• Journal for History of Mathematics
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• v.26 no.2_3
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• pp.123-130
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• 2013

It is well known that SuanXue QiMeng has given the greatest contribution to the development of Chosun mathematics and that the topics and their presentation including TianYuanShu in the book have been one of the most important backbones in the developement. The purpose of this paper is to reveal that Zhu ShiJie emphasized decidedly mathematical structures in his SuanXue QiMeng, which in turn had a great influence to Chosun mathematicians' structural approaches to mathematics. Investigating structural approaches in Chinese mathematics books before SuanXue QiMeng, we conclude that Zhu's attitude to mathematical structures is much more developed than his precedent ones and that his mathematical structures are very close to the present ones.

• Journal for History of Mathematics
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• v.26 no.5_6
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• pp.323-328
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• 2013

The Division Algorithm is known to be the fundamental foundation for Number Theory and it leads to the Euclidean Algorithm and hence the whole theory of divisibility properties. In JiuZhang SuanShu(九章算術), greatest common divisiors are obtained by the exactly same method as the Euclidean Algorithm in Elements but the other theory on divisibility was not pursued any more in Chinese mathematics. Unlike the other authors of the traditional Chinese mathematics, Zhu ShiJie(朱世傑) noticed in his SuanXue QiMeng(算學啓蒙, 1299) that the Division Algorithm is a really important concept. In [4], we claimed that Zhu wrote the book with a far more deeper insight on mathematical structures. Investigating the Division Algorithm in SuanXue QiMeng in more detail, we show that his theory of Division Algorithm substantiates his structural apporaches to mathematics.

• Journal for History of Mathematics
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• v.29 no.6
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• pp.325-333
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• 2016

Chinese Mathematics during the period of Jin (1115-1234) and Yuan (1271-1368) is an integral part of the high achievements of traditional mathematics during the Song (962-1279) and Yuan dynasties, which is another peak in the history of Chinese mathematics, following the footsteps of the high accomplishments during the Warring States period (475-221 BCE), the Western Han (206 BCE-24 ADE), Three Kingdoms (220-280 AD), Jin dynasty (265-420 AD), and Southern and Northern Dynasties (420-589 AD). During the Jin-Yuan period, Quanzhen Taoism was a dominating branch in Taoism. It offered certain political protection and religious comforts to many during troubled times; it also provided a relatively stable environment for intellectual development. Li Ye (1192-1279), Zhu Shijie (fl. late 13th C to early 14th C) and Zhao Youqin (fl. late 13th C to early 14th C), the major actors and contributors to the Jin-Yuan Mathematics achievements, were either heavily influenced by the philosophy of Quanzhen Taoism, or being its followers. In certain Taoist Classics, Li Ye read the records of the relations of a circle and nine right triangles which has been known as Dongyuan jiurong 洞渊九容 of Quanzhen Taoism. These relations made significant contributions in the study of the circles inscribed in a right triangle, the reasoning of which directly led to the birth of the Method of Celestial Elements (Tianyuan shu 天元术), which further developed into the Method of Two Elements (Eryuan shu ⼆元术), the Method of Three Elements (Sanyuan shu 三元术) and the Method of Four Elements (Siyuan shu 四元术).

• Journal for History of Mathematics
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• v.25 no.4
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• pp.11-19
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• 2012

Zhu Shi Jie's Suan Xue Qi Meng (算學啓蒙) is one of the most important books which had a great influence to the development of Chosun Mathematics and Gyung SunJing's Muk Sa Jib San Bub is the oldest Chosun mathematics book. In this paper, comparing Suan Xue Qi Meng (算學啓蒙) with Muk Sa Jib San Bub, we study the mathematics educational constructions and structures in books and then conclude that their structure can be used in present school mathematics.

• Journal for History of Mathematics
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• v.22 no.2
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• pp.1-12
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• 2009

Zhu Shi Jie's Suan Xue Qi Meng is one of the most important books which gave a great influence to the development of Chosun Mathematics. Investigating San Hak Gye Mong Ju Hae(算學啓蒙註解) published in the middle of the 19th century, we study the development of Chosun Mathematics in the century. The author studied western mathematics together with theory of equations in Gu Il Jib (九一集) written by Hong Jung Ha(洪正夏) and then wrote the commentary, which built up a foundation on the development of Algebra of Chosun in the century.

• Journal for History of Mathematics
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• v.20 no.1
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• pp.1-16
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• 2007

In the 19th century, Chosun mathematicians studied the most distinguished mathematicians Qin Jiu Shao(泰九韶), Li Ye(李治) Zhu Shi Jie(朱世傑) in Song(宋), Yuan(元) Dynasty and they established a solid theoretical development on the theory of equations. These studies began with their study on Si yuan yu jian xi cao(四元玉鑑細艸) compiled by Luo Shi Lin(羅士琳). Among those Chosun mathematicians, Lee Sang Hyuk(李尙爀, $1810{\sim}?$) and Nam Byung Gil(南秉吉 $1820{\sim}1869$) contributed prominently to the research. Relating to Si yuan yu jian xi cao, Nam Byung Gil and Lee Sang Hyuk compiled OgGamSeChoSangHae(玉監細艸詳解) and SaWonOgGam(四元玉鑑), respectively and then later they wrote SanHakJeongEi(算學正義) and IkSan(翼算), respectively. The latter in particular contains most creative results in Chosun Dynasty mathematics. Using these books, we study the relation between the development of Chosun mathematics and Si yuan yu jian.