Before we can finally move on to the actually subject of this series, The Renaissance, we first need to take a brief look at the European medieval university to which the Renaissance was to some extent a reaction. Actually, the European is superfluous as the medieval university is a unique European invention but it has become a bad habit in recent years to label different institutions of higher education from other cultures universities, particularly when claiming that they are older. Yes, other culture had institutes of higher education, many of them much earlier than the medieval universities. For example, the ancient Greek schools of philosophy were institutions of higher education. But the institutions of higher education of each culture have different roots, different structures and different aims and labelling them all universities is simply wrong. A madrasa is not a university and a university is not a madrasa. To use the term university exclusively for the medieval European institution also does not imply some sort of superiority, which some people try to suggest is what is wrong with this exclusive usage.
View of the Qarawiyyin Mosque on the skyline of central Fes el-Bali: the green-tiled roofs of the prayer hall and the minaret (white tower on the left) are visible.Founded by Fatima al-Fihri in 859 and falsely called the oldest university in the world Source: Wikimedia Commons
The European universities have their roots in the cathedral schools that began to appear in the seventh century, following the collapse of the Western Roman Empire. The education in these institutions was nominally based on the seven liberal arts, an educational ideal that goes back to the Pythagoreans. It consists of the trivium–grammar, logic and rhetoric–and the quadrivium–arithmetic, geometry, music and astronomy. However, if we look at the description of the quadrivium by Isidore of Seville (c. 560–636), in his Etymologiae, offered at the early cathedral schools, arithmetic, geometry and music are little more than a short list of empty definition with only astronomy having some substance as a discipline. This schools taught little more than Latin and the basics of Christian theology.
A page of Etymologiae, Carolingian manuscript (8th century), Source: Brussels, Royal Library of Belgium via Wikimedia Commons
The Carolingian Renaissance, which I described in the first post of this series was basically an upgrading of the cathedral schools to proper institutes of education with a fairly low level but much fuller curriculum. Between the tenth and twelfth centuries a series of great teaching masters very much raised the standard of cathedral schools and increased and improved the scientific content of the curriculum. These men attracted large numbers of students and trained other teaching masters. Amongst the most well-known were Gerbert of Arillac (c. 964–1003), Adalberon of Laon (d. 1030), John of Auxerre, Thierry of Chartres (d. c. 1150), Fulbert of Chartres (c.960–1128) a pupil of Gerbert, Peter Abelard (c. 1079–1142), Bernard of Chartres (d. after 1124), William of Conches (c. 1090–c. 1160) pupil of Bernard of Chartres, Clarenbold of Arras (c. 1110–c. 1187) also school of Chartres, and John of Salisbury (late 1110s–1180), a pupil of William of Conches. Most of these were Neo-Platonists heavily influenced by the Timaeus, one of the few Greek natural philosophy texts known throughout the Middle ages.
Chartres Cathedral by night Source: Wikimedia Commons
Europe saw some major changes in the period between 800 CE and 1200 CE, which was a comparatively stable political period. The major changes were in agriculture. In this period the most important innovation was the mouldboard plough and the related heavy plough. Along with this was the invention of the horse collar and the horseshoe, which meant that the horse could replace the ox as the ploughing animal. This meant that much heavier land could be used for crop production and ploughing took much less time. Another significant improvement was the introduction of a three-field rotation system to replace the earlier two-field one. This led to a major increase in food production, which in turn led to a large population increase.
Medieval horse drawn heavy plough Source: Wikimedia Commons
This was paralleled by a growth in the town and cities with more and more people moving from rural to urban residency. The same period saw a major economic upturn within Europe with a substantial increase in long distance trading and a move to a money-based economy.
These developments led to the transition of some of the cathedral schools to becoming the first universities. The towns and cities attracted increasing numbers of students looking for teachers and teachers looking for students. A major change came in the twelfth century with the rediscovery of the Corpus Juris Civilis. The codification of Roman law was originally created in the sixth century but almost totally disappeared during the Early Middle Ages. This reintroduced the concept of a corporation from the Latin corpus meaning body or body of people recognised as a legal entity. This led to merchant traders and artisans forming corporations, known in the case of artisans as guilds, with legally defined membership, giving the members a collective legal status and collective protection under the law.
German medieval guild symbols
The travelling students and masters, as individuals living in cities other than their hometowns and cities, had very little legal status or legal protection, so they too formed corporations, for which one Latin term was universitas, meaning whole or the whole. There were universitas magistrorum or universities of masters, universitas scholarium or universities of students and universitas magistrorum et scholarium or universities of masters and students.
universitas scholarium
Originally universitas referred to these corporate bodies and also to individual faculties, such as the faculty of arts, faculty of theology, faculty of law or faculty of medicine. The masters and students of each faculty forming their own corporation or universitas. The term for what we now call a university was studium generale, which was only applied to a school with at least three of the four traditional faculties or was a highly prestigious school such as Paris, Oxford and Bologna, or both.
At some point the term universitas ceased to be used for corporations of traders and crafts guilds being then only used for academic corporation, as a consequence universitas began to replace studium generale for the whole academic institution. The big three–Paris, Oxford and Bologna–were the first to become universities in something approaching the modern meaning of the term. As there was a gradual transition from cathedral school to university it is impossible to say exactly when any of them became a university, but it is general acknowledged that in each case it occurred before twelve hundred with Bologna the first medieval university. Bologna concentrated more on law and theology, whereas Paris and Oxford concentrated more on philosophy. By fifteen hundred there were about seventy European university with, in general, those in Northern Europe following the Paris-Oxford model and those in the South and Italy modelled on Bologna.
