How was The Nine Chapters on the Mathematical Art recovered after parts of it were lost?

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East Asian mathematics Counting boards and markers, or counting rods, were used in China to solve systems of linear equations. This is an example from the 1st century ce.

The complete version of The Nine Chapters on the Mathematical Art known today was reconstructed through 18th-century philological work.1

Because the original text suffered from gaps over time, scholars restored the work by combining two primary sources:1

The oldest extant copy: A printed version dating to 1213, which contains only the first five chapters.1
Exhaustive quotations: Extensive excerpts found within the Yongle dadian, a 15th-century Chinese encyclopedia compiled under the Yongle emperor.1

This restoration effort was part of a larger movement at the end of the 18th century to edit and recover ancient Chinese mathematical texts that had become rare or poorly understood by the 17th century.1