• 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).

• The Bulletin of The Korean Astronomical Society
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• v.43 no.2
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• pp.48.4-49
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• 2018

We studyed an Korean astrolabe made by Ryu Geum (1741~1788), the late Joseon Confucian scholar. It has a diameter of 17 cm and a thickness of 6 mm and is now owned by Museum of Silhak. In the 1267 of the reign of Kublai Khan of Mogol Empire, Jamal al Din, an Ilkhanate astronomer, present an astrolabe to his emperor together with 6 astronomical instruments. In 1525, an astrolabe was first made in Korea by Lee, Sun (李純, ?~?), a Korean astronomer and royal official of Joseon Dynasty. He was referred to Gexiang xinshu, a Mongloian-Chinese book by Zhao, Youqin (1280-1345), an astronomer of Mongolian Empire. This astrolabe has not been left. In the mid-17th century, an astrolabe was introduced to Joseon again through Hungai tongxian tushuo (渾蓋 通憲圖設) edited by Chinese Mathematician Li Zhi-zao (李之藻, 1565~1630), that originated from Astrolabium (1593) of Christoph Clavius (1538-1612). It seems that Ryu refered to Hungai tongxian tushuo which affect to Hongae-tongheon-ui (渾蓋通憲儀) edited by Nam, Byeong-Cheol (南秉哲, 1817~1863). We analysis lots of circles on the mother and a set of index from the rete of of Ryu's astrolabe. We find that the accuracy of circles has about 0.2~0.4 mm in average if the latitude of this astrolabe is 38 degrees. 11 indices of the rete point bright stars of the northern and southern celestial hemisphere. Their tip's accuracies are about $2^{\circ}.9{\pm}3^{\circ}.2$ and $2^{\circ}.3{\pm}2^{\circ}.8$ on right ascension and declination of stars respectively.