• Title, Summary, Keyword: 홍정하(洪正夏)의 구일집(九一集)

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Gou Gu Shu in the 18th century Chosun (18세기(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.20 no.4
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    • pp.1-21
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    • 2007
  • We investigate the Gou Gu Shu(句股術) in Hong Jung Ha's Gu Il Jib(九一集) and Cho Tae Gu's Ju Su Gwan Gyun(籌書管見) published in the early 18th century. Using a structural approach and Tien Yuan Shu(天元術), Hong has obtained the most advanced results on the subject in Asia. Using Cho's result influenced by the western mathematics introduced in the middle of the 17th century, we study a process of a theoretical approach in Chosun mathematics in the period.

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Chosun Mathematics Book Suan Xue Qi Meng Ju Hae (조선(朝鮮) 산서(算書) 산학계몽주해(算學啓蒙註解))

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

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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.

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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Hong JeongHa's Tianyuanshu and Zhengcheng Kaifangfa (홍정하(洪正夏)의 천원술(天元術)과 증승개방법(增乘開方法))

  • Hong, Sung Sa;Hong, Young Hee;Kim, Young Wook
    • Journal for History of Mathematics
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    • v.27 no.3
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    • pp.155-164
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    • 2014
  • Tianyuanshu and Zengcheng Kaifangfa introduced in the Song-Yuan dynasties and their contribution to the theory of equations are one of the most important achievements in the history of Chinese mathematics. Furthermore, they became the most fundamental subject in the history of East Asian mathematics as well. The operations, or the mathematical structure of polynomials have been overlooked by traditional mathematics books. Investigation of GuIlJib (九一集) of Joseon mathematician Hong JeongHa reveals that Hong's approach to polynomials is highly structural. For the expansion of $\prod_{k=11}^{n}(x+a_k)$, Hong invented a new method which we name Hong JeongHa's synthetic expansion. Using this, he reveals that the processes in Zhengcheng Kaifangfa is not synthetic division but synthetic expansion.

Hong Jung Ha's Number Theory (홍정하(洪正夏)의 수론(數論))

  • Hong, Sung-Sa;Hong, Young-Hee;Kim, Chang-Il
    • Journal for History of Mathematics
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    • v.24 no.4
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    • pp.1-6
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    • 2011
  • We investigate a method to find the least common multiples of numbers in the mathematics book GuIlJib(구일집(九一集), 1724) written by the greatest mathematician Hong Jung Ha(홍정하(洪正夏), 1684~?) in Chosun dynasty and then show his achievement on Number Theory. He first noticed that for the greatest common divisor d and the least common multiple l of two natural numbers a, b, l = $a\frac{b}{d}$ = $b\frac{a}{d}$ and $\frac{a}{d}$, $\frac{b}{d}$ are relatively prime and then obtained that for natural numbers $a_1,\;a_2,{\ldots},a_n$, their greatest common divisor D and least common multiple L, $\frac{ai}{D}$($1{\leq}i{\leq}n$) are relatively prime and there are relatively prime numbers $c_i(1{\leq}i{\leq}n)$ with L = $a_ic_i(1{\leq}i{\leq}n)$. The result is one of the most prominent mathematical results Number Theory in Chosun dynasty. The purpose of this paper is to show a process for Hong Jung Ha to capture and reveal a mathematical structure in the theory.

Liu Yi and Hong Jung Ha's Kai Fang Shu (유익(劉益)과 홍정하(洪正夏)의 개방술(開方術))

  • Hong, Sung-Sa;Hong, Young-Hee;Kim, Young-Wook
    • Journal for History of Mathematics
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    • v.24 no.1
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    • pp.1-13
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    • 2011
  • In Tian mu bi lei cheng chu jie fa(田畝比類乘除捷法) of Yang Hui suan fa(楊輝算法)), Yang Hui annotated detailed comments on the method to find roots of quadratic equations given by Liu Yi in his Yi gu gen yuan(議古根源) which gave a great influence on Chosun Mathematics. In this paper, we show that 'Zeng cheng kai fang fa'(增乘開方法) evolved from a process of binomial expansions of $(y+{\alpha})^n$ which is independent from the synthetic divisions. We also show that extending the results given by Liu Yi-Yang Hui and those in Suan xue qi meng(算學啓蒙), Chosun mathematican Hong Jung Ha(洪正夏) elucidated perfectly the 'Zeng cheng kai fang fa' as the present synthetic divisions in his Gu il jib(九一集).

Chosun Mathematics in the early 18th century (18세기(世紀) 초(初) 조선(朝鮮) 산학(算學))

  • Hong, Sung-Sa;Hong, Young-Hee
    • Journal for History of Mathematics
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    • v.25 no.2
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    • pp.1-9
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    • 2012
  • After disastrous foreign invasions in 1592 and 1636, Chosun lost most of the traditional mathematical works and needed to revive its mathematics. The new calendar system, ShiXianLi(時憲曆, 1645), was brought into Chosun in the same year. In order to understand the system, Chosun imported books related to western mathematics. For the traditional mathematics, Kim Si Jin(金始振, 1618-1667) republished SuanXue QiMeng(算學啓蒙, 1299) in 1660. We discuss the works by two great mathematicians of early 18th century, Cho Tae Gu(趙泰耉, 1660-1723) and Hong Jung Ha(洪正夏, 1684-?) and then conclude that Cho's JuSeoGwanGyun(籌 書管見) and Hong's GuIlJib(九一集) became a real breakthrough for the second half of the history of Chosun mathematics.

Finite Series in Chosun Dynasty Mathematics (조선(朝鮮) 산학(算學)의 퇴타술)

  • Hong Sung-Sa
    • 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.

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