<P> Legal studies advanced during the 12th century . Both secular law and canon law, or ecclesiastical law, were studied in the High Middle Ages . Secular law, or Roman law, was advanced greatly by the discovery of the Corpus Juris Civilis in the 11th century, and by 1100 Roman law was being taught at Bologna . This led to the recording and standardisation of legal codes throughout Western Europe . Canon law was also studied, and around 1140 a monk named Gratian (fl . 12th century), a teacher at Bologna, wrote what became the standard text of canon law--the Decretum . </P> <P> Among the results of the Greek and Islamic influence on this period in European history was the replacement of Roman numerals with the decimal positional number system and the invention of algebra, which allowed more advanced mathematics . Astronomy advanced following the translation of Ptolemy's Almagest from Greek into Latin in the late 12th century . Medicine was also studied, especially in southern Italy, where Islamic medicine influenced the school at Salerno . </P> <P> In the 12th and 13th centuries, Europe produced economic growth and innovations in methods of production . Major technological advances included the invention of the windmill, the first mechanical clocks, the manufacture of distilled spirits, and the use of the astrolabe . Concave spectacles were invented around 1286 by an unknown Italian artisan, probably working in or near Pisa . </P> <P> The development of a three - field rotation system for planting crops increased the usage of land from one half in use each year under the old two - field system to two - thirds under the new system, with a consequent increase in production . The development of the heavy plough allowed heavier soils to be farmed more efficiently, aided by the spread of the horse collar, which led to the use of draught horses in place of oxen . Horses are faster than oxen and require less pasture, factors that aided the implementation of the three - field system . </P>

What describes the pattern of the black death during the middle ages