Practices of reasoning: persuasion and refutation in a seventeenth-century Chinese mathematical treatise of "linear algebra".

This article documents the reasoning in a mathematical work by Mei Wending, one of the most prolific mathematicians in seventeenth-century China. Based on an analysis of the mathematical content, we present Mei's systematic treatment of this particular genre of problems, fangcheng, and his efforts to refute the traditional practices in works that appeared earlier. His arguments were supported by the epistemological values he utilized to establish his system and refute the flaws in the traditional approaches.