study of medieval European astrolabes is still in its infancy. There is material for the epigrapher (forms of letters), the philologist (regional forms), the historian of number notations and numeral forms (unusual Roman numerals, developing Gothic forms of the Hindu-Arabic numerals), the specialist on calendars (lists of saints’ days), the art historian (astrolabes are scientific works of art, often very beautiful), the general medievalist (there is not a single book on the Middle Ages that displays an astrolabe with a sensible caption), the historian of technology (how were they made?), the metallurgist (what were they made of?), the historian of astronomy (these were the principal tools of medieval astronomers and astrologers), and, last but not least, the cynic (did people actually use them?) and the devil’s advocate (do we have a documented provenance over the centuries so that we can be sure that a given astrolabe is not a fake?).

Quadrants

The second most popular astronomical instrument of the European Middle Ages was the quadrant. It is essentially a device for timekeeping by the Sun. It bears a set of markings that are graphical representations of the altitude of the Sun at the hours throughout the year. One holds the quadrant vertically with one axis towards the sun, and a movable bead on a thread with plummet, set to the appropriate solar longitude, falls on the appropriate markings to indicate the hour of day. The horary markings are either for a specific latitude or for all latitudes, markings of the latter variety being necessarily approximate. Both kinds of quadrants were invented in Baghdad in the ninth century.

Quadrants for a fixed latitude are known for London (1398 and 1399, brass) and Vienna (1438, ivory). Medieval tables displaying the altitude of the Sun as a function of the time of day for, say, each sign of the ecliptic, which one needs to construct the markings on such a quadrant are known for many more cities from Rome to Oxford.

Quadrants for all latitudes are much more common, not least because they were usually included on the backs of astrolabes. The universal horary quadrant provides a quick means of finding the time in seasonal hours for any latitude, whereas with the front of the astrolabe one can, albeit with more effort, determine the time in equatorial hours or seasonal hours for any latitude represented by the plates.

The universal horary quadrant with six circular arcs for the seasonal hours is sufficient unto itself, but already in ninth-century Baghdad an optional movable calendrical-cum-solar scale was proposed. In this form the quadrans vetus was introduced into Europe (probably first to Montpellier, France, in the late twelfth century), and several examples from the medieval period survive. European astronomers do not seem to have understood that whereas the formula (actually of Indian origin) underlying the markings yielded good results throughout the year in Mediterranean latitudes, it produced increasingly inaccurate results in more northerly latitudes. In Montepellier in the late thirteenth century the Jewish scholar Ibn Ben Tibbon or *Profatius Judaeus proposed a quadrans novus, which combined the approximate horary markings of the quadrans vetus with accurate astrolabic projections of the ecliptic and the horizons of various latitudes. This unhappy combination could not be sensibly used for timekeeping, but the instrument became popular anyway, and several medieval European examples survive.

See also Astronomy, Islamic; Astronomy, Latin; Calendar

Bibliography

Gunther, Robert T. The Astrolabes of the World. 2 vols., Oxford: Oxford University Press, 1932. Reprinted in one vol. London: The Holland Press, 1976.

King, David A. “Astronomical Instruments between East and West.” In Kommunikation zwischen Orient und Okzident—Alltag und Sachkultur. Edited by Harry Kühnel, Vienna: Österreichische Akademie der Wissenschaften, 1994, pp. 143–198.

———. The Ciphers of the Monks–A Forgotten Number Notation of the Middle Ages. Stuttgart: Franz Steiner, 2001.

———. In Synchrony with the Heavens. Vol. 2: Instruments of Mass Calculation. Leiden: E.J. Brill, 2005.

North, John D. Chaucer’s Universe. Oxford: Clarendon Press, 1988.

Poulle, Emmanuel. Un constructeur d’instruments astronomiques au 15e siècle–Jean Fusoris. Paris: Honoré Champion, 1963.

Stevens, Wesley M. et al., eds. The Oldest Latin Astrolabe. Florence: Leo S. Olschki, 1995. (a special issue of Physis 32: 2–3).

Zinner, Ernst. Deutsche und niederländische astronomische Instrumente des 11.-18. Jahrhunderts. 2nd ed. Munich: C.H. Beck, 1967, repr. 1972.

DAVID A. KING

Astrology

The modern distinction between astronomy and astrology is not pertinent for the medieval period. For Christian and Muslim scholars of the Middle Ages, in a world created by God and for man, where Earth occupies a central place in the cosmological representations of the universe, where the human being is a little world (microcosmus) corresponding with the entire creation (macrocosmus), the basic idea on which astrology is founded (i.e., belief that events on Earth are influenced by power emanating from the stars and planets) is a matter of consensus.

This consensus is broken when medieval scholars have to define the precise nature and extent of astral influence. Do the Sun, the Moon, the planets, and the stars have an effect on natural phenomena—tides, floods, meteorological catastrophes, earthquakes, epidemics? Do they also cause or determine, directly or through passions and humors, collective and individual human actions? Is there a good astrology, confined to the study and prevision of these natural phenomena, and a bad astrology, going through this frontier? The debate had a considerable echo in the Middle Ages, in the Arabic world, the Byzantine Empire, and Christian Europe. Supporters of a very deterministic astrology, such as the ninth-century philosophers *al-Kindi and *Abu Ma‘shar (Albumasar) and their thirteenth-century Italian followers Guido Bonatti and *Pietro d’Abano, can thus be opposed to some of the main adversaries of astral divination, such as the famous doctor *Ibn Sina (Avicenna), the fourteenth-century historian Ibn Khaldun, the French theologians *Nicole Oresme (1322–1382) and Jean Gerson (1363–1429), and the Italian humanist Picco della Mirandola (1463–1494).

