• Journal for History of Mathematics
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• v.21 no.4
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• pp.11-18
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• 2008

In this paper, we investigate Lee Sang Hyuk (李尙爀, $1810{\sim}?$)'s first mathematical work ChaGeunBangMongGu(借根方蒙求, 1854) and its relation with Shu li jing yun and Chi shui yi zhen. We then study an influence of western mathematics for establishing his study on algebra.

• Journal for History of Mathematics
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• v.26 no.4
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• pp.213-218
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• 2013

This paper is a sequel to the paper [8], where we discussed the connection between ShiShou KaiFangFa originated from JiuZhang SuanShu and ZengCheng KaiFangFa. Investigating KaiFangShu in a Chosun mathemtics book, SanHak JeongEui and ShuLi JingYun, we show that its authors, Nam ByungGil and Lee SangHyuk clearly understood the connection and gave examples to show that the KaiFangShu in the latter is not exact. We also show that Chosun mathematicians were very much selective when they brought in Chinese mathematics.

• Journal for History of Mathematics
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• v.22 no.4
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• pp.1-14
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• 2009

Since western mathematics and astronomy had been introduced in Chosun dynasty in the 17th century, most of Chosun mathematicians studied Shu li jing yun(數理精蘊) for the western mathematics. In the last two decades of the 19th century, Chosun scholars have studied them which were introduced by Japanese text books and western missionaries. The former dealt mostly with elementary arithmetic and the latter established schools and taught mathematics. Lee Sang Seol(1870~1917) is well known in Korea as a Confucian scholar, government official, educator and foremost Korean independence movement activist in the 20th century. He was very eager to acquire western civilizations and studied them with the minister H. B. Hulbert(1863~1949). He wrote a mathematics book Su Ri(數理, 1898-1899) which has two parts. The first one deals with the linear part(線部) and geometry in Shu li jing yun and the second part with algebra. Using Su Ri, we investigate the process of transmission of western mathematics into Chosun in the century and show that Lee Sang Seol built a firm foundation for the study of algebra in Chosun.

• Journal for History of Mathematics
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• v.20 no.2
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• pp.1-18
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• 2007

In the middle of 19th century, Chosun mathematicians Nam Byung Gil(南秉吉) and Lee Sang Hyuk(李尙爀) studied mathematical structures developed in Song(宋) and Yuan(元) eras on top of their early studies on Jiu zhang suan shu(九章算術) and Shu li jing yun(數理精蘊). Their studies gave rise to a momentum for a prominent development of Chosun mathematics in the century. In this paper, we investigate Nam Byung Gil's JipGoYunDan(輯古演段) and MuIHae(無異解) and then study his theory of equations. Through a collaboration with Lee, Sang Hyuk, he consolidated the eastern and western structure of theory of equations.

• Journal for History of Mathematics
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• v.31 no.6
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• pp.273-289
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• 2018

The KaiFangFa開方法 of traditional mathematics was completed in ${\ll}$JiuZhang SuanShu九章算術${\gg}$ originally, and further organized in Song宋 $Yu{\acute{a}}n$元 dinasities. The former is the ShiSuoKaiFangFa釋鎖開方法 using the coefficients of the polynomial expansion, and the latter is the ZengChengKaiFangFa增乘開方法 obtaining the solution only by some mechanical numerical manipulations. ${\ll}$SanHak JeongEui算學正義${\gg}$ basically used the latter and improved the estimate-value array by referring to the written-calculation in ${\ll}$ShuLi JingYun數理精蘊${\gg}$. As a result, ZengChengKaiFangFa was more refined so that the KaiFangFa algorithm is more consistent.

• The Journal of Korean Medical History
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• v.14 no.2
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• pp.109-152
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• 2001

