Horner's Method in Chinese Mathematics : Its Origins in the Root-Extraction Procedures of the Han Dynasty

Horner's Method in Chinese Mathematics : Its Origins in the Root-Extraction Procedures of the Han... HORNER'S METHOD IN CHINESE MATHEMATICS : ITS ORIGINS IN THE ROOT-EXTRACTION PROCEDURES OF THE HAN DYNASTY BY L. WANG (WANG LING & JOSEPH NEEDHAM University of Cambridge, England 1. Introduction It is now generally accepted by historians of mathematics that the method of Horner (1810) for solving higher numerical equations appeared in a substantially equivalent form in the works of the Sung algebraists such as Ch'in Chiu-shao (1247) 1). This method took its origin much earlier in the procedures for root extraction 1) D. E. Smith, (1925) vol. I, pp. 270, 73; vol. 2, p. 471; F. Cajori (I92¢), p. ;:71.; G. Sar- ton (1927); vol. 2, part 2, p. 626; vol. 3, part i, p. 7oi; Y. Mikami, p. 76. T'ollng Pao XLIII 23 346 of the Han dynasty. These are to be found in the "Nine Chapters of Mathematics" (Chiu Chang Suan Wi) but the text has long been very obscure, and it is the purpose of the present paper to attempt an explanation of its meaning. It has been pointed out by Mikami (1913), and later by Ch'ien Pao-tsung (1932) and Li Nien (1931) that there are distinct simil- arities between the ancient root-extraction methods http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png T'oung Pao Brill

Horner's Method in Chinese Mathematics : Its Origins in the Root-Extraction Procedures of the Han Dynasty

T'oung Pao, Volume 43 (1): 345 – Jan 1, 1954

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Publisher
Brill
Copyright
© 1954 Koninklijke Brill NV, Leiden, The Netherlands
ISSN
0082-5433
eISSN
1568-5322
D.O.I.
10.1163/156853254X00146
Publisher site
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Abstract

HORNER'S METHOD IN CHINESE MATHEMATICS : ITS ORIGINS IN THE ROOT-EXTRACTION PROCEDURES OF THE HAN DYNASTY BY L. WANG (WANG LING & JOSEPH NEEDHAM University of Cambridge, England 1. Introduction It is now generally accepted by historians of mathematics that the method of Horner (1810) for solving higher numerical equations appeared in a substantially equivalent form in the works of the Sung algebraists such as Ch'in Chiu-shao (1247) 1). This method took its origin much earlier in the procedures for root extraction 1) D. E. Smith, (1925) vol. I, pp. 270, 73; vol. 2, p. 471; F. Cajori (I92¢), p. ;:71.; G. Sar- ton (1927); vol. 2, part 2, p. 626; vol. 3, part i, p. 7oi; Y. Mikami, p. 76. T'ollng Pao XLIII 23 346 of the Han dynasty. These are to be found in the "Nine Chapters of Mathematics" (Chiu Chang Suan Wi) but the text has long been very obscure, and it is the purpose of the present paper to attempt an explanation of its meaning. It has been pointed out by Mikami (1913), and later by Ch'ien Pao-tsung (1932) and Li Nien (1931) that there are distinct simil- arities between the ancient root-extraction methods

Journal

T'oung PaoBrill

Published: Jan 1, 1954

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