This controversy, however, must not obscure the main point: during the Middle Ages, astronomy and astrology were generally considered by scholars as two complementary faces of the same discipline. Astrological prevision was the primary purpose of astronomical calculations and a possible help for the practice of medicine. The fact that many doctors took astral influences into account and that astronomia was part of the late antique *quadrivium allowed astrology to claim a scientific status.

Origins and Diffusion

The scientific status of astrology went back to the first appearance of horoscopes in the fifth century B.C.E., in Babylonia, yet medieval Christian astrology is derived mainly from Greco-Arabic science. *Ptolemy’s Tetrabiblos, written in the second century C.E., is the most famous astrological book ever written. This work and that of several Greek authors, including Dorotheus of Sidon and Vettius Valens, spread to Byzantium, and then to the Islamic world, where they were enriched by Indian and Persian elements. During the Abbassid period (eighth–thirteenth centuries), the judgment of the stars (ahkam al-nujum) featured prominently in the work of several famous authors including *Masha’allah (Messahalla), Abu Ali al-Khaiyat, Umar al-Tabari, and Abu Ma‘shar. One of the widespread works of Arabic astrology was the Karpos or Centiloquium, a collection of one hundred aphorisms falsely ascribed in the tenth century to Ptolemy; a manual frequently used was The Introduction to Astrology of al-Qabisi, astrologer of the Emir of Aleppo Sayf ad-Dawla (945–967); and the most complete compendium in this field was the Kitab al-Bari, written by Ali ibn Abi l-Rijal (Hali Abenragel), counsellor of the Zirid prince al-Mu’izz, in Kairouan (eleventh century). Byzantine astrology, very dynamic in the sphere of political horoscopes from the fifth century, benefited from Islamic contributions from the eighth century, and prospered until the fall of Constantinople, especially in the fourteenth century, with the astrological school of Johannes Abramius.

In the Latin West, the situation was radically different until the beginning of the twelfth century, since the work of Greek and Arab mathematical astronomers and astrologers was almost unknown there. During the High Middle Ages, astrology was not considered very differently from the augural divination condemned by the Fathers of the Church. Simple forms of astrological prevision translated from Greek flourished from the eighth century: spheres of life and death ascribed to Pythagoras, Petosiris, and Apuleus; predictions founded on the thirty days of an imaginary lunar cycle (lunaria) or the zodiacal positions of the Sun or the Moon (zodiologia). In the absence of accurate astronomical tables and instruments, horoscopes were totally ignored until the appearance in the second half of the tenth century of the “Alchandreana corpus,” partly translated from Arabic, which allowed some horoscopes to be compiled on numerological principles.

The appearance in Christian Europe of a learned astrology, taking into account a great number of celestial parameters and forming a clearly organized and hierarchical system of knowledge, took place in the twelfth century, at a time when translations from Arabic to Latin were providing astronomical tables and instruments to place in horoscopes the position of the planets, ascendants and astrological houses, and were giving the basic rules of the “judgments of the stars.” More than seventy astrological treatises were translated into Latin in the twelfth and thirteenth centuries. Among the clerks and courts, the diffusion of these translations and some original texts contributed to the promotion of a sophisticated astrological knowledge, potentially useful for medicine and political action. Inserting itself into a philosophy of nature taught in schools and universities, astrology claimed more than ever to be a real science. It is in this context that, before 1277, Guido Bonatti compiled the main summa of medieval Latin astrology, the Liber introductorius ad judicia stellarum, and managed to become, in Duke Guido da Montefeltro’s service, the most notorious court astrologer of his time. The considerable attraction of Arabo-Latin astrology in the university world of the thirteenth century set off reactions in the Church. The most important response was that of the Bishop of Paris, Etienne Tempier, who, in 1277, condemned two hundred nineteen propositions, some thirty of which led directly to astral determinism. But astrologers managed to avoid that difficulty by two means: first, they appropriated to themselves the famous sentence ascribed to Ptolemy and previously quoted by *Albertus Magnus and *Thomas Aquinas, Vir sapiens dominabitur astris (“the wise man will dominate the stars”); second, they declared that astrological predictions were compatible with God’s absolute power and human free will.

Therefore, astrology was largely tolerated by the Church in the late Middle Ages and used by emperors and kings (*Frederick II, *Alfonso X and Peter I of Castille, Charles V of France, Matthias Corvinus of Hungary, etc.), popes (Clement VI, Sixtus IV, Alexander VI) and many princes and prelates. But the personal status of court astrologers was less in England and France than in Italy, Germany, and Poland, where they could be considered as spokesmen of their employers. And even in Italy, the seriousness with which astrology was taken was criticized by the likes of Pico della Mirandola and Girolamo Savonarola.

From 1470 the spread of printing gave a new stimulus to astrological output. It was vulgarized through almanacs and annual predictions, published notably in Italy and Germany and addressed to the whole of the learned public. At the start of the Renaissance, the practice of astrology nevertheless remained the prerogative of a small elite of clerics who were for the most part mainly doctors, the professional astrologer being an exception.

The Four Parts of Astrology

Medieval Arabic and Arabo-Latin astrology is commonly divided into four main branches: nativities, revolutions, elections, and interrogations.

