• Journal for History of Mathematics
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• v.3 no.1
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• pp.89-94
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• 1986

• Journal of Educational Research in Mathematics
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• v.13 no.4
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• pp.429-446
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• 2003

Gu-il-jip is a mathematical book of Chosun dynasty in the 18c. It consists of nine chapters including more than 473 problems and their solutions. Analyzing the problems and their solutions, we can appreciate the mathematical researches by the professional mathematicians of Chosun. Especially, it is worth noting the followings: - units for measuring and decimal notations - $\pi$, area of circle, volume of sphere - naming the powers - counting rods - excess and deficit: calculation technique for excess-deficit relations among quantities - rectangular arrays: calculation technique for simultaneous linear equations - 'Thien Yuan' notation: method for representing equations - 'Khai Fang': algorithm for numerical solution of quadratic, cubic and higher equations Based on these analyses, some pedagogical applications are proposed.

• Journal for History of Mathematics
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• v.27 no.4
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• pp.259-269
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• 2014

In China and Joseon, the measurement of the areas of various plane figures is a very important subject for mathematical officials because it is connected directly with tax problems. Most of mathematical texts in China and Joseon contained Chinese character '田', which means a field for farming, in title name for parts that dealt with problems of areas and treated as areas of plane figures. The form of mathematical texts in Joseon is identical with those in China because mathematicians in Joseon referred to texts in China. Gyeong SeonJing and Hong JeongHa also referred to Chinese texts. But they added their interpretations or investigated new methods for the measurement of areas. In this paper, we investigate the history of the measurement of areas in Joseon, which described in two books MukSaJibSanBeob and GuIlJib, with comparing some mathematical texts in China.

• Journal for History of Mathematics
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• v.17 no.4
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• pp.1-16
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• 2004

Investigating theory of equations in Chosun Dynasty mathematics books Mooksa-jipsanbub, Guiljib(九一集), Chageunbangmonggu(借根方夢求), Sanhakjungeui (算學正義), and Iksan(翼算), we study the history of equation theory in Chosun Dynasty. We first deal with development of representation of polynomials and equations and then method how to solve them.

• Journal for History of Mathematics
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• v.22 no.4
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• pp.41-52
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• 2009

This study investigates a mathematical subject, 'triangles' in mathematics books of Chosun Dynasty, in special Muk Sa Jib San Bub(默思集算法), Gu Il Jib(九一集), San Hak Ib Mun(算學入門), Ju Hae Su Yong(籌解需用), and San Sul Gwan Gyun(算術管見). It is likely that they apt to avoid manipulating general triangles except the right triangles and the isosceles triangles etc. Our investigation says that the progress of triangle-related contents in Chosun mathematics can fall into three stages: measurement of the triangle-shaped fields, transition from the object of measurement to the object of geometrical study, and examination of definition, properties and validation influenced by western mathematics.

• 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.

• 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.

• 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.28 no.5
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• pp.233-248
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• 2015

Year 2014 was very special to Korean mathematical society. Year 2014 was the Mathematical Year of Korea, and the International Congress of Mathematicians "ICM 2014" was held in Seoul, Korea. The year 2014 was also the 330th anniversary year of the birth of Joseon mathematician Hong JeongHa. He is one of the best, in fact the best, of Joseon mathematicians. So it is worth celebrating his birth. Joseon dynasty adopted a caste system, according to which Hong JeongHa was not in the higher class, but in the lower class of the Joseon society. In fact, he was a mathematician, a middle class member, called Jungin, of the society. We think over how Hong JeongHa was able to write his mathematical book GuIlJib in Joseon dynasty.