Throughout this paper, I adjusted the study of 'Qian Yi'(錢乙)'s Medical Thought, and the following is the summary. 1. 'Qian Yi' wrote 'Xiao Er Yao Zheng Zhi Jue'("小兒藥證直訣", edited by 誾季忠), and there were 'Shang Han Lun Zhi Wei'("傷寒論指微"), 'Ying Ru Lun', however those are loss of the record. 2. Qian Yi's 'Zhi Jue'("直訣") was influenced by 'Lu Xin Jing', yet if we compare the quality of 'Sheng Li, Byeng Li, Bang Jae'(生理, 病理, 方劑), 'Lu Xin Jing' cannot be the foundation of 'Zhi Jue'. He took over 'Nei Jing, Shang Han Lun, Jin Gui Yao Lue, Shen Long Ben Cao Jing, Tai Ping Sheng Hui Fang'("內經", "傷寒論", "金?要略", "神膿本草經", "太平聖惠方") and put them together to the direct clinical experiences of pediatrics. 3. There is no reference regarding the difficulties of pediatric diagnosis and diseases in 'Huang Di Nei Jing'("黃帝內經") Before 'Bei Song'(北宋), regardless of the lack of data related to pediatric diseases, 'Qian Yi' established the pediatric system in 'Xiao Er Yao Zheng Zhi Jue' for the first time. 4. In his diagnosis of the pediatric diseases, he 'Si Zhen He Can'(四診合參), also considered in the eye exam seriously. In addition, he closely combined 'Wu Zang Bian Zheng'(五臟辨證), and diagnosis the pediatric diseases. 5. 'Wu Zang Bian Zheng', what Qian established method was based on 'Zheng Ti Guan'(整體觀) in 'Huang Di Nei Jing'. It was based on clinical experiences and established the perspectives of 'Tian Ren Xiang Ying'(天人相應). First of all, he pinpointed 'Zhu Zheng'(主證) clearly. Secondly, he pinpointed the relationships to symptoms and then, he distinguished a generic character of 'Xu, Shi, Han, Re'(虛, 實, 寒, 熱). Finally, he made an induction from genealogical pediatric physiology. 6. 'Qian Yi' took a serious view of 'Ban Zhen'(斑疹), the inadequate field in those days. At that time, he criticized on the habituation of the misuse of medication. He treated separately which 'Ji Jing'(急驚) as 'Liang Xie'(凉瀉) and 'Man Jing'(慢驚) as 'Wen Bu'(溫補). He proposed 'Cong Gan Zhu Feng, Xin Zhu Jing'(從肝主風, 心主驚) theory and formulated 'Jing Feng'(驚風) theory as well. 7. As an opponent of a tendency to misusage of medicine, 'Qian Yi' made out a prescription with pliant medicine. He emphasized on the treatment to 'Gong Bu Shang Zheng, Bu Bu Zhi Xie, Xiao Bu Jian Shi'(攻不傷正, 補不滯邪, 消補兼施) because he had so lucid demonstration to 'Xu Shi Han Re'(虛實寒熱) of the five viscera in the field of 'Bang Yak'(方藥). 8. There were no pediatrics schools at that time, however, the pediatrics was being made up gradually by 'Jin Yuan Si Da Jia'(金元四大家) who was influenced by 'Qian Yi'. He raised an objection to medical treatment using pliant medicine. 'Qian Yi' applied 'Qu Xia'(驅下) treatment using 'Han Liang'(寒凉) medicine. 'Han Liang Pai'(寒凉派) is greatly influenced by Qian. 'Chen Wen Zhong'(陳文中) had a great impact on 'Han Liang Pai' who used a 'Zao Shu Wen Bu'(燥熟溫補) medicine for treatment. Since 'Song Jin'(宋金), he had a tremendous influence on pediatrics treating patients in both 'Han Wen'(寒溫) ways. 9. 'Qian Yi' had an influence on his medical thoughts on future generations, especially to 'Wan Quan'(萬全) of 'Ming Dai', 'Wu Tang'(吳塘) of 'Qing Dai'(淸代) and 'Yun Shu Jie'(?樹珏) of 'Min Guo'(民國). 'Wan Quan' is an advocate of 'You Yu, Bu Zu Zhi Shuo'(有餘, 不足之說)of 'Xiao Er Wu Zang'(小兒五臟) that he revealed Qian's 'Wu Zang Bian Zheng'(五臟辨證). 'Wu Tang' disclosed Qian's 'Xiao Er Ti Zhi Shuo'(小兒體質說) and 'Xiao Er Ke'(小兒科)'s 'Yong Yao Lun'(用藥論), therefore, he uncovered pediatric physiological characteristics through the advocate of Qian's 'Zang Fu Rou Ruo, Ji Gu Nen Qie, Yi Xu Yi Shi, Yi Han Yi Re' (臟腑柔弱, 肌骨嫩怯, 易虛易實, 易寒易熱). 'Yun Shu Jie' developed intrinsic relationships among time, symptom and 'Tian Ren Xiang Ying Guan'(天人相應觀), What 'Qian Yi' stated about them. And also, he developed Qian's 'Di Huang Wan'(地黃丸), 'Xie Qing Wan'(瀉靑丸), 'Yi Huang San'(益黃散) clinical usages as well. 10. Regarding Qian's 'Wu Zang Xu Shi'(五臟虛實), it has an influence on 'Zhang Yuan Su'(張元素)'s 'Zang Fu Bing Ji Bian Zheng'(臟腑病機辨證). 'Di Huang Wan', 'Xie Qing Wan', 'Xie Xin Tang'(瀉心湯), 'Yi Huang San', 'Xie Huang San'(瀉黃散) are the standard prescription of 'Wu Zang Bu Xie'(五臟補瀉). It is under the influence of Qian's treatment. Besides, 'Qian Yi' took a serious view of 'Xiao Er'(小兒)'s 'Pi Wei'(脾胃). 'Qian Yi' had an impact on 'Li Dong Yuan'(李東垣) one of the member of 'Bu Tu Pai'(補土派). 'Di Huang Wan', which placed great importance on 'Bu Yi Shen Yin'(補益腎陰), had a great impact on 'Da Bu Yin Wan'(大補陰丸) and 'Jin Yuan Si Da Jia' as well. 11. In a theory of Qian's 'Wu Zang Bian Zheng', though it had been stated clearly in 'Wu Zang Bian Zheng', but he neglected in 'Liu Fu Bian Zheng'(六腑辨證). In prescription field, The problem with the medicine is that it is either toxic or mineral, therefore, we are not able to use those medicine in a clinical testing at the present time.

