Editing Chinese mathematics (section)

=== ''The Nine Chapters on the Mathematical Art'' ===
''[[The Nine Chapters on the Mathematical Art]]'' dates archeologically to 179 CE, though it is traditionally dated to 1000 BCE, but it was written perhaps as early as 300–200 BCE.{{sfn|Dauben|2013}} Although the author(s) are unknown, they made a major contribution in the eastern world. Problems are set up with questions immediately followed by answers and procedure.<ref name=":42" /> There are no formal mathematical proofs within the text, just a step-by-step procedure.<ref>{{Cite journal |last=Straffin |first=Philip D. |date=1998-06-01 |title=Liu Hui and the First Golden Age of Chinese Mathematics |url=http://www.jstor.org/stable/2691200 |journal=Mathematics Magazine |language=en |volume=71 |issue=3 |pages=163–181 |doi=10.2307/2691200 |jstor=2691200}}</ref> The commentary of Liu Hui provided geometrical and algebraic proofs to the problems given within the text.<ref name=":03" />

''The Nine Chapters on the Mathematical Art'' was one of the most influential of all Chinese mathematical books and it is composed of 246 problems.{{sfn|Dauben|2013}} It was later incorporated into ''The [[Ten Computational Canons]]'', which became the core of mathematical education in later centuries.<ref name=":42" /> This book includes 246 problems on surveying, agriculture, partnerships, engineering, taxation, calculation, the solution of equations, and the properties of right triangles.<ref name=":42" /> ''The Nine Chapters'' made significant additions to solving quadratic equations in a way similar to [[Horner's method]].{{sfn|Needham|1955}} It also made advanced contributions to ''fangcheng'', or what is now known as linear algebra.{{sfn|Hart|2011|pages=11–85}} Chapter seven solves [[Rod calculus#System of linear equations|system of linear equations]] with two unknowns using the false position method, similar to The Book of Computations.{{sfn|Hart|2011|pages=11–85}} Chapter eight deals with solving determinate and indeterminate simultaneous linear equations using positive and negative numbers, with one problem dealing with solving four equations in five unknowns.{{sfn|Hart|2011|pages=11–85}} The Nine Chapters solves systems of equations using methods similar to the modern [[Gaussian elimination]] and [[Triangular matrix|back substitution]].{{sfn|Hart|2011|pp=11–85}}

The version of ''The Nine Chapters'' that has served as the foundation for modern renditions was a result of the efforts of the scholar Dai Zhen. Transcribing the problems directly from ''Yongle Encyclopedia'', he then proceeded to make revisions to the original text, along with the inclusion his own notes explaining his reasoning behind the alterations.{{sfn|Hart|2011|pp=32–33}} His finished work would be first published in 1774, but a new revision would be published in 1776 to correct various errors as well as include a version of ''The Nine Chapters'' from the Southern Song that contained the commentaries of Lui Hui and Li Chunfeng. The final version of Dai Zhen's work would come in 1777, titled ''Ripple Pavilion'', with this final rendition being widely distributed and coming to serve as the standard for modern versions of ''The Nine Chapters''.{{sfn|Dauben|2013|pp=211–216}} However, this version has come under scrutiny from Guo Shuchen, alleging that the edited version still contains numerous errors and that not all of the original amendments were done by Dai Zhen himself.{{sfn|Hart|2011|pp=32–33}}