• Title, Summary, Keyword: 남병길(南秉吉)

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Nam Byung Gil and his Theory of Equations (남병길(南秉吉)의 방정식논(方程式論))

  • Hong, Sung-Sa;Hong, Young-Hee
    • 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.

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Gou Gu Shu in the 19th century Chosun (19세기(世紀) 조선(朝鮮)의 구고술(句股術))

  • Hong, Sung-Sa;Hong, Young-Hee;Kim, Chang-Il
    • 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.

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Mathematics in Chosun Dynasty and Si yuan yu jian (조선(朝鮮) 산학(算學)과 사원옥감(四元玉鑑))

  • Hong, Sung-Sa;Hong, Young-Hee
    • 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.

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Mathematics of Chosun Dynasty and $Sh\grave{u}\;l\breve{i}\;j\bar{i}ng\;y\grave{u}n$ (數理精蘊) (조선(朝鮮) 산학(算學)과 수리정온(數理精蘊))

  • Hong Young-Hee
    • 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.

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Gou Gu Shu and Theory of equations in Chosun (조선(朝鮮)의 구고술(勾股術)과 방정식론)

  • Yun, Hye-Soon
    • 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.

남병길의 성경(星鏡) 별자리를 활용한 혼상(渾象) 제작

  • Ham, Seon-Yeong;Kim, Sang-Hyeok;Lee, Yong-Sam
    • The Bulletin of The Korean Astronomical Society
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    • v.37 no.2
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    • pp.92.2-92.2
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    • 2012
  • 조선(朝鮮)의 혼상(渾象)은 세종대(世宗代, 1418~1450)에 처음 제작되었다. 그 후 중종대(中宗代, 1506~1544)와 명종대(明宗代, 1545~1567)에 이를 보수를 하고, 선조대(宣祖代, 1567~1608)에 중수되었으나 현존하지 않고 있다. 민간에서 제작한 혼상은 16세기에 만든 도산서원의 혼상 유물이 유일한 것이다. 그 후 18세기에 만들어진 홍대용(洪大容, 1731~1783)의 혼상의(渾象儀)는 문헌으로만 전해지고 있다. 17세기 이전에 만들어진 혼상은 구법(舊法) 천문도에 의해 만들어졌지만, 17세기 이후에는 서양 과학의 유입으로 신법(新法)의 별자리를 사용하고 있다. 중국과 일본의 현존하는 혼상 유물 중에는 신법 별자리로 표기되어 있으며, 조선 후기 조선의 유물 가운데 평혼의(平渾儀) 유물은 신법의 별자리를 활용하고 있다. 최근 국내에서 복원한 혼상들은 구법 천문도로 제작되어왔다. 이 연구에서는 1861년 남병길(南秉吉, 1820~1869)이 저술한 조선의 신법을 대표할 수 있는 성표(星表)인 "성경(星鏡)"의 별자리를 활용하여 혼상을 제작하였다. 혼상구(渾象球)에는 적도좌표(赤道座標)와 황도좌표(黃道座標)를 함께 표기한 경선(經線)과 위선(緯線)을 각각 $30^{\circ}$ 간격으로 표기하였다. 또한 적도환(赤道環)에는 12궁(宮)을 표기하였고, 황도환(黃道環)에는 $15^{\circ}$ 간격으로 24기(氣)를 표기하였다. 별을 표기할 때 성경에 제시한 밝기와 같이 6등급으로 나누어 별의 크기를 제작하였다. 남병길의 "성경" 별자리를 활용한 혼상 제작으로 신법 별자리의 천상(天象)에 대한 이해와 연구 모델로 활용할 수 있게 되었다.

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History of Fan Ji and Yi Ji (번적과 익적의 역사)

  • Hong, Sung-Sa;Hong, Young-Hee;Chang, Hye-Won
    • 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.

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