• Journal for History of Mathematics
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• v.21 no.4
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• pp.1-10
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• 2008

In this paper, we investigate the part dealing with algebra in Hong Gil Ju's GiHaSinSul to analyze his algebraic structure. The book consists of three parts. In the first part SangChuEokSan, he just renames Die jie hu zheng(疊借互徵) in Shu li jing yun to SangChuEokSan and adds a few examples. In the second part GaeBangMongGu, he obtains the following identities: $$n^2=n(n-1)+n=2S_{n-1}^1+S_n^0;\;n^3=n(n-1)(n+1)+n=6S_{n-1}^2+S_n^0$$; $$n^4=(n-1)n^2(n+1)+n(n-1)+n=12T_{n-1}^2+2S_{n-1}^1+S_n^0$$; $$n^5=2\sum_{k=1}^{n-1}5S_k^1(1+S_k^1)+S_n^0$$ where $S_n^0=n,\;S_n^{m+1}={\sum}_{k=1}^nS_k^m,\;T_n^1={\sum}_{k=1}^nk^2,\;and\;T_n^2={\sum}_{k=1}^nT_k^1$, and then applies these identities to find the nth roots $(2{\leq}n{\leq}5)$. Finally in JabSwoeSuCho, he introduces the quotient ring Z/(9) of the ring Z of integers to solve a system of congruence equations and also establishes a geometric procedure to obtain golden sections from a given one.

• Education of Primary School Mathematics
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• v.14 no.2
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• pp.103-116
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• 2011

'The nine chapters on the mathematical art' has dominated the history of Chinese mathematics. It contains 246 problems and their solutions, which fall into nine categories that are firmly based on practical needs. But it has been greatly by improved by the commentary given Liu Hui and it was transformed from arithmetic text to mathematics. The improved book served as important textbook in China but also the East Asian countries for the past 2000 years. Also It is comparable in significance to Euclid's Elements in the West. In the middle of 19th century, Chosun mathematicians Nam Byung Gil(南秉吉) and Lee Sang Hyuk(李尙爀) studied mathematical structures developed in Song(宋) and Yuan(元) eras on top of their early on 'The nine chapters' and 'ShuLiJingYun(數理精蘊)'. Their studies gave rise to a momentum for a prominent development of Choson mathematics in the century. Nam Byung Gil is also commentator on 'The Nine Chapters'. His commentary is 'GuJangSulHae(九章術解)'. This book provides figures and explanations of how the algorithms work. These are very helpful for prospective elementary teachers. We try to plan programs of elementary teacher education on the basis of 'The Nine Chapters' and 'GuJangSulHae'.

• Communications of Mathematical Education
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• v.25 no.4
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• pp.641-651
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• 2011

In 2007, a Taiwanese mathematics historian Wann-Sheng HORNG made a visit to Kyujanggak(the royal library of Joseon Dynasty) in Seoul, Korea. During this visit, he found the Korean math book An abridged version of the Joseon Mathematics (<數學節要>, Su-Hak-Jeol-Yo), which was written by Jong-Hwa AN(9 Nov 1860 - 24 Nov 1924) in 1882. Then he mentioned the possible importance of AN's book in his article in the Journal Kyujanggak(vol. 32, June 2008). Jong-Hwa AN is a Korean scholar, activist of patriotism and enlightenment in the latter era of Joseon Dynasty. He passed the last examination of Joseon Dynasty to become a high government officer in 1894. The father of the modern mathematics education in Korea, Sang-Seol LEE(1870-1917) also passed the same examination with him. It is interesting that government high officer AN and LEE both wrote mathematics books in 19th century. In this talk, we now analyze this mathematics book of Joseon written in 1882.