History of science in the Middle Ages
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The history of science in the Middle Ages is concerned with the study of nature—including practical disciplines, the mathematical sciences, and natural philosophy—throughout the Middle Ages: the "middle" period in a traditional schematic division of European history. According to Pierre Duhem, who founded the academic study of medieval science as a critique of the Enlightenment-positivist theory of a 17th century anti-Aristotelian and anticlerical scientific revolution, the various conceptual origins of that alleged revolution lay in the 12th to 14th centuries, in the works of churchmen such as Aquinas and Buridan. Although the term "Middle Ages" usually refers to European history, scientific advances in the Eastern world will also be accounted for in the present article.
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[edit] The Middle Ages: Western Europe
[edit] Overview
Scientific inquiry was never particularly strong in the Latin side of the Roman Empire, especially when compared with its Greek/Hellenistic counterpart. With the end of Roman civilization, Western Europe entered the Middle Ages with great difficulties that affected the continent's intellectual production dramatically. Most classical scientific treatises of classical antiquity (in Greek) were unavailable, leaving only simplified summaries and compilations. Notwithstanding, with the beginning of the Renaissance of the 12th century, interest in natural investigation was renewed. Science developed in this golden period of Scholastic philosophy focused on logic and advocated empiricism, perceiving nature as a coherent system of laws that could be explained in the light of reason. With this view the medieval men of science went in search of explanations for the phenomena of the universe and achieved important advances in areas such as scientific methodology and physics, among many others. These advances, however, were suddenly interrupted by the Black Plague and are virtually unknown to the lay public of today, partly because most theories advanced in medieval science are today obsolete, and partly because of the stereotype of Middle Ages as supposedly "Dark Ages".
[edit] Early Middle Ages
See also: Medieval medicine, Medieval philosophy
The Western Roman Empire, although united by Latin as a common language, still harbored a great number of different cultures that were not completely assimilated by the Roman culture. Debilitated by migrations, barbarian invasions and the political disintegration of Rome in the 5th century, and isolated from the rest of the world by the spread of Islam in the 7th century, the European West became a tapestry of rural populations and semi-nomad peoples. The political instability and the downfall of urban life had a strong, negative impact on the cultural life of the continent. The Catholic Church, being the only institution to survive the process, maintained what was left of intellectual strength, especially through monasticism.
In the ancient world, Greek was the primary language of science. Even under the Roman Empire, Latin texts were mainly compilations drawing on earlier Greek work; while advanced scientific research and teaching continued to be carried on in the Hellenistic side of the empire, in Greek. Late Roman attempts to translate Greek writings into Latin had limited success.[1]
As the knowledge of Greek declined during the transition to the Middle Ages, the Latin West found itself cut off from its Greek philosophical and scientific roots. Most scientific inquiry came to be based on information gleaned from sources which were often incomplete and posed serious problems of interpretation. Latin-speakers who wanted to learn about science had access to only a couple of books by Boethius (c. 470-524) and the works of other Latin encyclopedists. Much had to be gleaned from non-scientific sources: Roman surveying manuals were read for what geometry was included.[2]
Deurbanization reduced the scope of education and by the sixth century teaching and learning moved to monastic and cathedral schools, with the center of education being the study of the Bible.[3] Education of the laity survived modestly in Italy, Spain, and the southern part of Gaul, where Roman influences were most long-lasting. In the seventh century, learning began to emerge in Ireland and the Celtic lands, where Latin was a foreign language and Latin texts were eagerly studied and taught.[4]
The leading scholars of the early centuries were clergyman for whom the study of nature was but a small part of their interest. They lived in an atmosphere which provided little institutional support for the disinterested study of natural phenomena and they concentrated their attention on religious topics. The study of nature was pursued more for practical reasons than as an abstract inquiry: the need to care for the sick led to the study of medicine and of ancient texts on drugs,[5] the need for monks to determine the proper time to pray led them to study the motion of the stars,[6] the need to compute the date of Easter led them to study and teach rudimentary mathematics and the motions of the Sun and Moon.[7] Modern readers may find it disconcerting that sometimes the same works discuss both the technical details of natural phenomena and their symbolic significance.[8]
Around 800, the first attempt at rebuilding Western culture occurred (see: Carolingian Renaissance). Charles the Great, having succeeded at uniting a great portion of Europe under his domain, and in order to further unify and strengthen the Frankish Empire, decided to carry out a reform in education. The English monk Alcuin of York elaborated a project of scholarly development aimed at resuscitating classical knowledge by establishing programs of study based upon the seven liberal arts: the trivium, or literary education (grammar, rhetoric and dialectic) and the quadrivium, or scientific education (arithmetic, geometry, astronomy and music). From the year 787 on, decrees began to circulate recommending, in the whole empire, the restoration of old schools and the founding of new ones. Institutionally, these new schools were either under the responsibility of a monastery, a cathedral or a noble court.
