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It is well-known to historians of mathematics in East Asia that the tianyuan shu 天元術 was one of the distinct features of mathematics in the late Joseon period. Joseon Confucian scholars' studies on the tianyuan shu have yet to be analyzed. From the late seventeenth to the early eighteenth century, there were two extant mathematical works by Korean Confucian scholars concerning the tianyuan shu: Sanhak wonbon 算學原本 by Bak Yul (朴繘, 1621-1668) and Sanhak bonwon 算學本源 by Hwang Yun-seok (黃胤錫, 1729-1791). By analyzing these two works, this paper examines the characteristics of their views and interpretations of the tianyuan shu. The Confucian authors extended the usage of the tianyuan shu into other mathematical fields to which it had never been applied before. They also preferred to use mathematical tables that showed the relationships between the numbers popping up during the performance of the method or the visual diagrams that explained the algorithms. [ABSTRACT FROM AUTHOR]

Early modern Europe went through two distinct types of revolution ᅳ scientific and military. Military historians have employed the term, Military Revolution, to account for several significant changes in the seventeenth century, such as advent of new weapons, enlargement of military forces, and extension of battle length. Under these circumstances, it is reasonable to assume a certain degree of correlation between the Scientific Revolution and the Military Revolution, both of which took place in the same place at the same time. This paper features Maurits van Nassau and Simon Stevin to show the interactions between two revolutions. They were patron and client in private, and general and officer in public. Maurits is considered to have brought about the Military Revolution, while Stevin is valued highly as a mathematician that invented decimal fraction system and laid the foundation for the new mathematics through innovating traditional number concept. Maurits is well-known for the 'scientific war,' particularly the scientific siege warfare. I suggest that his scientific wars were carried out through systematic deployment of armed forces, detection of the weakest point based on mathematical analysis, calculation of safe attacking routes, and intensive attack on target points. Stevin's publications on the art of war will show how much they influenced on Maurits' strategies and tactics. This shows that the clear correlation between science and war, characterized by goal-driven research for warfare tactics, elevated social status of relevant scientists, and strong recognition of victor nations as the centre of science, already started slowly in the seventeenth century. [ABSTRACT FROM AUTHOR]