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Since Roman times, the word mathematici had applied especially to mathematicians, and in the thirteenth century Roger Bacon still strove at length to convince his audience of the difference between false mathematics and true mathematics. Boethius produced an influential Latin work on arithmetic, which was closely based on the Greek Introduction to Arithmetic of the neo-Pythagorean Nicomachus of Gerasa and also a substantial treatise on music, a science that was then regarded as intimately dependent upon arithmetic. Geometrical figures themselves could perform important semiotic functions, as when in the fourteenth century Nicole Oresme used graphic-like diagrams to symbolize variations of speeds and qualities. In standard histories of mathematics, the name of Jordanus de Nemore is linked with that of Leonardo of Pisa as another medieval mathematician of undoubted originality. A striking feature of medieval mathematics, especially in its theoretical genre, is the amount of discussion that was conducted in terms of ratios and their equalities or proportions.
During the medieval millennium, three overlapping phases and a coda characterize the schools of the Latin world. The three phases are monastic schools, urban schools, and universities. Boethius, a Christian layman, had been an advocate of the several liberal arts, which the Benedictine schools would eventually embrace as aids to their religious life. The masters of various trades likewise formed guilds, or universitates, that, within their domain, were literally autonomous. By the mid-thirteenth century, the guild (universitas) of masters of arts controlled its own teaching and degrees. The universities made natural philosophy, however ill-fitting, a central feature of their arts curriculum, and they turned into higher faculties the three disciplines of law, theology, and medicine, each of which had recently undergone a major transformation. As for members of the universities, students in Italy generally did not have clerical status by virtue of their matriculation. Both colleges and the institutional practice of small-group supervision also favored specialization.
This chapter deals with medical practice in Western Europe, the institutions and circumstances that shaped it, and their evolution during the period from about 1050 to 1500. Only studies of medical profession can provide an accurate sense of the dynamics that shaped medieval health care and the enormous geographical and chronological variety of the institutions, laws, and practices that constituted it. Health care is formed, in which patients and their families moved back and forth between secular and saintly healers: 'between doctors and holy shrines', as the account of another of Gilbert's miracles specified. The effect of urbanization was to support a larger, more diverse, and more specialized community of medical practitioners. The chapter focuses on two principal kinds of medical institutions elaborated in the fourteenth and fifteenth centuries: those concerned with regulating practice and defending the interests of practitioners, and those concerned with mobilizing medical expertise.
Islamic astronomy designates the astronomy of Islamic civilization, the civilization of regions where Islam was the religion of either the rulers or the majority of the populace. In observational activity, and often the patronage that supported it, were central to the enterprise of Islamic astronomy, people must quaint with the practical applications of astronomy. The astrolabe was the instrument suited to all of these applications of observational astronomy in timekeeping, astrology, and sacred geography. Traditionally, scholars have focused their attention on how translations of texts on astronomy from Greek, Sanskrit, and Pahlavi flourished under the Abbasid caliphs to establish an identity apart from those of their predecessors, the Umayyads. The need to correct parameters posed by the translations of the Almagest brought the first documented program of systematic astronomical observation. Ptolemy's planetary models relied on two devices, the eccentric and the epicycle, that were known as early as the time of Apollonius. The religious applications of observational astronomy remained prominent.
Cosmology was not an independent discipline during the late Middle Ages but an undifferentiated part of the broad domain of natural philosophy. Throughout the Middle Ages, the creation of the world from nothing was an article of faith. In Aristotle's Meteorology, he speaks clearly of a world that is divided into two radically different parts. Medieval natural philosophers had to choose between Aristotle's system of purely concentric orbs, which assumed that the Earth was at rest in the geometric center of the world. Each planet had its own total concentric orb, at least eight orbs from the Moon to the fixed stars were required for the celestial bodies. Since uniform circular motion was the only kind of motion deemed appropriate for celestial bodies, natural philosophers were expected to identify the cause of such motions. The dimensions were measured only from the Earth to the sphere of the fixed stars.
To humanity at large, astronomy has always had an appeal linked more to the vastness of the world we inhabit than to the details of any scientific analysis of it. This chapter explores the literary style of John of Sacrobosco. His book dealt with only elementary spherical astronomy and geography, and included virtually nothing on planetary theory. John of Murs compiled tables for the conjunctions and oppositions of the Sun and Moon, which had a direct bearing on the subject of ecclesiastical calendar reckoning. Paris, beginning in the 1320s, was the single most important point of diffusion of the Alfonsine Tables. In a work written in 1364 in Paris, Ptolemy vented his feelings in petty academic criticism of the standard university text, Theorica planetarum. The rapid rise in astrology's respectability during the fourteenth century led to its increasing use in literature, architecture, book illustration, and the visual arts generally.
The religious sciences emerged early in Islamic history as a way of understanding and interpreting the revelation and systematizing and authenticating the sayings and actions of the Prophet. Products of Islamic civilization will often be referred as Islamic to indicate a shared intellectual heritage. From the tenth century until modern times, diverse regional centers emerged with their own distinctive intellectual and cultural styles. The Islamic appropriation of Hellenistic natural philosophy, mathematical sciences, medicine, and philosophical teachings is one of the remarkable events in the history of learning. As one of the most important intellectual movements in human history, the translation movement in Islam resulted from the coincidence of a number of factors. Of fundamental significance was the new urban, multicultural, multireligious, and multilingual milieu of Baghdad. The natural philosophy tradition in Islam was part of a larger tradition of philosophy.