However, the 840s saw renewed disorder, with the breakup of the Frankish Empire and the beginning of a new cycle of barbarian raids. The significance of Charlemagne's educational measures would only be felt centuries later. The teaching of dialectic (a discipline that corresponds to today's logic) was responsible for the rebirth of the interest in speculative inquiry; from this interest would follow the rise of the Scholastic tradition of Christian philosophy. Moreover, in the 12th and 13th century, many of those schools founded under the auspices of Charles the Great, especially cathedral schools, would become universities.
[edit] High Middle Ages
See Also: Renaissance of the 12th century, Medieval technology
By the year 1000 AD, Europe remained a backwater compared to other civilizations such as Islam, or China. Constantinople has a population of about 300,000, but Rome has a mere 35,000 and Paris 20,000. [1][2] By the time, however, Christianization of the continent is making rapid progress and will prove itself the long-term solution to the problem of barbarian raiding. Western Europe became more politically organized and would see a rapid increase in population during the next centuries, which brought about great social and political change from the preceding era.
The cultural scenario starts to change when the contact with the Arabs after the Reconquista and during the Crusades allowed Europeans access to preserved copies of Greek and Roman works. During the 800s and 900s, a mass of classical Greek texts were translated by Muslim scholars into Arabic, followed by a flurry of commentaries by Islamic thinkers. Around 1050, further translation into Latin had begun in Northern Spain, and the recapture of Toledo and Sicily by the Christian kingdoms near the end of the century allowed the translation to begin in earnest by Christians, Jews, and Muslims alike. Scholars came from around Europe to aid in translation.
Gerard of Cremona is a good example of an Italian who came to Spain to copy a single text and stayed on to translate over a thousand works.[9] His biography described how he came to Toledo, "There, seeing the abundance of books in Arabic on every subject and regretting the poverty of the Latins in these things, he learned the Arabic language, in order to be able to translate." [2]
This period also saw the birth of medieval universities, which aided materially in the translation, preservation and propagation of the texts of the ancients and became a new infrastructure for scientific communities. Some of these new Universities were registered as an institution of international excellence by the Holy Roman Empire, receiving the title of Studium Generale. Most of the early Studia Generali were found in Italy, France, England, and Spain, and these were considered the most prestigious places of learning in Europe. This list quickly grew as new Universities were founded throughout Europe. As early as the 13th century, scholars from a Studium Generale were encouraged to give lecture courses at other institutes across Europe and to share documents, and this led to the current academic culture seen in modern European universities.
The rediscovery of the works of Aristotle through medieval Jewish and Muslim Philosophy (Maimonides, Avicenna, and Averroes) allowed the full development of the new Christian philosophy and method of scholasticism. By 1200 there were reasonably accurate Latin translations of the main works of Aristotle, Plato, Euclid, Ptolemy, Archimedes and Galen, that is, of all the intellectually crucial ancient authors except Thucydides. During the thirteenth century the natural philosophy of these texts began to be extended by notable Scholastics such as Robert Grosseteste, Roger Bacon, Albertus Magnus, and Duns Scotus.