The study of nativities (genethlialogy) is founded on the horoscope of birth of an individual and of the new or full moon preceding the birth. The astrologer calculates the position of the planets, the ascendant, the astrological houses, and the partes (lots) on the zodiacal circle. Then he selects the most significant parameters in the horoscope, notably the planet hyleg or significator vite, and he is supposed to be able to predict the main steps of the subject’s life. But this implies that he knows the precise place, date, and hour of the birth, which was very rare outside the courtly milieu before the end of the Middle Ages. He is thus frequently obliged to verify the time of birth by a method called annimodar.

Revolutions are related to the return of the Sun to the precise zodiacal point occupied at an initial moment. The study of revolutions of nativities is based on the examination of the sky at the time of the subject’s birthday, while that of the revolutions of years rested on the horoscope of the vernal equinox of a particular year, and of the new or full moon preceding it. Examining these horoscopes, the astrologer is supposed to predict the weather of the next year, natural catastrophes, epidemics, the immediate future of peoples, and other political events. He is helped in this by a system of relations between zodiacal signs, planets, countries, and social categories. These annual predictions appeared to have been regularly preserved in Europe from the end of the fourteenth century.

Connected to annual revolutions, analysis of the conjunctions of the three superior planets, Saturn, Jupiter, and Mars, as well as that of comets, belongs to historical astrology. Conjunctions of Saturn and Jupiter occur every twenty years, and conjunctions of Saturn and Mars in Cancer, supposed to be malefic, occur every thirty years. According to the doctrine of great conjunctions standardized by Albumasar, they influence the major natural, political, and religious events: the birth of Muhammad and of Islam after the conjunction of Saturn and Jupiter of 571; the demise of the Caliphate of Córdoba, related to the conjunction Saturn and Jupiter in 1007; the hypothetical tempests of 1186, linked to the presence of all the planets in the sign of Libra; the Black Death of 1348 and the Great Schism of 1378, interpreted post eventum as the consequences of the Saturn–Jupiter conjunctions of 1345 and 1365; the possible defeat of the king of France by the English after the conjunction of Saturn and Mars in 1357; the appearance of a false prophet after the conjunctions of 1484 and 1504; the false flood of 1524, and so on. As for comets, they were usually taken to foretell catastrophes, notably the imminent death of some king or prince, as in the case of Giovanni Galeazzo Visconti, Duke of Milan, in 1402.

Elections (or catarchic astrology) deal with the forecasting of undertakings and the choice of proper times for initiate actions: the mythical or real foundation or refoundation of cities such as Constantinople, Gaza, Baghdad (founded by al-Mansur in 762), Cairo, Vittoria (near Parma, founded by Frederick II in 1247), Florence, Venice, Bologna, and Milan; the foundation of a university such as that in Bratislava by Matthias Corvinus in 1467; declarations of war; consecrations of marriage; the begetting of a child; the beginning of a difficult medical operation, such as that performed on the cataract of the King John II of Aragon in 1468, etc. Elections may be established occasionally or by the use of an annual almanac, supposed to program all the owner’s activities or, more modestly, indicate the good days for bleeding and purgatives, which were among the basic practices of medieval medicine.

Interrogations deal with responses to queries, which may be of special or general interest. Will my pregnant wife have a boy or a girl? Where is my stolen golden cup? Will a new pope be elected during the Council of Constance before Christmas? The astrologer draws up a horoscope of the precise moment of the question and tries to answer it.

With and after the condemnations of 1277, the attitude of Church to these different activities was clarified, but some ambiguities and contradictions remained. The ecclesiastical hierarchy tolerated nativities and revolutions up to a certain point, but condemned energetically elections and interrogations, which were considered to be forms of augural divination. Some astrologers who specialized in interrogations, such as Simon de Phares in France at the end of the fifteenth century, may thus have been easily suspected by the vox populi to be diviners, and might be quickly attacked and condemned as diviners, even if no astrologer was ever executed for such reason.

Astrology and Astrologers in Society

At first glance, a comparison would be useful between the two major historiographical sources, the Faraj almahmum, a history of astrologers completed in 1252 in Iraq by the Shi’ite scholar Ibn Tawus, and the Recueil des plus célèbres astrologues of Simon de Phares, written between 1494 and 1498 for Charles VIII of France. The former is very well documented but the latter is a largely mythical prosopography: even if astrologers played a more and more important role in the public life of European countries in the late Middle Ages, astrology was in fact a secondary way of counsel, information, propaganda, and power. It seems to have been quite different in Islamic lands, according to the work of Ibn Tawus and some other sources such as Albumasar in Sadan, a famous collection of scientific talks emanating from the caliphal court of Baghdad in the ninth century. These texts show the persistent favor of astrology in the courtly milieu during the Abbassid period and the deep integration of astrologers in social life: between the chief astrologer of the caliphal court and the modest street diviner, incomes were very different but the prestige of divinatory knowledge was the same. Astrology, as a guide to individual and collective initiatives, played an important role in the urban daily life of medieval Islam, particularly among Shi’ite people. The “science of the stars” also played a real part in politics in Samarkand in the fifteenth century, as well as in Baghdad and Córdoba five centuries earlier.

We may therefore conclude that, globally, astrology was assimilated more successfully by medieval Islam than by Christian Europe: for example, no cathedral was ever built after an astral election, like the Bibi Hanum mosque in Samarkand in 1399. But astrology has played, mainly from the twelfth century, an increasingly important role in the cultural and artistic life of European elites. Far from being a sign of obscurantism, the medieval “science of the stars” has contributed significantly to progress in several fields, most notably astronomy, horology, civil status, and hygiene.

