Was 'Jade Mirror of the Four Unknowns' published in 1303, and how do we know?
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Towards the end of one of the prefaces of the book (there were two prefaces, 前序 and 松庭先生後序), it states:
大德癸卯上元日，臨川前進士莫若序。
which can be roughly translated as:
On the day of Shangyuan (lit. first full moon festival) in the Kuí-Mǎo year during Dà-Dé era, 臨川前進士 (this was most likely the honorary title of the author of the preface) presents this preface.
大德 (Dà-Dé) was the era name of emperor Chengzong of Yuan, otherwise known as Temür Öljeytü Khan. 癸卯 (Kuí-Mǎo) was the ganzhi name (see Sexagenary cycle for more information) of the year. Knowing that one sexagenary cycle accounts for 60 years, it thus becomes quite simple for us to deduce which year it was -- since 1963 CE was the most recent year in the cycle bearing the same ganzhi and we know that emperor Chengzong ruled from 1294 to 1307, therefore the preface must had been written in 1303, the only year that fell into Chengzong's reign and took the ganzhi 癸卯.
Obviously it would be another matter as to whether chapters of the book were indeed composed in the same year, but as far as we can draw from the original text, 1303 was indeed the year Zhu finalized his three volumes.
For reference, I found the original Chinese text of Jade Mirror of the Four Unknowns on Chinese Wikisource, and there's also a listing of the aformentioned preface from the digital library Chinese Text Project.
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