Scholastics believed in empiricism and supporting Roman Catholic doctrines through secular study, reason, and logic. The most famous was Thomas Aquinas (later declared a "Doctor of the Church"), who led the move away from the Platonic and Augustinian and towards Aristotelianism (although natural philosophy was not his main concern). Meanwhile, precursors of the modern scientific method can be seen already in Grosseteste's emphasis on mathematics as a way to understand nature and in the empirical approach admired by Roger Bacon.
Grosseteste was the founder of the famous Oxford franciscan school. He was the first scholastic to fully understand Aristotle's vision of the dual path of scientific reasoning. Concluding from particular observations into a universal law, and then back again: from universal laws to prediction of particulars. Grosseteste called this "resolution and composition". Further, Grosseteste said that both paths should be verified through experimentation in order to verify the principals. These ideas established a tradition that carried forward to Padua and Galileo Galilei in the 17th century.
Under the tuition of Grosseteste and inspired by the writings of Arab alchemists who had preserved and built upon Aristotle's portrait of induction, Bacon described a repeating cycle of observation, hypothesis, experimentation, and the need for independent verification. He recorded the manner in which he conducted his experiments in precise detail so that others could reproduce and independently test his results - a cornerstone of the scientific method, and a continuation of the work of researchers like Al Battani.
Bacon and Grosseteste conducted investigations into optics, although much of it was similar to what was being done at the time by Arab scholars. Bacon did make a major contribution to the development of science in medieval Europe by writing to the Pope to encourage the study of natural science in university courses and compiling several volumes recording the state of scientific knowledge in many fields at the time. He described the possible construction of a telescope, but there is no strong evidence of his having made one.
[edit] Late Middle Ages
The first half of the 14th century saw the scientific work of great thinkers. The logic studies by William of Occam led him to postulate the principle known today as Occam's Razor. According to Occam, philosophy should only concern itself with subjects on which it could achieve real knowledge, a principle often referred to as parsimony. This should lead to a decline in fruitless debates and move philosophy toward experimental science.
By the time, some scholars, such as Jean Buridan, started to question the received wisdom of Aristotle's mechanics, he developed the theory of impetus which was the first step towards the modern concept of inertia. Buridan anticipated Isaac Newton when he wrote:
- ...after leaving the arm of the thrower, the projectile would be moved by an impetus given to it by the thrower and would continue to be moved as long as the impetus remained stronger than the resistance, and would be of infinite duration were it not diminished and corrupted by a contrary force resisting it or by something inclining it to a contrary motion
Thomas Bradwardine and his partners, the Oxford Calculators of Merton College, distinguished kinematics from dynamics, emphasizing kinematics, and investigating instantaneous velocity. They first formulated the mean speed theorem: a body moving with constant velocity travels distance and time equal to an accelerated body whose velocity is half the final speed of the accelerated body. They also demonstrated this theorem -- essence of "The Law of Falling Bodies" -- long before Galileo is credited with this.
In his turn, Nicole Oresme showed that the reasons proposed by the physics of Aristotle against the movement of the earth were not valid and adduced the argument of simplicity for the theory that the earth moves, and not the heavens. In the whole of his argument in favor of the earth's motion Oresme is both more explicit and much clearer than that given two centuries latter by Copernicus. He was also the first to assume that color and light are of the same nature and the discoverer of the curvature of light through atmospheric refraction; even though, up to now, the credit for this latter achievement has been given to Hooke.