Bibliography

Abu Ma‘Shar al-Balhi [Albumasar]. Liber introductorii majoris ad scientiam judiciorum astrorum, édition critique par Richard Lemay, 9 vol., Napoli: Istituto Universitario Orientale, 1995–1996.

———. Le Recueil des plus célèbres astrologues de Simon de Phares, présenté par Jean-Patrice Boudet, 2 vol., Paris: Honoré Champion, 1997–1999.

Abu Ma‘Shar on Historical Astrology. The Book of Religions and Dynasties (On the Great Conjunctions). K. Yamamoto, C. Burnett ed., 2 vols., Leiden: E.J. Brill, 2000.

Al-Qabisi (Alcabitius). The Introduction of Astrology. Editions of the Arabic and Latin Texts and an English Translation. C. Burnett, K. Yamamoto, M. Yano ed., London/Torino: The Warbug Institute—Nino Aragno Editore, 2004.

Blume, Dieter. Regenten des Himmels. Astrologische Bilder in Mittelalter und Renaissance. Berlin: Akademie Verlag, 2000.

Carey, Hilary M. Courting Disaster. Astrology at the English Court and University in the Later Middle Ages. London: Macmillan, 1992.

Carmody, Francis J. Arabic Astronomical and Astrological Sciences in Latin Translations. A critical Bibliography. Berkeley/Los Angeles: University of California Press, 1956.

Caroti, Stefano. L’astrologia in Italia. Profezie, oroscopi e segreti celesti, dagli zodiaci romani alla tradizione islamica, dalle corti rinascimenti alle scuole moderne: storia, documenti, personaggi. Roma: Newton Compton Editori, 1983.

Juste, David. “Les doctrines astrologiques du Liber Alchandrei.” In I. Draelants, A. Tihon, B. van den Abeele ed., Occident et Proche-Orient: contacts scientifiques au temps des Croisades. Actes du colloque de Louvain-la-Neuve (24–25 mars 1997). Turnhout: Brepols, 2000, pp. 277–311.

Page, Sophie. Astrology in Medieval Manuscripts. London: The British Library, 2002.

Préaud, Maxime. Les astrologues à la fin du Moyen Age. Paris: Lattès, 1984.

Saliba, Georges. “The Role of the Astrologer in Medieval Islamic Society.” Bulletin d’études orientales (1992) 44: 45–67, repr. in Savage-Smith, Emilie ed., Magic and Divination in Early Islam. Aldershot: Ashgate, 2004, pp. 341–370.

Sezgin, Fuat. Geschichte des arabischen Schrifttums, Band VII, Astrologie—Meterologie und Verwandtes bis ca. 430 H. Leiden: E.J. Brill, 1979.

Tester, Jim. A History of Western Astrology. Woodbridge: The Boydell Press, 1987.

Thorndike, Lynn. A History of Magic and Experimental Science. 8 volumes. New York: Columbia University Press, 1923–1958.

Weill-Parot, Nicolas. Les «images astrologiques» au Moyen Age et à la Renaissance. Spéculations intellectuelles et pratiques magiques. Paris: Honoré Champion, 2002.

Whitfield, Peter. Astrology. A History. New York, Harry N. Abrams, Inc., 2001.

Zambelli, Paola. The Speculum astronomiae and its Enigma. Astrology, Theology and Science in Albertus Magnus and his Contemporaries. Dordrecht/Boston/London: Kluwer Academic Publishers, 1992.

JEAN-PATRICE BOUDET

Astronomy, Islamic

Pre-Islamic Arabs living in the Arabian Peninsula had a very primitive knowledge of a certain kind of folk-astronomy mainly related to the stars, the Moon (their *calendar was luni-solar) and the Sun (a system of heliacal risings and achronical settings of certain stars formed the backbone of their luni-solar calendar). The arrival of Islam helped the development of a specialized kind of astronomy (miqat) applied to the needs of religious worship, notable establishing the qibla—the direction towards Mecca—prediction of the visibility of the new moon, and determination of the times of Muslim prayers. The solutions given for these kinds of problems were initially crude, but they developed in the course of time towards a fully scientific level.

Indo-Iranian Astronomy in Islam

The accession to the Caliphate of the Abbasid dynasty in 750 C.E. inaugurated a period of assimilation of the Indian, Iranian, and, especially, Greek heritage which lasted until the end of the tenth century. The Indo-Iranian astronomical tradition, which has a Greek, pre-Ptolemaic, origin, began to penetrate Islamic lands as early as the Umayyad period (from c. 679), and experienced an important development from the caliphate of al-Mansur (754–775). The first collections of astronomical tables, known as zij (Arkand, Zij al-Shah, Sindhind) began to arrive; these were translated into Arabic and used for the computation of horoscopes. The recension of the Sindhind prepared by *al-Khwarizmi (fl. 800–847) reached al-Andalus where it was adapted to the Islamic calendar and to the geographical coordinates of Córdoba by *Maslama of Madrid (d. 1007) and translated in the twelfth century, at least twice, into Latin. As a result of this, it knew a great success in Latin Europe.

