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Philosophy and Conceptual History of Science in Taiwan pp 167–208Cite as

Chinese Mathematics at the Turn of the 19th Century: Jiao Xun, Wang Lai and Li Rui

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Part of the book series: Boston Studies in the Philosophy of Science ((BSPS,volume 141))

Abstract

As is well-known, ancient Chinese mathematics is basically ‘algorithmic’.1 That is, in justifying their methods and formulas, ancient Chinese mathematicians paid less attention to theoretical aspects of mathematics:rather they concentrate on the relevant algorithmic procedures. Once the numerical results were attained, they would therefore assume that everything was done. In particular, to the great Song-Yuan mathemanticians Qin Jiushao, Li Ye and Zhu Shijie, obtaining one positive, rational solution of a given algebraic equation with numerical coefficients would mean the problem was completely solved. They never went further to investigate whether the equation had other roots or what was the essential nature of the roots, etc. It was Wang Lai who for the first time in the history of Chinese mathematics confronted this problem while collating and studying the mathematical texts of Qin Jiushao and Li Ye in the academic milieu of the Qian-Jia school. In Book 5 of his Heng Zhai Suan Xue (‘Collected Mathematical Works of Wang Lai’), Wang Lai listed all the various types of quadratic and cubic equations and noted whether they had just one positive root or more than one.

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Authors
  1. Wann-Sheng Horng
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Editors and Affiliations

  1. Department of Philosophy, National Taiwan University, Taipei, Taiwan

    Cheng-Hung Lin   (林正弘)

  2. Institute of History, National Tsing-Hua University in Taiwan, Hsinchu, Taiwan

    Daiwie Fu   (傅大爲)

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© 1993 Springer Science+Business Media New York

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Horng, WS. (1993). Chinese Mathematics at the Turn of the 19th Century: Jiao Xun, Wang Lai and Li Rui. In: Lin, CH., Fu, D. (eds) Philosophy and Conceptual History of Science in Taiwan. Boston Studies in the Philosophy of Science, vol 141. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2500-0_10

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  • DOI: https://doi.org/10.1007/978-94-011-2500-0_10

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5103-3

  • Online ISBN: 978-94-011-2500-0

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