The historian of science Ronald Numbers notes that the modern scientific assumption of methodological naturalism can be also traced back to the work of these medieval thinkers:
- By the late Middle Ages the search for natural causes had come to typify the work of Christian natural philosophers. Although characteristically leaving the door open for the possibility of direct divine intervention, they frequently expressed contempt for soft-minded contemporaries who invoked miracles rather than searching for natural explanations. The University of Paris cleric Jean Buridan (a. 1295-ca. 1358), described as "perhaps the most brilliant arts master of the Middle Ages," contrasted the philosopher’s search for "appropriate natural causes" with the common folk’s erroneous habit of attributing unusual astronomical phenomena to the supernatural. In the fourteenth century the natural philosopher Nicole Oresme (ca. 1320-82), who went on to become a Roman Catholic bishop, admonished that, in discussing various marvels of nature, "there is no reason to take recourse to the heavens, the last refuge of the weak, or demons, or to our glorious God as if He would produce these effects directly, more so than those effects whose causes we believe are well known to us." [10]
However, a series of events that would be known as the Crisis of the Late Middle Ages was under its way. When came the Black Death of 1348, it sealed a sudden end to the previous period of massive scientific change. The plague killed a third of the people in Europe, especially in the crowded conditions of the towns, where the heart of innovations lay. Recurrences of the plague and other disasters caused a continuing decline of population for a century.
[edit] Renaissance of the 15th century
- See also: History of science in the Renaissance
The 15th century saw the beginning of the cultural movement of the Renaissance.
The rediscovery of ancient texts was accelerated after the Fall of Constantinople, in 1453, when many Byzantine scholars had to seek refuge in the West, particularly Italy. Also, the invention of printing was to have great effect on European society: the facilitated dissemination of the printed word democratized learning and allowed a faster propagation of new ideas.
But this initial period is usually seen as one of scientific backwardness. There were no new developments in physics or astronomy, and the reverence for classical sources further enshrined the Aristotelian and Ptolemaic views of the universe. Humanism stressed that nature came to be viewed as an animate spiritual creation that was not governed by laws or mathematics. At the same time philosophy lost much of its rigour as the rules of logic and deduction were seen as secondary to intuition and emotion.
It would not be until the Renaissance moved to Northern Europe that science would be revived, with such figures as Copernicus, Francis Bacon, and Descartes (though Descartes is often described as an early Enlightenment thinker, rather than a late Renaissance one).
[edit] Great names of science in medieval Europe
Bede the Venerable (ca. 672-735), monk of the monasteries of Wearmouth and Jarrow who wrote a work On the Nature of Things, several books on the mathematical / astronomical subject of computus, the most influential entitled On the Reckoning of Time. He made original discoveries concerning the nature of the tides and his works on computus became required elements of the training of clergy, and thus greatly influenced early medieval knowledge of the natural world.
Robert Grosseteste (1168-1253), Bishop of Lincoln, was the central character of the English intellectual movement in the first half of the 13th century and is considered the founder of scientific thought in Oxford. He had a great interest in the natural world and wrote texts on the mathematical sciences of optics, astronomy and geometry. In his commentaries on Aristotle's scientific works, he affirmed that experiments should be used in order to verify a theory, testing its consequences. Roger Bacon was influenced by his work on optics and astronomy.[11]
Albert the Great (1193-1280), Doctor Universalis, was one of the most prominent representatives of the philosophical tradition emerging from the Dominican Order. He is one of the thirty-three Saints of the Catholic Church honored with the title of Doctor of the Church. He became famous for his vast knowledge and for his defence of the pacific coexistence between science and religion. Albert was an essential figure in introducing Greek and Islamic science into the medieval universities, although not without hesitation with regard to particular Aristotelian theses. In one of his most famous sayings he asserted: "Science does not consist in ratifying what others say, but of searching for the causes of phenomena." Thomas Aquinas was his most famous pupil.
Roger Bacon (1214-1294), Doctor Admirabilis, joined the Franciscan Order around 1240 where, influenced by Grosseteste, he dedicated himself to studies where he implemented the observation of nature and experimentation as the foundation of natural knowledge. Bacon was responsible for making the concept of "laws of nature" widespread, and contributed in such areas as mechanics, geography and, most of all, optics.
The optical research of Grosseteste and Bacon made possible the beginning of the fabrication of eyeglasses at the end of the 13th century. The same research would also prove invaluable for the later invention of such instruments as the telescope and the microscope.
