The revival of learning in Western Europe

While Islamic scholarship flourished, learning in Western Europe stagnated. The disintegration of the Roman Empire resulted in the almost total disappearance of the Greek language and, thus, most of the great Greek scientific works were inaccessible to European scholars. A few secondary works had been translated into Latin, including the first part of Plato's Timaeus - which

Described in detail in Kennedy (1990).

represented the main source of knowledge concerning Greek cosmology - and a few Latin works (e.g. Pliny the Elder's Natural History (first century) and Martianus Capella's popular mythological allegory The Marriage of Philology and Mercury (fifth century)) described some basic astronomy. Euclidean geometry was available only through an incomplete sixth-century translation by Boethius, and the detailed Ptolemaic theory of the heavens appears to have been completely unknown. Time-keeping, both on a daily basis and for fixing religious observances within the calendar was, of course, very important and the ability to do this had to be maintained. In the eighth century the Venerable Bede, who lived in northern England, wrote works on this subject that were used for over 1000 years.

Trade routes between Western Christendom and the Arab world had been established by the ninth century, but the transmission of scientific knowledge to the West did not really begin until contact with Islamic scholarship was made when European scholars started visiting Spanish monasteries in the eleventh century. Latin translations of previously unknown works began to be made from about 1000, the rate at which they appeared reaching a peak in the twelfth century - often referred to as the 'century of translation'. The Spanish city of Toledo was conquered by Alfonso VI in 1085 and, in the twelfth century, became the main centre for translation from Arabic into Latin. Many of the works that were translated were highly technical, and specialized words which were not understood were often simply transliterated. Some of these words now form part of our technical vocabulary, such as 'zenith' and 'nadir' (the nadir is the point on the celestial sphere diametrically opposed to the zenith). Aristotelian natural philosophy was rendered into Latin through translations of his Meteorology, Physics and On the Heavens; Europe became aware of the enormous achievements of the Greeks in mathematics through translations of Euclid, Archimedes and Apollonius, and as far as astronomy was concerned, scholars at last were able to appreciate the sophistication of Ptolemy's Almagest -translated in 1175 by Gerard of Cremona - as well as the results of the previous 400 years of Islamic endeavour.37 From the end of the twelfth century, more and more translations were made direct from the original Greek texts, rather than through the intermediate Arabic translations.

Also significant was the introduction into Europe of the Hindu-Arabic numerals by Leonardo of Pisa (better known as Fibonacci). Leonardo spent a great deal of his early life travelling around the Mediterranean and came into

For details of early medieval astronomy, see, for example, Eastwood (1997),

McCluskey (1998).

A list of translations made during this period can be found in Crombie (1959).

contact with the mathematics of the Islamic world. It was problems that arose in the world of commerce that provided the motivation for his own work but its influence was much broader. In his widely read Book of Calculation (1202), he described algorithms by which all the basic operations of arithmetic could be performed on numbers written using the decimal positional system. (This was for integers only; it would be another 400 years or so before decimal fractions were introduced.) Fibonacci also introduced Europeans to the algebraic techniques of men such as al-KhwàrizmT

Works such as the Almagest intrinsically were difficult, and the problems often were exacerbated in the Latin translations. As a result, a number of greatly simplified versions began to appear, e.g. the many manuscripts going by the name Theory of the Planets but only containing simple descriptions of epicyclic motion, and the hugely popular On the Sphere by Johannes de Sacrobosco.38 Sacrobosco's book, which was used in schools until the early seventeenth century, was very short and contained the basic results of geocentric astronomy. The work has four sections, but only the final part contained information on the Ptolemaic theories for the Sun, Moon and planets, and the treatment was extremely rudimentary. Many commentaries on On the Sphere were written, some of which were attempts to supplement the brief details of the original work, but the first complete account of Ptolemy's astronomical system that was actually written in the West, which included numerical details from the Almagest as well as the physical interpretation from the Planetary Hypotheses, was written by

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