• Journal for History of Mathematics
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• v.20 no.3
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• pp.1-16
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• 2007

In order to generalize theory of series in Iksan(翼算), we introduce a concept of double sequence of partial sums and elementary double sequence of partial sums, which play a dominant role in the study of double sequences of partial sums. We introduce a concept of finitely generated double sequence of partial sums and find a necessary and sufficient condition for those double sequences. Finally we prove a multiplication theorem for tetrahedral numbers and for 4 dimensional tetrahedral numbers.

• 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.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.

• Journal for History of Mathematics
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• v.23 no.3
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• pp.1-20
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• 2010

Hong Jung Ha(洪正夏, 1684~?) is the greatest mathematician in Chosun dynasty and wrote a mathematics book Gu Il Jib(九一集) which excels in the area of theory of equations including Gou Gu Shu. The purpose of this paper is to find his influence on the history of Chosun mathematics. He belongs to ChungIn(中人) class and works only in HoJo(戶曹) and hence his contact to other mathematicians is limited. Investigating his colleagues and kinship relations including the affinity and consanguinity, we conclude that he gave a great influence to those people and find that three great ChungIn mathematicans Gyung Sun Jing(慶善徵, 1684~?), Hong Jung Ha and Lee Sang Hyuk(李尙爀, 1810~?) are all related through marriage.

• Journal for History of Mathematics
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• v.24 no.4
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• pp.7-20
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• 2011

Investigating constructions of equations by Gou gu shu(勾股術) in Hong Jung Ha(洪正夏)'s GuIlJib(九一集), Nam Byung Gil(南秉吉)'s YuSiGuGoSulYoDoHae(劉氏勾股術要圖解) and Lee Sang Hyuk(李尙爀)'s ChaGeunBangMongGu(借根方蒙求), we study the history of development of Chosun mathematics. We conclude that Hong's greatest results have not been properly transmitted and that they have not contributed to the development of Chosun mathematics.

• Journal for History of Mathematics
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• v.19 no.2
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• pp.25-46
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• 2006

We investigate the process of western mathematics into Chosun and its influences. Its initial and middle stages are examined by Choi Suk Jung(崔錫鼎, $1645\sim1715$)'s Gu Su Ryak(九數略), Hong Jung Ha(洪正夏, $1684\sim?$)'s Gu Il Jib(九一集) and Hwang Yun Suk(黃胤錫, $1719\sim1791$)'s I Su Shin Pyun(理藪新編), Hong Dae Yong(洪大容, $1731\sim1781$)'s Ju Hae Su Yong(籌解需用), respectively. Western mathematics was transmitted for the study of the Shi xian li(時憲曆) when it was introduced in Chosun. We also analyze Su Ri Jung On Bo Hae(數理精蘊補解, 1730?) whose author studied $Sh\grave{u}\;l\breve{i}\;j\bar{i}ng\;y\grave{u}n$ most thoroughly, in particular for astronomy, and finally Lee Sang Hyuk(李尙爀, $1810\sim?$), Nam Byung Gil(南秉吉, $1820\sim1869$) who studied together structurally western mathematics.

• Journal for History of Mathematics
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• v.19 no.2
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• pp.1-24
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• 2006

We study the theory of finite series in Chosun Dynasty Mathematics. We divide it into two parts by the publication of Lee Sang Hyuk(李尙爀, 1810-?)'s Ik San(翼算, 1868) and then investigate their history. The first part is examined by Gyung Sun Jing(慶善徵, 1616-?)'s Muk Sa Jib San Bub(默思集算法), Choi Suk Jung(崔錫鼎)'s Gu Su Ryak(九數略), Hong Jung Ha(洪正夏)'s Gu Il Jib(九一集), Cho Tae Gu(趙泰耉)'s Ju Su Gwan Gyun(籌書管見), Hwang Yun Suk(黃胤錫)'s San Hak Ib Mun(算學入門), Bae Sang Sul(裵相設)'s Su Gye Soe Rok and Nam Byung Gil(南秉吉), 1820-1869)'s San Hak Jung Ei(算學正義, 1867), and then conclude that the theory of finite series in the period is rather stable. Lee Sang Hyuk obtained the most creative results on the theory in his Ik San if not in whole mathematics in Chosun Dynasty. He introduced a new problem of truncated series(截積). By a new method, called the partition method(分積法), he completely solved the problem and further obtained the complete structure of finite series.

• Journal for History of Mathematics
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• v.34 no.5
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• pp.165-191
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• 2021

The simple simultaneous linear congruence equation solution in 《Sunzi Suanjing孫子算經》 has developed into a systematic general solution in 《Shuxue Jiuzhang數書九章》. The most important parts of it is the creation of the Dayan Qiuyishu大衍求一術. The reason why 《Sanhak Jeongeui算學正義》 deals with the Dayanshu大衍術 which has lost its practicality in the calculation of astronomical calendar, is that one of the best achievement of traditional mathematics cannot be omitted. It is written with an emphasis on the disclosure of the calculation principle. It shows that Nam Byeong-gil南秉吉 and Lee Sang-hyeok李尙爀 had a fairly structural understanding of the Dayan Qiuyishu.