Ptolemaic Astronomy and Islamic Observatories

The caliphate of al-Ma‘mun (813–833) marked a turning point, for it was then that Ptolemaic astronomy was introduced. A Syriac translation of the Almagest was the first to appear, followed by three Arabic translations and several revisions, only two of which survive. Other Ptolemaic works such as the Planetary Hypotheses and the Handy Tables were also translated into Arabic. The three known traditions (Indian, Persian, and Greek) used different parameters and planetary models, and a program of astronomical observations was designed to solve the problem of their discrepancy. This was carried out in Baghdad (828–829) and near Damascus (831–832). Several Ptolemaic zij modelled on the Handy Tables were compiled using the results of these observations. These tables accepted Ptolemy’s kinematic models but used new parameters; they rejected some dogmatic beliefs of the Almagest, such as the invariability of the obliquity of the ecliptic, the constant character of the precession of equinoxes, the immobility of the solar apogee, and the impossibility of annular solar eclipses. Some of the alterations are accurate improvements, while others are understandable mistakes due to the belief of Muslim astronomers in the accurateness of ancients, and of their own observations. This was the start of a process of critical analysis of Ptolemaic astronomy, as well as of a serious theoretical effort which continued through the ninth and tenth centuries. *Thabit ibn Qurra (d. 901) was one of its main representatives.

It also marked the appearance of one of the essential institutions of Islamic astronomy, the observatory; this began with al-Ma‘mun and continued, almost without interruption, in small private observatories or in more or less organized institutions with official support. Fakhr al-Dawla (977–997) subsidized an observatory at Rayy (near Teheran) and the astronomer al-Khujandi (d. c. 1000) built a large sextant with a radius of c. 65 feet (20 m) for solar observations. Although it is possible that al-Ma‘mun’s observatories already used large instruments, al-Khujandi’s sextant seems to be the earliest clear instance of this kind of Islamic device; these reappear in the observatory founded in Maragha (1259) by *Nasir al-Din al-Tusi (1201–1274), which survived until 1316. The Maragha model was imitated, notably in the observatory built in Samarkand in 1420 by prince Ulugh Beg, who was himself a highly competent astronomer. The buildings of the Samarkand observatory were still in place c. 1500 and they contained huge instruments, of which a good part of the meridian one (probably a sextant) still exists. Islamic observatories continued with the foundation of the Istanbul observatory in 1577, which was destroyed in 1580. This tradition survived until the 1700s for Jay Singh, Muslim maharajah of Amber (India) built between 1699 and 1734 five observatories, following the models of Maragha and Samarkand, in Jaypur, Delhi, Benares, Mathura, and Ujjayn. In the age of the telescope, these were already obsolete, but they testify to the persistence of the tradition.

Observations or simple computational work were the origin of new zij, of which we know of the existence of some two hundred twenty-five (eighth to nineteenth centuries). Planetary positions computed with a zij were in agreement with the observed ones for a short period of time (about forty years according to an Andalusi estimation). When the disagreement was clear, a new set of tables had to be computed. Corrections affected mainly mean motion parameters; equation tables, with the exception of those for the Sun and Venus, were usually taken from the Handy Tables. This effort to adjust computation to observation led to the conclusion, reached in Europe during the Scientific Revolution, that it was neessary to change the Ptolemaic paradigm. At the same time, these astronomical tables introduced a new spherical trigonometry which has remote Indian roots but is mainly an Islamic creation: all the trigonometry Copernicus knew was Islamic.

The Role of Al-Andalus

In the second half of the tenth century astronomy in al-Andalus benefited from an original development which preserved many elements of the Indo-Iranian tradition. This reached its summit in eleventh-century *Toledo where *Ibn al-Zarqalluh made important contributions to astronomical theory. These were continued both in the Iberian peninsula and in the Maghrib until the end of the fourteenth century and were well known by the astronomers of the European Renaissance. This was due to the translation of astronomical works from Arabic into Latin or Castilian which began around 1000 C.E. and reached its apogee during the twelfth and thirteenth centuries. This allowed Latin Europe to recover the Greek astronomical tradition together with the modifications and criticisms made by eastern Islamic astronomers up to the end of the tenth century: translations could only be made of Eastern books which had reached al-Andalus before contact with the Islamic east was lost with the fall of the Cordovan Umayyad Caliphate c. 1031. Arabic astronomical works written in the eleventh century or later which were translated into Latin and known in Europe were usually Andalusi.

The Hay’a (Cosmology) Tradition

Ptolemy’s Almagest is a mathematical tool, the purpose of which is to predict planetary longitudes. *Ptolemy also wrote the Planetary Hypotheses, a good part of which is only known through an Arabic translation, in which he defends his astronomical system in physical terms, projecting his geometrical models into three dimensions and using these to compute the sizes of planets and their distance from Earth. The interest in planetary sizes and distances appears in Islamic astronomy as early as the eighth century. Later, the great physicist *Ibn al-Haytham (945–c. 1040) made a serious attempt in his Hay’at al-‘alam (On the Configuration of the World) to give a new interpretation of the geometrical models of the Almagest in physical terms. This led him to the criticism of Ptolemy which appears in his al-Shukuk ‘ala Batlamiyus (Doubts on Ptolemy): Ibn al-Haytham discusses Ptolemy’s failure in the Hypotheses to justify physically all the motions described in the Almagest, as well as certain aspects of the geometrical models of this latter work which he considers to be physically impossible. The most important of these criticisms is concerned with the equant point (the center of mean motion in longitude of Ptolemy’s planetary models), a device which clearly violated the principle that any celestial motion must be a combination of uniform circular motions.

