If you were studying at, say, Cambridge, during the late Middle Ages, you would have been expected to master a fair amount of natural science and mathematics in order to gain an MA degree (which in those days was not a just freebie for those with BAs). But unlike today, you would have found everything you needed to know from books and lecturers rather than being expected to do any practical work. These books and lectures, of course, were all in Latin which was the only language students were allowed to speak at any time.
Mathematics and Geometry
Mathematics was broken down into four sub-subjects - arithmetic, geometry, music and astronomy – so it was known as the quadrivium. At Cambridge arithmetic meant learning how to do sums, extracting roots and solving equations. Surprisingly, though, it seems to have been very different at Oxford. There, you would have studied the properties of prime and perfect numbers with the aim of reaching a philosophical understanding of them rather than learning about practical applications. At both universities, music was devoted to the theory of ratios and harmony and consequently was not seen as a particularly useful subject. The evidence suggests many students paid no attention to it and the music lecturers sometimes asked to change their course because no one was turning up. Geometry was based squarely on the Elements of Euclid which is an ancient Greek textbook that can still be used with profit today. He starts from the simplest definitions and proceeds to erect the entire edifice of geometry onto this solid bedrock in logical and indisputable steps. So perfect was Euclid’s system that it was used as an analogy for the work of God when he produced the heavens.
Astronomy and Geography
The final of the four sub-subjects making up the quadrivium was astronomy. The greatest misconception about science in the Middle Ages is that people thought the earth was flat. In fact every educated person knew it was a sphere and they also believed that the whole vastness of the universe was the same shape. The most popular textbook for astronomy was by the Englishman, John Sacrobosco, who wrote a short treatise called The Sphere in the thirteenth century. This was especially for university students and it was still being used up to the scientific revolution as a basic introduction from which more advanced topics could be introduced. Sacrobosco, following the nearly unanimous opinion of the ancient Greeks, did place the earth at the centre of the universe but this made a lot of sense. After all, the earth is obviously not moving and if it were rushing through space as Copernicus required, presumably we would notice.
Geography was another subject, generally considered part of mathematics, that was becoming increasingly popular through the sixteenth century. Despite the discovery of the New World in 1492, the most popular textbooks had been written over a thousand years before by ancient Greeks and Romans. However, modern authors like the Germans, Peter Apian and Sebastian Münster, began to produce up-to-date books that made it part of their selling point to include all the latest details about Peru or Mexico. We find these being used side by side with the ancient authorities.
After mastering the quadrivium, students moved on to natural science proper. This was based almost entirely on the work of Aristotle, but after 1535 the English Government ordered the universities to stop using the old medieval commentaries and concentrate on the original texts or new works by humanists. Consequently, the scholastics, who had dominated philosophy for centuries, were hardly studied at Cambridge after this date. Instead the emphasis was on modern interpretations of Aristotle including a good deal of criticism of his thought. This meant that although Aristotle seemed to provide answers for everything about the universe, people realised that they were not necessarily the right ones.
Science and Religion
The influence of Christianity on Cambridge University in the Middle Ages was obviously profound, but it does not seem to have had a negative impact on the study of science. It was commonly believed at the time that by studying God’s creation and marvelling at his work, you were engaged in a religious duty. This meant that doing science was something that was of interest to even the most religious of men. As we have seen. the main effect of the Reformation was to give an opportunity for the syllabuses to be radically overhauled and most of the medieval texts removed from them. There is a famous story related by the antiquarian, Anthony à Wood, about the Protestant Reformers ransacking Oxford’s libraries for mathematical books they thought were Satanic. However, there is no evidence for that happening at Cambridge and the evidence from Oxford turns out to be pretty shaky as well. So, we should certainly dispose of the idea of religion holding back science even during a period when Christianity was the absolutely dominant social reality and the Reformation had heightened religious sensibilities even further.
In the end, the subjects being studied at Cambridge before the scientific revolution were nothing like modern science. But it was a period of rapid change when Platonic number theory was being replaced by practical arithmetic and algebra, when the classical view of the earth was being radically overhauled and when new knowledge and interpretations were often welcomed and studied. It was this that provided the foundations upon which the scientific revolution could be built.
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