• Journal for History of Mathematics
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• v.30 no.4
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• pp.203-219
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• 2017

As is well known, the most important development in the history of Chinese mathematics is materialized in Song-Yuan era through tianyuanshu up to siyuanshu for constructing equations and zengcheng kaifangfa for solving them. There are only two authors in the period, Li Ye and Zhu Shijie who left works dealing with them. They were almost forgotten until the late 18th century in China but Zhu's Suanxue Qimeng(1299) had been a main reference for the Joseon mathematics. Commentary by Luo Shilin on Zhu's Siyuan Yujian(1303) was brought into Joseon in the mid-19th century which induced a great attention to Joseon mathematicians with a thorough understanding of Zhu's tianyuanshu. We discuss the history that Joseon mathematicians succeeded to obtain the mathematical structures of Siyuan Yujian based on the Zhu's tianyuanshu.

• Journal for History of Mathematics
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• v.28 no.6
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• pp.301-310
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• 2015

Since Jiuzhang Suanshu, the main tools in the theory of right triangles, known as Gougushu in East Asia were algebraic identities about three sides of a right triangle derived from the Pythagorean theorem. Using tianyuanshu up to siyuanshu, Song-Yuan mathematicians could skip over those identities in the theory. Chinese Mathematics in the 17-18th centuries were mainly concerned with the identities along with the western geometrical proofs. Jeong Yag-yong (1762-1836), a well known Joseon scholar and writer of the school of Silhak, noticed that those identities can be derived through algebra and then wrote Gugo Wonlyu (勾股源流) in the early 19th century. We show that Jeong reveals the algebraic structure of polynomials with the three indeterminates in the book along with their order structure. Although the title refers to right triangles, it is the first pure algebra book in Joseon mathematics, if not in East Asia.

• Journal for History of Mathematics
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• v.29 no.6
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• pp.325-333
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• 2016

Chinese Mathematics during the period of Jin (1115-1234) and Yuan (1271-1368) is an integral part of the high achievements of traditional mathematics during the Song (962-1279) and Yuan dynasties, which is another peak in the history of Chinese mathematics, following the footsteps of the high accomplishments during the Warring States period (475-221 BCE), the Western Han (206 BCE-24 ADE), Three Kingdoms (220-280 AD), Jin dynasty (265-420 AD), and Southern and Northern Dynasties (420-589 AD). During the Jin-Yuan period, Quanzhen Taoism was a dominating branch in Taoism. It offered certain political protection and religious comforts to many during troubled times; it also provided a relatively stable environment for intellectual development. Li Ye (1192-1279), Zhu Shijie (fl. late 13th C to early 14th C) and Zhao Youqin (fl. late 13th C to early 14th C), the major actors and contributors to the Jin-Yuan Mathematics achievements, were either heavily influenced by the philosophy of Quanzhen Taoism, or being its followers. In certain Taoist Classics, Li Ye read the records of the relations of a circle and nine right triangles which has been known as Dongyuan jiurong 洞渊九容 of Quanzhen Taoism. These relations made significant contributions in the study of the circles inscribed in a right triangle, the reasoning of which directly led to the birth of the Method of Celestial Elements (Tianyuan shu 天元术), which further developed into the Method of Two Elements (Eryuan shu ⼆元术), the Method of Three Elements (Sanyuan shu 三元术) and the Method of Four Elements (Siyuan shu 四元术).