Sophisticated theories of light, color, and vision were produced in the ancient Greek world, committed to writing and transmitted in treatises by Aristotle, Euclid, Ptolemy, Galen, and others. Perspectiva represented in the thirteenth century by influential standard texts that treated the physics and mathematics of light, color, and vision. Although scholars in early-medieval Christian Europe had only fragmentary access to the Greek traditions, the major Greek works were translated into Arabic after the advent of Islam and stimulated scholarly activity within the Islamic world in each of the areas of Greek achievement. The intellectual life of Europe was enriched and transformed in the twelfth and thirteenth centuries by the translation of Greek and Arabic books into Latin. Nobody contributed more to the development of the science of Perspectiva in the West than Roger Bacon. Rainbows, spectacular natural phenomena as well as symbols of God's promise to Noah, could be overlooked by medieval scholars claiming an interest in light and vision.
The medieval period saw the creation of a body of Hebrew scientific literature. There is a certain chronological overlap between the production of this corpus of Hebrew writings and the first instances of Jewish writers composing scientific treatises in Arabic. Jews who contributed to the scientific enterprise during the main period of concern resided in communities ranging from the Atlantic seaboard to Mesopotamia, reaching as far north as England and as far south as Yemen. The medieval period saw a most meaningful engagement of Jewish thought with the sciences. Some scientific teachings caused a real crisis in Jewish thought; for example, the persuasive arguments against creation ex nihilo. Many Jews had believed that recognition of the deity and its design of and upon the cosmos were the exclusive privilege of their tradition, having been delivered directly from God through the Jewish prophets.
Throughout medieval Islamic society, a medical pluralism existed as a continuum running from the formal theories and practices of learned medicine to those of local custom and magic. In the pre-Islamic Near East, there were medical concerns and practitioners who tended the needs of the sick and injured. For several centuries prior to the rise of Islam, Alexandria, as well as Rome, Constantinople, Antioch, Edessa, and Amida, had flourished as centers of scientific and medical activity. In the tenth and early eleventh centuries, several Arabic medical encyclopedias were composed that proved to be particularly influential in the learned medical tradition. Ophthalmology was the subject of specialized treatises and a topic in which medieval Islamic writers displayed considerable originality. The Arabic literature on pharmacology quickly assumed a different form from that inherited from the Hellenistic world. In contrast to ophthalmology and pharmaceutics, the Islamic writings concerned with anatomy remain quite conservative, deviating little from their Hellenistic models.
Knowledge of the natural world was an integral part of a broader kind of learning. Medieval natural knowledge juxtaposed practical knowledge with the theoretical findings of classical antiquity. Ostrogothic leader Theodoric, who had received some education in Constantinople, valued the Roman ideal of learning. Medieval scholars saw the order of nature as an expression of the Creator's activity. The relation between God's dominion and the natural order was elaborated in an eighth-century gloss on the Psalms by an unknown Northumbrian or Irish author. One widespread practical use of the concept of natural order in the early Middle Ages was to provide a guide for religious rituals. Thus the solstices and equinoxes provided a framework for a cycle of Christian feasts marking the turnings of the year. Computus became an essential part of the education of clerics and guided much of the preservation, transmission, and development of natural knowledge from the time of Bede to the rise of the universities.
Anatomical accuracy depends both on a sufficient stock of bookish knowledge, in order to be aware of the different structures of the body, and on an ability to observe reality and to depict it faithfully. Academic medical readings were supplied by the numerous translations made from Greek and Arabic throughout the medieval period up to the middle of the fourteenth century. The Arabic Galenism that underlay medieval Latin physiology took its principles from Aristotelian physics. Scholastic debates focused more on the definitions of the other constituents of the human body on which medical practice could act, namely, besides anatomical parts, complexions, humors, spirits, virtues, and operations. Explanations of health and disease thus involved a complex system of interactions between qualities. From the thirteenth to the fifteenth century, medical theory had revealed, through the scholastic method of reading sources and reasoning, some failures that to a modern mind seem irreparable.
The translation of scientific texts from Greek and Arabic in the twelfth and thirteenth centuries is both a symptom and a cause of one of the greatest shifts in Western science. In the twelfth century, Toledo became the center for the translation of scientific works, and the separate streams of mathematical, medical, and philosophical translations were united there. Jews played an important role both in circulating and in translating scientific works in Christendom. The motivation for the translations was the perceived lacunae in Latin scientific education, as Burgundio of Pisa and the biographers of Gerard of Cremona both state. If the goal of the translators was to restore the ancient learning of Euclid, Ptolemy, Aristotle, and Galen, they had two sources: the centers of Greek and Arabic learning. For translations to be made, either the Latin scholar must go in search of the texts or the texts must be sent or brought to the Latin center of learning.