Mathematics in humanistic schools and at the university had a theoretical focus that did not serve any practical purpose in the world of Renaissance commerce. Students planning to enter the business world needed another sort of mathematics, which would teach them how to determine the cost of merchandise, deal with the varying standards of weights and measures, measure for surveying, and handle similar problems of daily business. In practical mathematics each problem was reasoned through on its own, sometimes with educated
11.2 Allegory of Arithmetic. Woodcut by Gregor Reisch in the Margarita philosophica (Philosophical Pearl, 1504). (Bibliotheque de la Faculte de Medecine, Paris, France/Archives Charmet/Bridgeman Art Library)
Handbook to Life in Renaissance Europe
Guesses to test possible conclusions. The basic textbook for this study was Liber abbaci (Book of abaci, early 13 th century). Although the title was derived from the abacus used for calculations by sliding counters along rods, the reasoning process called abbaco in Italian was accomplished on paper. The book’s author was the medieval mathematician Leonardo Fibonacci (c. 1170-after 1240), or Leonardo of Pisa. A businessman who studied Arabic and visited Arab regions, Fibonacci was instrumental in popularizing the Hindu-Arabic systems of numerals in western Europe. These replaced the Roman numerals and made computation much simpler. Abbaco loosely translates as “accounting,” the single most important skill of any Renaissance merchant. Textbooks for teaching abbaco often included woodcut illustrations, such as pictorial tables for reckoning on the fingers while computing long division and multiplication. The fingers on the left hand were bent and straightened in various combinations while the right hand noted the answers on a piece of paper. The final stage of learning in abbaco mathematics was algebra, including the solving of cubic equations.
Apprenticeship
Apprenticing, which derives from the Latin word apprendere (to learn), was the system by which young men learned a trade. Many of today’s young people learn how to be a tradesperson, such as an electrician or plumber, by apprenticeship. in spite of the number of universities in Europe by 1500, the majority of people did not attend them; rather they learned to work with their hands or in a commercial activity such as banking. some of the greatest artists of the period never attended a university, absorbing their knowledge of color, line, form, and materials from master painters, sculptors, and builders. The apprenticeship system was rigorous, and today students might be shocked at the young age of novice apprentices (usually between 12 and 14 years of age) and the strict working conditions under which they labored for several years (occasionally as long as 12 years).
11.3 Carpenter’s apprentice cutting wood. This 15th-century French woodcut illustrates one of the menial tasks assigned to apprentices. (Bibliotheque des Arts Decoratils, Paris, France/Archives Charmet/Bridgeman Art Library)
World History
