• Communications of Mathematical Education
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• v.30 no.3
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• pp.419-434
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• 2016

Ju-Seo-Gwan-Gyeon is a mathematical book of Chosun dynasty in the early 18th century. This study is to analyze and compare the contents between Ju-Seo-Gwan-Gyeon and Gu-Jang-San-Sul. From this study, we are able to see the contents of Ju-Seo-Gwan-Gyeon that has been unknown in detail so far. In this comparative study, the following facts are found. First, many problems in Ju-Seo-Gwan-Gyeon are similar to the Gu-Jang-San-Sul on the contents and frame. Most of them are same type. But some of problems in Ju-Seo-Gwan-Gyeon have been developed. Second, there are distinct differences of description type. And Ju-Seo-Gwan-Gyeon was influenced by Gu-Jang-San-Sul but also other mathematical books. We expect that the results provide basic information for mathematics history in Korea.

• Journal for History of Mathematics
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• v.36 no.4
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• pp.61-78
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• 2023

By virtue of the characteristics inherent in diagrams, diagrammatic reasoning has potential and limitations that distinguish it from general thinking. It is natural that diagrams rarely appeared in Joseon mathematical books, which were heavily focused on computation and algebra in content, and preferred linguistic expressions in form. However, as the late Joseon Dynasty unfolded, there emerged a noticeable increase in the frequency of employing diagrams, due to the educational purposes to facilitate explanations and the influence of Western mathematics. Analyzing the role of diagrams included in Jo Taegu's 'JuseoGwangyeon', an exemplary book, this study includes discussions on the utilization of diagrams from the perspective of mathematics education, based on the findings of the analysis.

• 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.

• East Asian mathematical journal
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• v.37 no.4
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• pp.427-441
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• 2021

Ju-Seo-Gwan-Gyeon is a mathematical book of Chosun dynasty by Jo Tae Gu. This study is to analyze his understanding for the 'Gujang' in the 'Gujang-Mundab'. From this study, we were able to see the contents of 'Gujang-Mundab' that has been unknown in detail so far. In this study, the following facts are found. Most parts of 'Gujang' in 'Gujang-Mundab' was explained the same as Gu-Jang-San-Sul. This indicates that Ju-Seo-Gwan-Gyeon was influenced by Gu-Jang-San-Sul. However, Ju-Seo-Gwan-Gyeon also contains what he wrote with his own understanding. We expect that the results provide basic information for mathematics history in Korea.

• Journal for History of Mathematics
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• v.25 no.3
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• pp.1-14
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• 2012

Since JiuZhang SuanShu(九章算術), the basic field of the traditional mathemtics in Eastern Asia is the field of rational numbers and hence irrational solutions of equations should be replaced by rational approximations. Thus approximate solutions of equations became a very important subject in theory of equations. We first investigate the history of approximate solutions in Chinese sources and then compare them with those in Chosun mathematics. The theory of approximate solutions in Chosun has been established in SanHakWonBon(算學原本) written by Park Yul(1621 - 1668) and JuSeoGwanGyun(籌書管見, 1718) by Cho Tae Gu(趙泰耉, 1660-1723). We show that unlike the Chinese counterpart, Park and Cho were concerned with errors of approximate solutions and tried to find better approximate solutions.

• Journal for History of Mathematics
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• v.31 no.2
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• pp.55-72
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• 2018

Matteo Ricci and Xu Gwangqi translated the first six Books of Euclid's Elements and published it with the title Jihe Yuanben, or Giha Wonbon in Korean in 1607. It was brought into Joseon as a part of Tianxue Chuhan in the late 17th century. Recognizing that Jihe Yuanben deals with universal statements under deductive reasoning, Jo Tae-gu completed his Juseo Gwan-gyeon to associate the traditional mathematics and the deductive inferences in Jihe Yuanben. Since Jo served as a minister of Hojo and head of Gwansang-gam, Jo had a comprehensive understanding of Song-Yuan mathematics, and hence he could successfully achieve his objective, although it is the first treatise of Jihe Yuanben in Joseon. We also show that he extended the results of Jihe Yuanben with his algebraic and geometric reasoning.

• 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.

• 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.