Thomas Aquinas (1227-1274), Doctor Angelicus, was an Italian theologian and friar in the Dominican Order. As his mentor Albert the Great, he is a Catholic Saint and Doctor of the Church. His interests were not only in philosophy; he was also interested in alchemy, having written an important treatise titled Aurora Consurgens. However, his greatest contribution to the scientific development of the period was having been mostly responsible for the incorporation of Aristotelianism into the Scholastic tradition, and in particular his Commentary on Aristotle's Physics was responsible for developing one of the most important innovations in the history of physics, first posited by his mentor Averroes for celestial bodies only, namely the notion of the inertial resistant mass of all bodies universally, subsequently further developed by Kepler and Newton in the 17th century. (See Pierre Duhem's analysis The 12th century birth of the notion of mass which advised modern mechanics. from his Systeme Du Monde at [3])
John Duns Scotus (1266-1308), Doctor Subtilis, was a member of the Franciscan Order, philosopher and theologian. Emerging from the academic environment of the University of Oxford. where the presence of Grosseteste and Bacon was still palpable, he had a different view on the relationship between reason and faith as that of Thomas Aquinas. For Duns Scotus, the truths of faith could not be comprehended through the use of reason. Philosophy, hence, should not be a servant to theology, but act independently. He was the mentor of one of the greatest names of philosophy in the Middle Ages: William of Ockham.
William of Ockham (1285-1350), o Doctor Invincibilis, was an English Franciscan friar, philosopher, logician and theologian. Ockham defended the principle of parsimony, which could already be seen in the works of his mentor Duns Scotus. His principle later became known as Occam's Razor and states that if there are various equally valid explanations for a fact, then the simplest one should be chosen. This became a foundation of what would come to be known as the scientific method and one of the pilars of reductionism in science. Ockham probably died of the Black Plague. Jean Buridan and Nicole Oresme were his followers.
Jean Buridan (1300-1358) was a French philosopher and priest. Although he was one of the most famous and influent philosophers of the late Middle Ages, his work today is not renowned by people other than philosophers and historians. One of his most significant contributions to science was the development of the theory of Impetus, that explained the movement of projectiles and objects in free-fall. This theory gave way to the dynamics of Galileo Galilei and for Isaac Newton's famous principle of Inertia.
Nicole Oresme (c.1323-1382) was an intellectual genius and perhaps the most original thinker of the 14th century. A theologian and Bishop of Lisieux, he was one of the principal propagators of the modern sciences. Notwithstanding his strictly scientific contributions, Oresme strongly opposed astrology and speculated about the possibility of extraterrestrial life. He was the last great European intellectual to live before the Black Plague, an event that had a very negative impact in the intellectual life of the ending period of the Middle Ages.
[edit] Science in Asia
[edit] Islamic science
- Main article: Islamic science
In the Middle East, Greek philosophy was able to find some short-lived support by the newly created Islamic Caliphate (Islamic Empire). With the spread of Islam in the 7th and 8th centuries, a period of Islamic scholarship lasted until the 15th century. In the Islamic World, the Middle Ages is known as the Islamic Golden Age, when Islamic civilization and Islamic scholarship flourished. This scholarship was aided by several factors. The use of a single language, Arabic, allowed communication without need of a translator. Translations of Greek texts from Egypt and the Byzantine Empire, and Sanskrit texts from India, provided Islamic scholars a knowledge base to build upon. In addition, there was the Hajj. This annual pilgrimage to Makkah facilitated scholarly collaboration by bringing together people and new ideas from all over the Islamic world.
In Islamic versions of early scientific method, ethics played an important role. Islamic scholars used previous work in medicine, astronomy and mathematics as bedrock to develop new fields like alchemy. In mathematics, the Islamic scholar Muhammad ibn Musa al-Khwarizmi gave his name to what we now call an algorithm, and the word algebra is derived from al-jabr, the beginning of the name of one of his publications in which he developed a system of solving quadratic equations. Researchers like Al-Batani (850-929) contributed to the fields of astronomy and mathematics and Al-Razi to chemistry. Examples of fruits of these contributions can be seen in Damascus steel (wootz steel). Arab alchemy proved to be an inspiration to Roger Bacon, and later to Isaac Newton. Also in astronomy, Al-Batani improved the measurements of Hipparchus, preserved in the translation of the Greek Hè Megalè Syntaxis (the great treatise) translated as Almagest. About 900, Al-Batani improved the precision of the measurement of the precession of the earth's axis, thus continuing a millennium's legacy of measurements in his own land (Babylonia and Chaldea- the area now known as Iraq).
