|
==On the meaning of ''fangcheng''==
There is no ambiguity in the meaning of the first character ''fang''. It means “rectangle”"rectangle" or “square"square.”" But different interpretations are given to the second character ''cheng'':<ref name=Hart01/>
#The earliest extant commentary, by [[Liu Hui]], dated 263 CE defines ''cheng'' as "measures,”" citing the non-mathematical term ''kecheng'', which means “collecting"collecting taxes according to tax rates.”" Liu then defines ''fangcheng'' as a “rectangle"rectangle of measures.”" The term ''kecheng'', however, is not a mathematical term and it appears nowhere else in the Nine Chapters. Outside of mathematics, ''kecheng'' is a term most commonly used for collecting taxes.
#Li Ji’sJi's "Nine Chapters on the Mathematical Arts: Pronunciations and Meanings" also glosses ''cheng'' as "measure," again using a nonmathematical term, ''kelü'', commonly used for taxation. This is how Li Ji defines ''fangcheng'': "''Fang'' means [on the] left and right. ''Cheng'' means terms of a ratio. Terms of a ratio [on the] left and right, combining together numerous objects, therefore [it] is called a "rectangular array"."
#[[Yang Hui]]’s's "Nine Chapters on the Mathematical Arts with Detailed Explanations" defines ''cheng'' as a general term for measuring weight, height, and length. Detailed Explanations states: What is called “rectangular”"rectangular" (''fang'') is the shape of the numbers; “measure”"measure" (''cheng'') is the general term for [all forms of] measurement, also a method for equating weights, lengths, and volumes, especially referring to measuring clearly and distinctly the greater and lesser.
Since the end of the 19th century, in Chinese mathematical literature the term ''fangcheng'' has been used to denote an "equation." However, as already been noted, the traditional meaning of the term is very different from "equation."
|