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題 名 | 語言數對歐洲中古算術的影響--兼論中國除法運算的特性=Number-Words and the Development of Arithmetic in Medieval Europe: With a Comparison of the "Method of Division" in China |
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作 者 | 陳良佐; | 書刊名 | 清華學報 |
卷 期 | 27:3 1997.09[民86.09] |
頁 次 | 頁257-286 |
分類號 | 311.1 |
關鍵詞 | 語言數; 歐洲中世紀; 四則運算; 補助法; 中國古代的除法; Number-words; Medieval europe; Arithmetic; Complementary methods; Division in ancient China; |
語 文 | 中文(Chinese) |
中文摘要 | 歐洲語言數有倒算、超算、半算等多種形式。這些語言數都是以間接形式表數, 不利於算術的發展。倒算語言數影響了羅馬符號數,羅馬符號表數制與語言數一致,不利於 筆算。在算板上運算時,間接表示的語言數和符號數需要轉化成直接表示的算子數。歐洲中 世紀的減、乘、除等運算所採用的「補足算法」是受了倒算語言數的影響。歐洲中世紀的除 法複雜、難學。中國古代語言數與符號數一致,都是直接表數。漢語沒有倒算語言數;因此 ,未曾出現「補足算法」。中國古代利用九九乘法表進行乘除運算,乘除法則原則上古今不 變。中國古代除法來自已知矩形土地的面積與一邊,求矩形面積的另一邊。 |
英文摘要 | 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 numberwords 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. |
本系統中英文摘要資訊取自各篇刊載內容。