Title

Number-Words and the Development of Arithmetic in M edieval Europe: with a Comparison of the “ Method of Division ” in China

Author

Liang-tso Chen

Genre

Article  

Pages

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Key words

number-words, Medieval Europe, Arithmetic, complementary methods, division in ancient 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 numer als 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 ex pression. 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 area: 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.