The problem of the equant point became crucial in all attempts to create a physically admissible astronomical system, and there were unsuccessful attempts to design planetary models without equant from the eleventh century onward. A great revival of this tradition took place shortly before the foundation of the Maragha observatory in 1259, but as many of the theoretical innovations were made by a group of astronomers who worked in this observatory, the denomination of “Maragha school” has often been applied to them. Mu‘ayyad al-Din al-‘Urdi (d. 1266) and Nasir al-Din al-Tusi described physically admissible non-Ptolemaic planetary models which are as successful as those of Ptolemy: many of them present remarkable similarities to those of Copernicus, although no mention is made of heliocentrism. This kind of enterprise was continued by al-Tusi’s disciple Qutab ad-Din al-Shirazi (1236–1311) and, later, by the Syrian astronomer Ibn al-Shatir (c. 1305–c. 1375) who computed a new zij based in his own models (the lunar one is clearly better than Ptolemy’s) and on the observations he made in Damascus. The geometrical models of the “Maragha school,” like those of Copernicus, replace Ptolemy’s equant by combinations of from two to four epicycles, the radii of which are linked like vectors of constant length rotating at uniform speed. Although it is not clear how the information about the Maragha models reached Copernicus (the best hypothesis points to a transmission through a Byzantine Greek translation) it is obvious that the great Renaissance astronomer knew about these theoretical efforts: besides many other similarities, his lunar model is identical to that of Ibn al-Shatir and he uses two lemmas discovered by al-‘Urdi and al-Tusi which are the main mathematical tools of all the Maragha and Copernican models.

See also Astronomy, Latin; Ptolemy; Translation movements; Translation norms and practice

Bibliography

al-Hassan, A.Y., Maqbul Ahmed and A.Z. Iskandar, eds. The Different Aspects of Islamic Culture. Volume Four: Science and Technology in Islam. Part I: The Exact and Natural Sciences. Paris: UNESCO, 2001.

Kennedy, E.S. A Survey of Islamic Astronomical Tables. Transactions of the American Philosophical Society (1956) n.s. 46: 123-175.

———. Astronomy and Astrology in the Medieval Islamic World. Aldershot: Variorum, 1998.

Kennedy, E.S., Colleagues and Former Students. Studies in the Islamic Exact Sciences. Beirut: American University of Beirut, 1983.

Kennedy, E.S. and I. Ghanem, eds. The Life and Work of Ibn al-Shatir. An Arab Astronomer of the Fourteenth Century. Aleppo: Institute for the History of Arabic Science, 1976.

King, D.A. Islamic Mathematical Astronomy. London: Variorum, 1986.

———. Astronomy in the Service of Islam. Aldershot: Variorum, 1993.

———. World-maps for finding the direction and distance to Mecca. Innovation and tradition in Islamic science. Leiden: E.J. Brill, 1999.

———. In Synchrony with the Heavens. Studies in Astronomical Timekeeping and Instrumentation in Medieval Islamic Civilization (Studies I–IX). I: The Call of the Muezzin. Leiden: E.J. Brill, 2004.

King, D.A., J. Samsó and B.R. Goldstein. “Astronomical Handbooks and Tables from the Islamic World (750–1900): an Interim Report.” Suhayl (2001) 2: 9–105.

Rashed, Roshdi, ed. Encyclopedia of the History of Arabic Science. Vol. I. London: Routledge, 1996.

Saliba, G. A History of Arabic Astronomy. Planetary Theories during the Golden Age of Islam. New York: New York University Press, 1994.

Samsó, J. Las ciencias de los antiguos en al-Andalus. Madrid: Mapfre, 1992.

———. Islamic Astronomy and Medieval Spain. Aldershot: Variorum, 1994.

Sayili, A. The Observatory in Islam and its Place in the General History of the Observatory. Ankara: Türk Tarih Kurumu Publications, 1969 (reprint Ankara, 1988).

Van Dalen, B. Al-Khwarizmi’s astronomical tables revisited: analysis of the equation of time. In From Baghdad to Barcelona. Studies in the Islamic Exact Sciences in Honour of Prof. Juan Vernet. Edited by J. Casulleras and J. Samsó. Barcelona: Instituto Millás Vallicrosa de Historia de la Ciencia Arabe, 1996, 195–252.

JULIO SAMSÓ

Astronomy, Latin

Astronomy was well established as a scientific discipline in classical times. To the Greeks and their intellectual successors, not all study of the heavens qualified as astronomy. They regarded it as the mathematical study of the universe and of celestial bodies; in contrast, causal descriptions of the heavens were considered to be a part of physics or *cosmology. Ancient astronomy may be divided into three overlapping fields of study: (1) Measuring time and creating calendars based on the rising and setting of bright stars or constellations, often the signs of the zodiac; (2) Predicting the apparent positions of the seven planets, including the Sun and Moon, as measured against the background of the fixed stars; (3) Determining the diameters, volumes, and distances of the stars and planets. These activities had been developed to a sophisticated level by the Greeks, culminating with the Alexandrian mathematician *Ptolemy in the second century C.E.

Because Ptolemy and his predecessors wrote in Greek, their works became inaccessible to the medieval scholars of Western Europe, who read only Latin. Their knowledge was limited to the summaries of astronomy in *encyclopedias and handbooks by Roman and early Christian authors such as Pliny the Elder, *Macrobius, and *Isidore of Seville, along with a partial translation of *Plato’s Timaeus. Christianity added a new science of time-reckoning named *computus, which centered on the problem of determining the date of Easter. Since it involved the reconciliation of solar and lunar cycles, computus required some astronomical knowledge. The *translation movements of the twelfth and thirteenth centuries introduced Greek and Arabic astronomy to Latin speakers, although the general level of understanding remained modest. Undoubtedly folk astronomy could also be found in many areas, but its practitioners were seldom literate and left few records of their art.