Bologna University Interior view of the Porticum and Loggia of its oldest College, the Royal Spanish College. Source: Wikimedia Commons
A full university had four faculties, arts, law, medicine and theology. The arts faculty was the undergraduate faculty where nominally the seven liberal arts determined the curriculum. Here the first degree, BA, usually took four years but many students left the university after only two years, without a degree, having acquired the basic minimum of an education. Those who stayed after completing a BA, went on to acquire and MA, which was the teaching qualification and usually required a further two years of study. It was these MAs, who taught the undergraduates. Those with a MA could now progress to one of the higher faculties, law, medicine and theology, progressing through BA and MA till they finally graduated with a doctorate. This course of studies took a substantial number of years, so the number of students, who followed this course always remained relatively small.
It is no coincidence that the emergence of the universities coincided with the highpoint of the translation movement or Scientific Renaissance, and the texts brought into the European sphere had a major influence on the curriculum of the new universities.
The newly acquired knowledge radically upgraded the quadrivium with the first six books of Euclid’s Elements becoming the geometry course, arithmetic remained anchored in Boethius’ De institutione arithmetica, which was largely a Latin translation of the Introduction to Arithmetic of the Neopythagorean Nicomachus of Gerasa (c. 60–c. 120 CE). This was complimented by the study of Algorismus, that is the Hindu-Arabic number system, used in computos, the calculation of the date of Easter. Music was also taken from Boethius’ De musica in turn based on a lost work of Nicomachus and Ptolemaeus’ Harmonica. Over the course of the next three centuries the works of Boethius were replaced by new texts written by medieval masters. Astronomy was largely taught according to John of Sacrobosco’s (c. 1195–c. 1256) Tractatus de Sphera (c. 1230). Sacrobosco taught at the university of Paris and also wrote a widely used Algorismus, De Arte Numerandi. Because Sacrobosco’s Sphera was very basic it was complimented with a Theorica planetarum, by an unknown medieval author, which dealt with elementary planetary theory and a basic introduction to the cosmos.
13th century Manuscript of Sacrobosco’s Tractatus de Sphera, manuscript also contains his Algorimus Source
It should, however, be noted that the commitment to actually teaching the quadrivium during the High Middle Ages was in practice very low at most medieval universities. Lectures on the quadrivium were often only held on holidays, when normal teaching was suspended. The quadrium subjects were normally not examination subjects and it was even the case at many universities that if a student did not have the credit for a quadrivium course, he could acquire it simply by paying the lecture fees.
The biggest change, however, was in the trivium, which became basically the works of Aristotle. Having acquired a fairly complete model of the world and everything in it, in the works of Aristotle, the medieval scholars adopted it. This meant that the natural philosophy taught at the universities consisted mainly of Aristotle’s physics, meaning the general study of nature, and his cosmology. This was not necessarily that simple, as the universities were institutions of the Church and Aristotle was a pagan and various aspects of his philosophy contradicted the Church’s teachings. The biggest stumbling block was that Aristotle believed in an eternal cosmos with no beginning, whereas a central tenet of Christianity was the creation of the world by God, as described in Genesis. There were other philosophical problems that we don’t need to analyse in detail here.
Given the conflicts there were various attempts by powerful figures in the Church, particularly in Paris, to try to ban the study of Aristotle in the universities. The most famous one being the list of 219 philosophical and theological propositions issued by the Bishop of Paris, Étienne Tempier (d. 1279) in 1277, which were contradictory to Christian belief and should not be taught at the university.
Bishop Étienne Tempier
All such prohibitions failed to have a real affect but did create an interesting new method of thought into the medieval discourse. Scholars began to discuss these banned theses hypothetically, i.e., what if the universe were eternal or what if the Earth rotated on its axis once a day and the sphere of the fixed stars were still. One important point is that medieval Aristotelean philosophy was not Aristotle’s philosophy. Things had changed and progressed over the centuries; the most well-known example is that the impetus theory had replaced Aristotle’s theory of projectile motion. Also, thought was not as static on the medieval university, as it is often described, especially by the humanist scholars rebelling against the Aristotelean tradition in the Renaissance.
In the higher faculties it is only the faculty of medicine that is of direct interest for the history of science, although as we saw above the theologians determined what was permitted and what not. The curriculum of the faculty of medicine was informed with translations from Greek physicians, mostly Galen and Hippocrates but the major influence was Arabic medical texts, which were also based on the works of Galen and Hippocrates. One of the biggest were The Canon of Medicine (Al-Qanun fi’t-Tibb) a five-volume medical encyclopaedia written by Ibn Sina, known in the Middle Ages as Avicenna, which remained a central European university text for several centuries.
The Canon of Medicine (Al-Qanun fi’t-Tibb) Ibn Sina, known in the Middle Ages as Avicenna
Another was Kitāb al-Ḥāwī fī al-ṭibb (The Comprehensive Book on Medicine) by Abū Bakr Muhammad Zakariyyā Rāzī, known in the Middle Ages as Rhazes. Another nine-volume medical encyclopaedia. There were also many other Arabic texts translated into Latin. This predominance of Arabic influence would come to play a role in the changes demanded during the Renaissance.
It is important to note that medieval university knowledge, even in medicine, was literary or book knowledge, that is totally theoretical without any practical aspects. Scholars challenged the ideas of other scholars with theoretical arguments not with experiments or newly acquired empirical evidence. As we shall see this is the basis for the major change that took place during the Renaissance.
The above is, of course, a simplified sketch of a process that should have a complete series of its own but I hope will suffice as a background to the changes that took place during the Renaissance the actual subject of this series.
The Renaissance Mathematicus 