• Journal for History of Mathematics
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• v.18 no.3
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• pp.1-24
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• 2005

Although indeterminate equations were dealt in Jiu zhang suan shu and then in Sun zi suan fing and Zhang Giu Jian suan Jing in China, they did not get any substantial development until Qin Jiu Shao introduced da yan shu in his great book Shu shu jiu zhang which solves goneral systems of linear congruences. We first investigate his da yan shu and then study the history of indeterminate equations in Chosun Dynasty. Further, we compare Qin's da yan shu with that in San Hak Jung Eui written by Chosun mathematician Nam Byung Gil.

• Journal of Korean Medical classics
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• v.7
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• pp.113-160
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• 1994

The Sa-Ahm monk, who was believed to have existed in the middle of Cho-Seon Dynasty in Korea, have created an original Sa-Ahm's acupuncture method and written down, "Book of Sa-Ahm's 5 Element Acupuncture Method" using not only laws of creation and suppression in 5 element theory but also its main and other connected meridians according to the daignosis of visceras and bowels. Also the written time and background of its theory have not been known, and after obtaining Ji-San's book on Sa-Ahm's acupuncture method, I studied on them. The results are as follows : 1) The treatment chapter of Book of Sa-Ahm's 5 Element Acupuncture Method was written down by Sa-Ahm himself, and the chapter for Medical Experience was found to be written down by Ji-San. 2) It seemed that Sa-Ahm adopted the main ideas of "Eui Hak Jeong Jon(醫學正傳)" for the section of physiology, pathology and classification of disease symptoms the contents of which covered 40 of 43 parts, and the ideas of "Dong Eui Bo Gam(東醫寶鑑)" for YunGi treatise(運氣篇), and SangHan part(傷寒門) in classification of diease symptoms was intensified by the ideas of "Eui Hak Ip Moon(醫學入門)", and the contents of apoplexy, diseases characterized by acute diarrhea and vomiting, beriberi, diseases of oral cavity were intensified by the ideas of "Chim Ku Kyeong Hearn Bang(鍼灸經驗方)". 3) The written date of the Book of Sa-Ahm's 5 Element Acupuncture Method has been established as 1644 AD(22nd year of In Jo king of Cho-Seon Dynasty) after studying preface, contents and acknowledgement of Heo Im's "Chim Ku Kyeong Hearn Bang(鍼灸經驗方)". 4) The philosophic background of "Sa-Am Acupuncture Method(舍巖鍼法)" seems to be derived from the theories of "I Ching(周易)" and Yin Yang 5 Element Theory(陰陽五行學說), and to be influenced by such medical scholars as Tan Ke(丹溪), Woo Bak(虞搏), and Heo Im(許任).

• Journal for History of Mathematics
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• v.18 no.3
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• pp.39-54
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• 2005

In Chinese Mathematics, Jia Xian(要憲) introduced Zeng cheng kai fang fa(增乘開方法) to get approximations of solutions of Polynomial equations which is a generalization of square roots and cube roots in Jiu zhang suan shu. The synthetic divisions in Zeng cheng kai fang fa give ise to two concepts of Fan il(飜積) and Yi il(益積) which were extensively used in Chosun Dynasty Mathematics. We first study their history in China and Chosun Dynasty and then investigate the historical fact that Chosun mathematicians Nam Byung Gil(南秉吉) and Lee Sang Hyuk(李尙爀) obtained the sufficient conditions for Fan il and Yi il for quadratic equations and proved them in the middle of 19th century.