The Classical Legacy

In broad outline, the medieval idea of the cosmos was the same as that of Ptolemy, Plato, and Aristotle in the fourth century B.C.E. The center of the world was occupied by the four terrestrial elements. Earth, the heaviest element, collected in a sphere surrounded by layers of the other three elements, water, air, and fire. The celestial realm began with the sphere of the Moon, just beyond fire. The heavens consisted solely of spheres of the fifth element, aether, centered on the Earth. Most astronomers agreed that the Moon was closest to Earth, and that the planets were arranged in the order Moon–Mercury–Venus–Sun–Mars–Jupiter–Saturn, beyond which the fixed stars shared a single sphere. The order sometimes varied in ancient and medieval works, but there was general agreement that the Moon was nearest and the stars furthest away.

In contrast to the four elements, which moved in straight lines until reaching their natural place, aether moved perpetually in circles. All celestial objects complete a common revolution around the Earth in twenty-four hours, and we see them as rising and setting. But each object also has its own, more complicated motion. When compared to the fixed stars, the Sun appears to move through the zodiac on a path known as the ecliptic, which it completes in a year. The Moon takes about a month to complete its own revolution. Each of the five planets has its own cycle, in addition to drifting away from the ecliptic (motion in latitude) and periodically reversing its motion (retrogradation). Even the fixed stars share in a slow motion known as precession.

The variety of motions can be explained by attributing to each planet a set of orbs; combined, they cause the planet to appear to move irregularly. Aristotle adopted the system of Eudoxus (fourth century B.C.E.), in which each planet is assigned three or four orbs concentric with the Earth. But this scheme could neither predict planetary motion accurately, nor account for variations in brightness, which seemed to indicate changes in planetary distances.

In the Almagest, Ptolemy described an accurate system of prediction. The most basic element is the deferent (“carrying”) circle, which moves the planet around the Earth. The Sun, which has the simplest motion, has an eccentric deferent, meaning that it is slightly off-center. Because the observer is not at the center of the eccentric, the Sun appears to move most slowly when furthest from Earth. In reality, however it maintains a constant speed around its circle. Each of the remaining planets also has an epicycle, a smaller circle carried by the deferent; the planet is placed on the epicycle. In the lunar model, the epicycle simply changes speed and distance. For the other planets, the epicycle explains retrogradation: the planet retrogrades when the epicycle carries the planet in a motion opposite to the deferent. Finally, the five planets have equants. The equant is a point separate from the center of the deferent; the center of the epicycle moves uniformly with respect to the equant. In Planetary Hypotheses, Ptolemy explained how to convert the circles of motion into three-dimensional orbs, and how to calculate the sizes of the planets and their orbs.

The Early Middle Ages

Only a fraction of classical astronomy was available in the early Middle Ages. Through the efforts of *Boethius to preserve knowledge of the seven liberal arts, astronomy retained its status as part of the mathematical *quadrivium, but the level of knowledge remained superficial. A reader of one of the common handbooks could have learned about the division of the cosmos into celestial and terrestrial realms; the shape of the Earth and perhaps its measurement by Eratosthenes; the Earth’s five climatic zones (the torrid zone, two arctic zones, and two habitable temperate zones); the daily motion of the heavens; the names, natures, and arrangement of the seven planets; and the causes of eclipses. The most advanced treatments of astronomy included the approximate period of each planet, the Sun’s motion through the ecliptic, eccentric circles as a cause of variable apparent speed, and a qualitative description of retrogradation. Individual texts added variations on the theme. Macrobius, for example, gave a simple method of finding planetary distances in the Commentary on the Dream of Scipio. *Martianus Capella placed Mercury and Venus in motion around the Sun, not the Earth. Not one described details of astronomical models, such as the equant or the ratio of epicycle to deferent. With only these texts, it was impossible to predict planetary motion.

For prediction it was necessary to use the computus. Beginning as a method of predicting the date of Easter, computus developed into a mathematical art in its own right, demanding the ability to calculate celestial cycles. Some regarded it as a Christian response to the quadrivium, which was tainted by association with *astrology and pagan learning. *Bede wrote two books on computus. The longer of these, De ratione temporum, was among the most advanced Latin astronomical works of its time. Bede went beyond the creation of a *calendar to explain the underlying motions of the Sun and Moon, investigating such questions as the changing angle of the luminaries’ rising and setting, and the connection between the Moon and tides.

The High Middle Ages

The rediscovery of Ptolemy and Aristotle was part of a broad revival of learning facilitated by contact with Islamic scholarship, heavily dependent in its first stages on translation of Arabic works and of Greek texts in Arabic. *Gerbert of Aurillac may have helped initiate the process by bringing mathematical texts from a visit to Spain. An important first step towards predictive astronomy was mastering the astrolabe, an astronomical instrument for observation and calculation. During the twelfth century, translators produced Latin versions of zijat (singular, zij), *planetary tables with canons (instructions for use), including the Toledan Tables of *Ibn al-Zarqalluh. Around 1270 a new set of tables was prepared in Spain. The Alfonsine Tables—named for their patron, *King Alfonso X—gradually replaced the translated zijat and remained the primary tables until after the publication of Copernicus’s De revolutionibus (1543). Latin scholars also gave their attention to theoretical texts. The celebrated translator *Gerard of Cremona traveled to Spain and learned Arabic in order to study the Almagest, but few, if any, read and understood his translation of Ptolemy in toto.

