A History of Chinese Mathematics
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This book is made up of two parts, the first devoted to general, historical and cultural background, and the second to the development of each subdiscipline that together comprise Chinese mathematics. The book is uniquely accessible, both as a topical reference work, and also as an overview that can be read and reread at many levels of sophistication by both sinologists and mathematicians alike.
History of Chinese Mathematics in Western Languages 7 already been used in the 19th century by William Whewell (1794-1866), one of the pioneers of the history of science). Based on these presuppositions, he explained that the Chinese originality in mathematics should bc researched from the direction of algebra, in contrast to Western mathematics which is characterised by its geometric genius.27 Thus, with these premises he established a list of everything which, in his opinion, the West owed to
chkmonies, Paris, 1950, vol. 1, 2nd part, p. 673). See also Li Yan, Gudai, p. 21. 'The expression is due to Libbrecht (2), 1973, p. 5: "We have reason to believe that the 'independent mathematician' appears for the first time in the Sung, judging from what we can deduce from biographical data." 31bid. 4Libbrecht,op. cit., p. 62. 'See below, p. 152. 'See below, p. 159. 80 9. The Transmission of Knowledge family who preferred to remain independent rather than join the Manchu administration7 and
about Indian astronomy by questioning his contemporary, the famous monk, Hui Yan.3s We also know that the bibliography of the Suishu cites two mathematical (or perhaps numerological) works irremediably lost but obviously of Indian origin, the Poluomen suanfa (Computational Methods of the Brahmans) and the Poluomen suanjin,g (Computational Canon of the B r a h m a n ~ ) both , ~ ~ in three juan. In addition, the Shushu jzyz, one of the Ten Computational Canons of the Tang, uses Chinese terms
that night. Never before had I found m y knowledge of Euclid serve me so well. I went over i n memory the first book, proposition by proposition, and I was able to keep awake. Timothy Richard, Forty-Five Years i n China. London: T. Fisher Unwin Ltd., 1916, p. 42. We have already noted that prior to the 16th century, at the current stage of research, it is often impossible to determine exactly which parts of Chinese mathematics are borrowed and which are original developments. However, from the
si-shi ha y i liuqian liu-bai si-shi-sun ,wan qi-qian wu-bai; or, word for word: l/myriad/ 6/thousand/ 4/hundred/ 4/ten/ 8/hundred million/ 6/thousand/ 6/hundred/ 4/ten/myriad/ 7lthousandl 5/hundred). In this notation, the myriad plays a distinguished role, since it is used as a reference point for writing large numbers and dispenses with the need for special markers to transcribe one hundred thousand, one million, up to yi. In addition, 20, 30 and 40 may be transcribed in two different ways,