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Outside the capital, some Chinese literati also pursued the study of mathematics and astronomy. One of them, Mei Wending slowly rose to prominence as a scholar specialised in these fields. This chapter recounts his early career and analyzes some aspects of his mathematical work. In the *Discussion of rectangular arrays* Mei uses the Westerners' minute style of explanation as he had seen at work in the *Elements* and in other fields of measurement. He applied this style to calculation, the branch of mathematics that his contemporaries had in his view neglected, and of which the *Discussion of rectangular arrays* constitutes an apology. This is one of the many ways in which Mei Wending's mathematical work can be characterized as syncretistic. As one of the scholars best versed in the mathematical sciences in his time, he provided his contemporaries with treatises that aimed to enable them to acquire at least some of his expertise.

*Keywords: *
Chinese literati;
Mei Wending;
mathematics;
rectangular arrays;
syncretistic

*Chapter.*
*7985 words.*

*Subjects: *
History of Mathematics

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