Astronomy played a minor role in the curriculum of the new *universities. As part of the quadrivium, it was incorporated into the arts faculty, and as a prerequisite for astrology it supplemented the practice of medicine. New astronomical textbooks appeared in the thirteenth and fourteenth centuries to satisfy demand for instructional materials. Among the popular textbook authors were *Robert Grosseteste and *Campanus de Novara, but the most successful was *John of Sacrobosco. University statutes and manuscript anthologies confirm that three textbooks by Sacrobosco—the Algorismus on arithmetic, the Computus ecclesiasticus, and the Sphaera or “sphere” on elementary astronomy—formed the core of a course of astronomical studies, supplemented by books on instruments, an advanced genre of textbook called *theorica planetarum, and the Alfonsine Tables. Modern accounts of “epicycles on epicycles” are simply untrue; the planetary models of medieval texts are essentially identical to those of Ptolemy. The major exception is the theory of trepidation ascribed to *Thabit ibn Qurra, according to which a rotation of the sphere of fixed stars causes the equinoxes to oscillate.

Scholastic philosophers debated whether the eccentric circles and epicycles of astronomers could exist as ethereal orbs in the heavens. Many assented to the possibility that such orbs existed, but Averroists (followers of *Ibn Rushd, the great Islamic commentator on Aristotle) insisted that all celestial motion must be strictly concentric with the Earth, in accordance with Aristotelian physical doctrine. Averroists adopted a modified form of the Eudoxan system of homocentric orbs and dismissed Ptolemaic models as fictions meant only for predicting appearances from Earth.

The Renaissance

In the mid-fifteenth century Viennese professor *Georg Peuerbach began a commentary on the Almagest but was prevented by death from completing it. His student *Johannes Regiomontanus took up the task; in his hands, the Epitome of the Almagest became an invaluable technical supplement and critique of Ptolemy, based on an understanding of astronomy unmatched in the West since antiquity. Regiomontanus moved to Nuremberg in 1471 where he became the first scientific publisher; his publications included Peuerbach’s Theoricae novae planetarum, which he had transcribed while a student at Vienna. The Epitome was published posthumously in 1496. For over a century the methods, problems, and even many of the standard texts in astronomy continued to be what they had been in the Middle Ages. But printing and the new textbooks helped to create a critical mass of skilled astronomers who would ultimately discard the legacy of the classical world.

See also Almanacs; Aristotelianism; Astrolabes and quadrants; Astrology; Astronomy, Islamic; Cosmology; Elements and qualities; Latin Averroists; Macrobius; Martianus Capella; Michael Scot; Planetary tables

Bibliography

Bede. Bede: The Reckoning of Time. Translated with introduction, notes, and commentary by Faith Wallis. Liverpool: Liverpool University Press, 1999.

Grant, Edward, ed. A Source Book in Medieval Science. Cambridge: Harvard University Press, 1974.

Lindberg, David. The Beginnings of Western Science: The European Scientific Tradition in Philosophical, Religious, and Institutional Context, 600 B.C. to A.D. 1450. Chicago: University of Chicago Press, 1992.

McCluskey, Stephen. Astronomies and Cultures in Early Medieval Europe. New York: Cambridge University Press, 1997.

Pedersen, Olaf. “The Corpus astronomicum and the Traditions of Mediaeval Latin Astronomy: A Tentative Interpretation.” In Colloquia Copernicana III: Astronomy of Copernicus & Its Background, 57-96. Studia Copernicana 13. Wroclaw: Ossolineum, 1975.

———. Early Physics and Astronomy: A Historical Introduction. Revised edition. New York: Cambridge University Press, 1993.

Stahl, William Harris. Roman Science: Origins, Development and Influence to the Later Middle Ages. Madison: University of Wisconsin Press, 1962.

Stahl, William Harris, Richard Johnson, and E.L. Burge. Martianus Capella and the Seven Liberal Arts. 2 vols. New York: Columbia University Press, 1971–1977.

Thorndike, Lynn. The “Sphere” of Sacrobosco and Its Commentators. Chicago: University of Chicago Press, 1949.

KATHERINE A. TREDWELL

A

Abelard, Peter

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Abraham Bar Hiyya

Astrological Predictions

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Abu Ma‘shar

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Adelard of Bath

Luminary Among Mathematicians

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Agriculture

Northern European Regimes

Open Fields

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Agrimensores

Medieval Surveying

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Agronomy

English Estate Books

The Islamic Tradition

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Albert of Saxony

Peak of Career

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Albertus Magnus

Historical Significance and Scope

The Structure of Albert’s Natural Philosophy

Physics, Astronomy, and Alchemy

Plants and Animals

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Alchemy

Early Alchemical Literature

Influence of Philosophy and Science in Alchemy

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Alderotti, Taddeo

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Alfonso, Pedro

“Our Teacher”

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Alfonso X the Wise

The Scientific Collaborators of Alfonso X

A Typology of Alfonsine Translations

The Alfonsine Tables

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Alfred of Sareschel

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Algebra

Europe

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Almanacs

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Alum

Industrial Uses: Dyeing

Industrial Uses: Leather Preparation

The Alum Trade

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Anatomy

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Andalusi, Sa‘id al-

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Aquinas, Thomas

Science and Faith

Motion and Change

Mathematics and Physics

Creation and the Natural Sciences