[edit] Indian science
Prior to the Middle Ages, Indian philosophers in ancient India developed atomic theories, which included formulating ideas about the atom in a systematic manner and propounding ideas about the atomic constitution of the material world. The principle of relativity was also available in an early embryonic form in the Indian philosophical concept of "sapekshavad". The literal translation of this Sanskrit word is "theory of relativity" (not to be confused with Einstein's theory of relativity).
By the beginning of the Middle Ages, the wootz, crucible and stainless steels were invented in India. The spinning wheel used for spinning thread or yarn from fibrous material such as wool or cotton was invented in the early Middle Ages. By the end of the Middle Ages, iron rockets were developed in the kingdom of Mysore in South India.
The mathematician and astronomer Aryabhata in 499 propounded a heliocentric solar system of gravitation where he presented astronomical and mathematical theories in which the Earth was taken to be spinning on its axis and the periods of the planets were given as elliptical orbits with respect to the sun. He also believed that the moon and planets shine by reflected sunlight and that the orbits of the planets are ellipses. He carried out accurate calculations of astronomical constants based on this system, such as the periods of the planets, the circumference of the earth, the solar eclipse and lunar eclipse, the time taken for a single rotation of the Earth on its axis, the length of earth's revolution around the sun, and the longitudes of planets. He also introduced a number of trigonometric functions (including sine, versine, cosine and inverse sine), trigonometric tables, and techniques and algorithms of algebra. Arabic translations of his texts were available in the Islamic world by the 8th-10th century.
In the 7th century, Brahmagupta briefly described the law of gravitation, and recognized gravity as a force of attraction. He also lucidly explained the use of zero as both a placeholder and a decimal digit, along with the Hindu-Arabic numerals now used universally throughout the world. Arabic translations of his texts (around 770) introduced this number system to the Islamic world, where it was adapted as Arabic numerals. Islamic scholars carried knowledge of this number system to Europe by the 10th century and it has now displaced all older number systems throughout the world.
The Siddhanta Shiromani was a mathematical astronomy text written by Bhaskara in the 12th century. The 12 chapters of the first part cover topics such as: mean longitudes of the planets; true longitudes of the planets; the three problems of diurnal rotation; syzygies; lunar eclipses; solar eclipses; latitudes of the planets; risings and settings; the moon's crescent; conjunctions of the planets with each other; conjunctions of the planets with the fixed stars; and the patas of the sun and moon. The second part contains thirteen chapters on the sphere. It covers topics such as: praise of study of the sphere; nature of the sphere; cosmography and geography; planetary mean motion; eccentric epicyclic model of the planets; the armillary sphere; spherical trigonometry; ellipse calculations; first visibilities of the planets; calculating the lunar crescent; astronomical instruments; the seasons; and problems of astronomical calculations.
From the 12th century, Bhaskara, Madhava, and various Kerala School mathematicians first conceived of mathematical analysis, differential calculus, concepts of integral calculus, infinite series, power series, Taylor series, trigonometric series, floating point numbers, and many other concepts foundational to the overall development of calculus and analysis.
[edit] Chinese science
- Main article: Science and technology in China
The solid-fuel rocket was invented in China about 1150, about 200 years after the invention of gunpowder (which was its main fuel) and 500 years after the invention of the match. At the same time that the age of exploration was occurring in the West, the Chinese emperors of the Ming Dynasty also sent ships, some reaching Africa. But the enterprises were not further funded, halting further exploration and development. When Magellan's ships reached Brunei in 1521, they found a wealthy city that had been fortified by Chinese engineers, protected by a breakwater. Antonio Pigafetta noted that much of the technology of Brunei was equal to Western technology of the time. Also, there were more cannons in Brunei than on Magellan's ships, and the Chinese merchants to the Brunei court had sold them spectacles and porcelain, which were rarities in Europe. The scientific base for these technological developments appears to be quite thin, however. For example, the concept of force was not clearly formulated in Chinese texts of the period.
