• 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.21 no.2
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• pp.1-18
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• 2008

As a sequel to the previous paper Gou Gu Shu in the 18th century Chosun, we study the development of Chosun mathematics by investigating that of Gou Gu Shu in the 19th century. We investigate Gou Gu Shu obtained by Hong Gil Ju, Nam Byung Gil, Lee Sang Hyuk and Cho Hee Soon among others and find some characters of the 19th century Gou Gu Shu in Chosun.

• 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.

• East Asian mathematical journal
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• v.27 no.4
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• pp.433-451
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• 2011

In this paper, we investigate the contents of Da-won-sul in the third volume of San Hak Jeong Ui (Arithmetic Definition) compiled by Nam Byong Kil and corrcted by Lee Sang Hyok in the Choson Dynasty period (Emperor Ko Jong 4, 1867).

• Proceedings of the Korean Ceranic Society Conference
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• 2003.04a
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• pp.26.1-26
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• 2003

• 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.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.18 no.3
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• pp.1-24
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• 2005

Although indeterminate equations were dealt in Jiu zhang suan shu and then in Sun zi suan fing and Zhang Giu Jian suan Jing in China, they did not get any substantial development until Qin Jiu Shao introduced da yan shu in his great book Shu shu jiu zhang which solves goneral systems of linear congruences. We first investigate his da yan shu and then study the history of indeterminate equations in Chosun Dynasty. Further, we compare Qin's da yan shu with that in San Hak Jung Eui written by Chosun mathematician Nam Byung Gil.

• 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.

• Journal for History of Mathematics
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• v.18 no.3
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• pp.39-54
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• 2005

In Chinese Mathematics, Jia Xian(要憲) introduced Zeng cheng kai fang fa(增乘開方法) to get approximations of solutions of Polynomial equations which is a generalization of square roots and cube roots in Jiu zhang suan shu. The synthetic divisions in Zeng cheng kai fang fa give ise to two concepts of Fan il(飜積) and Yi il(益積) which were extensively used in Chosun Dynasty Mathematics. We first study their history in China and Chosun Dynasty and then investigate the historical fact that Chosun mathematicians Nam Byung Gil(南秉吉) and Lee Sang Hyuk(李尙爀) obtained the sufficient conditions for Fan il and Yi il for quadratic equations and proved them in the middle of 19th century.