The transmission of Greek and Arabic learning
In the 11th century a new phase of mathematics began with the translations from Arabic. Scholars throughout Europe went to Toledo, Córdoba, and elsewhere in Spain to translate into Latin the accumulated learning of the Muslims. Along with philosophy, astronomy, astrology, and medicine, important mathematical achievements of the Greek, Indian, and Islāmic civilizations became available in the West. Particularly important were Euclid's Elements, the works of Archimedes, and al-Khwārizmī's treatises on arithmetic and algebra. Western texts called algorismus (a Latin form of the name al-Khwārizmī), introduced the Hindu-Arabic numerals and applied them in calculations. Thus modern numerals first came into use in universities and then became common among merchants and other laymen. It should be noted that, up to the 15th century, calculations were often performed with board and counters. Reckoning with Hindu-Arabic numerals was used by merchants at least from the time of Leonardo of Pisa (beginning of the 13th century) first in Italy, then in the trading cities of southern Germany and France, where maestri d'abbaco or Rechenmeister taught commercial arithmetic in the various vernaculars. Some schools were private, while others were run by the community.
I. Read the passage and answer the questions:
1. What did a new phase of mathematics begin with?
2. Due to what important mathematical achievements of the Greek, Indian, and Islāmic civilizations became available in the West?
3. What writings were particularly important?
4. What did Western texts introduce?
5. How did modern numerals come into use?
6. Since what time was reckoning with with Hindu-Arabic numerals used?
II. How will you define the main idea of the passage? Comment on the development of mathematics in the 11th century.
Date: 2015-01-29; view: 824