[edit] Notes
- ^ William Stahl, Roman Science, (Madison: Univ. of Wisconsin Pr.) 1962, see esp. pp. 120-133.
- ^ a b Edward Grant (1996). The Foundations of Modern Science in the Middle Ages. Cambridge University Press. ISBN 0-521-56137-X.
- ^ Pierre Riché, Education and Culture in the Barbarian West: From the Sixth through the Eighth Century, (Columbia: Univ. of South Carolina Pr., 1976), pp. 100-129).
- ^ Pierre Riché, Education and Culture in the Barbarian West: From the Sixth through the Eighth Century, (Columbia: Univ. of South Carolina Pr., 1976), pp. 307-323).
- ^ Linda E. Voigts, "Anglo-Saxon Plant Remedies and the Anglo-Saxons," Isis, 70(1979):250-268; reprinted in M. H. Shank, ed., The Scientific Enterprise in Antiquity and the Middle Ages, (Chicago: Univ. of Chicago Pr., 2000).
- ^ Stephen C. McCluskey, "Gregory of Tours, Monastic Timekeeping, and Early Christian Attitudes to Astronomy," Isis, 81(1990):9-22; reprinted in M. H. Shank, ed., The Scientific Enterprise in Antiquity and the Middle Ages, (Chicago: Univ. of Chicago Pr., 2000).
- ^ Stephen C. McCluskey, Astronomies and Cultures in Early Medieval Europe, (Cambridge: Cambridge Univ. Pr., 1998), pp. 149-57.
- ^ Faith Wallis, "'Number Mystique' in Early Medieval Computus Texts," pp. 179-99 in T. Koetsier and L. Bergmans, eds. Mathematics and the Divine: A Historical Study, (Amsterdam: Elsevier, 2005).
- ^ Howard R. Turner (1995). Science in Medieval Islam:An Illustrated Introduction. University of Texas Press. ISBN 0-292-78149-0.
- ^ Ronald L. Numbers (2003). "Science without God: Natural Laws and Christian Beliefs." In: When Science and Christianity Meet, edited by David C. Lindberg, Ronald L. Numbers. Chicago: University Of Chicago Press, p. 267.
- ^ A. C. Crombie, Robert Grosseteste and the Origins of Experimental Science 1100-1700, (Oxford: Clarendon Press, 1971)
[edit] References
- Crombie, A. C. [1952] (1969). Augustine to Galileo: The History of Science A.D. 400 - 1650, Revised edition, Penguin. ISBN 0-14-055074-7.
- Grant, E. The Foundations of Modern Science in the Middle Ages: Their Religious, Institutional and Intellectual Contexts. Cambridge: Cambridge Univ. Pr., 1996. ISBN 0-521-56762-9
- Grant, E., ed. A Sourcebook in Medieval Science. Cambridge: Harvard Univ. Pr., 1974. ISBN 0-674-82360-5
- Lindberg, David C. (1992). The Beginnings of Western Science. Chicago: University of Chicago Press. ISBN 0-226-48230-8.
- Lindberg, David C., ed. Science in the Middle Ages. Chicago: Univ. of Chicago Pr., 1976. ISBN 0-226-48233-2
- Shank, M. H., ed. The Scientific Enterprise in Antiquity and the Middle Ages. Chicago: Univ. of Chicago Pr., 2000. ISBN 0-226-74951-7
- Walsh, James Joseph. The Popes and Science; the History of the Papal Relations to Science During the Middle Ages and Down to Our Own Time, Fordam University Press, 1908 - Google Books Reprinted 2003, Kessinger Publishing. ISBN 0-7661-3646-9 Reviews: [4][5]
[edit] External links
- Medieval Science Page (a comprehensive set of links to Internet resources of medieval science)
- Medieval Science, the Church and Universities
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