[[alternative]]Number-Words and the Development of Arithmetic in Medieval Europe: with a Comparison of the "Method of Division" in China

[[abstract]]In Europe there were various number-words such as back-counting, over-counting and half-counting. They were expressed in indirect forms that hindered the development of arithmetic skills. The back-counting number-words had some imprints on Roman numerals. The form of Roman numerals is corresponding to the spoken numbers, both were inconvenient for hand calculation: when operating on the counting-board, the indirect-expression form of the number-words and symbolic-words need to be transformed into direct form of expression. The complementary methods used in subtraction, multiplication and division in the medieval Europe were affected by the back-counting number-words. The division method in medieval Europe was therefore complicated and difficult to practice. In Chinese language there is no back-counting number-words nor complementary method. The spoken-number and symbol-number in ancient China were the same (correspondingly equivalent), they were expressed in direct form numbers. The methods of multiplication and division in China are operated with the help of the "multiplication-table", this technique was used in ancient time as well as in nowadays. The idea of "division" in ancient China was derived from the measurement of rice-field ares: if you know the area (the number to be divided) and the one-side length of the rectangular (the number used to divide), then the length of another side can be calculated. Key Words: number-words, Medieval Europe, Arithmetic, complementary methods, division in ancient China[[fileno]]JA01_1997_p25