1 Introduction

1 In the twentieth century, historians of science had recognized that Qin Jiushao's method for solving numerical higher degree equations was rediscovered separately by Ruffini and Horner in the early nineteenth century. However, according to a more recent argument by Stocchi (1998), Qin's method was more 'general' than that which was used by both Ruffini and Horner and was even simpler and more practical than all the methods known until the discovery of a general solution by G. Giovarosi (1889-1944).

2 Quoting from Libbrecht, U. (1973).

3 A vast amount on the subject of Chinese divination has been written. For a brief account see, for example, Needham, J. (1956), for a more detailed exposition see Smith, Richard J. (1991), and for a more recent approach from a different angle see Poo, Mu-chou (1998). Full-scale investigation of the subject is being carried out by the Divination, Science and Society in Mediaeval China project led by Marc Kalinowski and also at the Institute of History, National Tsing Hua University, Hsinchu, Taiwan.

4 For Chinese astrology, see Appendix I. See also Ho Peng Yoke (1965) and Ho Peng Yoke and Ho Koon-piu (1986). For divination, see Loewe, Michael (1988b).

5 See Ho Peng Yoke (1991c).

6 Xiangshu is rendered as 'Regularities underlying the Phenomena' in Sivin (1982) and 'the Doctrine of Images and Lines' in Fung Kam-wing (1987). There is as yet no generally adopted translation.

8 See Yan Dunjie (1985) and a Japanese translation by Hashimoto and Sakade in Science and Skills in Asia (Kyoto, 1982).

9 This work is not meant to replace the need for a full translation of Yang's works or other standard texts on the three cosmic boards. On the contrary, it is hoped that those who undertake such translations will find this work a useful reference.

10 See Fung Kam-Wing (1989) for an account of the publications of Yang Weide. Fung subsequently showed me a text by Yang that bears his official title as Director of the Astronomical Bureau.

Ill owe this point to M. Kalinowski.

12 Ho Peng Yoke (1988) gives an example of the application of the art of fate-calculation to check the date of a Song personality.

14 Wuli is the modern Chinese term for physics.

15 See Chang Yung-tang (1994) and Fung Kam-Wing (1989).

17 View expressed in Ho Peng Yoke (1998).

18 A verse entitled Li Weigong wang Jiangnan (Duke Wei Li Glancing the Region South of the Yangzi), containing references to the three cosmic boards, has been attributed to this famous Tang military commander. Jao, Tsung-i (1990) gives this work a Song origin.

19 No doubt there is a certain amount of inconvenience, but arbitrary enforcement of uniformity of romanization of Chinese personal names creates problems reminiscent of a futile attempt to standardize the spelling of English and Scottish names, especially when these versions have been adopted by the individuals officially.

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