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Mathematical Treasure: Zhu Shijie's New Arithmetic Enlightenment

Frank J. Swetz (The Pennsylvania State University Library)

Zhu Shijie (c. 1260-1320) was one of traditional China’s greatest algebraists. He is best known for his Siyuan yujian (Precious Mirror of the Four Elements, 1303), in which he demonstrated a technique for solving a system of higher degree polynomial equations containing four unknowns. However, he was also the author of several other influential mathematics texts. The first such book he wrote was Xin bian suan xue qi meng (New Arithmetic Enlightenment, 1299). Here is a selection of images from a 1660 Korean copy of this text, written in Chinese.

The first page of the text:

A page of numerical calculations:

A discussion of the areas of a circle, a triangle, and an isosceles trapezium:                

The images above were obtained through the cooperation of The Houghton Library, Harvard University, Cambridge, Massachusetts.

See images from a 19th century Chinese copy of this text in MAA Convergence.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University Library), "Mathematical Treasure: Zhu Shijie's New Arithmetic Enlightenment," Convergence (January 2016)