Suanjing 算經

Suanjing 算經, also written 筭經, is a brief text on mathematics written during the Tang period 唐 (618-907) by Xie Chawei 謝察微 (9th-10th cent.). The original title was Fameng suanjing 發蒙算經.

It is included in the series Shuofu 說郛 and Tang-Song congshu 唐宋叢書, but in an apparently fragmentary version. The bibliographical chapters in the Xintangshu 新唐書 and Songshi 宋史 list the book with a length of 3 juan, but the transmitted text is much shorter. Concerning the author, the Shuofu erroneously calls him a Song-period person. The debate on the origin and date of Xie Chawei's Suanshu is ongoing.

The Shuofu fragment briefly explains all important types of operations, namely multiplication with ten and its multiples (dashu 大數), fragments of ten (xiaoshu 小數), units of length (du 度), units of volume (liang 量), weight units (heng 衡), and area units (mu 畝). These chapters are derived from the book Xiahou Yang suanjing 夏侯陽算經.

In the section titled "Terms from the Nine Chapters" (Jiuzhang mingyi 九章名義), Xie's text replaces older expressions as known from the Jiuzhang suanshu 九章算術, namely sumi (粟米, millet and rice) by subu (粟布, millet and cloth), and the expression ying bu zu 盈不足 "surplus and deficiency" by ying nü 盈朒 "surplus and remnant". These novel terms were used by later scholars.

Particularly noteworthy is the explicit reference to the abacus (zhusuan 珠算), describing features not mentioned in other texts.

In the section titled "Explanations of terms used" (Yongzi liyi 用字例義), the author defines seventy-three mathematical terms. For terms with multiple meanings, different definitions are provided accordingly, for example, cheng 乘 is explained as "when the method involves multiple places" (fa zhi duo wei zhe 法之多位者, and "when the method combines actual variables" (fa shi he bian shu ye 法實合變數也). The book elucidates easily confused terms, such as "cha, a numerical difference in quantity" (cha, duoshao butong shu ye 差，多少不同數也), and "jiao, the remainder after subtraction" (jiao, xiang jian yu ye 較，相減餘也). However, some definitions lack precision and are simply illustrated by examples, such as "shuai means, for example: one, two, three, four, five together make fifteen" (shuai, ru yi er san si wu bing de shiwu shu ye 率，如一二三四五并得十五數也).