| 英文摘要 |
Liutou cheng 留頭乘 was a usual method of multiplication in rapid calculation by counting rods and in abacus arithmetic since the Yuan dynasty. Scholars have held different interpretations of the mnemonic rhyme and the history of liutou cheng, leaving several difficult questions awaiting our attention. The present article reexamines the development of liutou cheng and its methods of expression. By carefully analyzing the provided mnemonic rhymes, examples, and related captions concerning liutou cheng in ancient mathematics books, the article proves that the interpretations asserted by Li Peiye 李培業 and other scholars on the mnemonic rhyme of liutou cheng in Suanxue qimeng 算學啟蒙 (Introduction to Mathematics, 1299) are correct, whereas the explanations of Pan Fengxi 潘逢禧 and others do not accord with the original meaning of the mnemonic rhyme. This paper also proves that contrary to what several scholars have presumed, the caption under the title “chengfa” 乘法 (multiplication) in Jiuzhang suanfa bilei daquan 九章算法比類大全 (Comprehensive Collection of Analogical Methods of the Nine Chapters on Mathematical Methods, 1450) and several other books is not contradictory with the mnemonic rhyme; rather, among the examples in the mathematics books of the Ming dynasty, some are merely coincident with the mnemonic rhyme and caption, whereas others are not. These facets reflect the complexity of the compilations of ancient mathematics books. Finally, the present paper indicates that the content of liutou cheng found within Jiuzhang suanfa bilei daquan is based on earlier sources, and that the part regarding liutou cheng in Shuxue tonggui 數學通軌 (Clear Path to Mathematics, 1578) does not originate directly from Xiangming suanfa 詳明算法(Detailed and Clear Methods of Mathematics, earlier than 1369). |
本站僅提供期刊文獻檢索。
