Editing Reduction (mathematics) (section)

==History==
In the 9th century, [[Mathematics in medieval Islam|Persian mathematician]] [[Al-Khwarizmi]]'s ''[[Al-Jabr]]'' introduced the fundamental concepts of "reduction" and "balancing", referring to the transposition of subtracted terms to the other side of an equation and the cancellation of like terms on opposite sides of the equation. This is the operation which Al-Khwarizmi originally described as ''al-jabr''.<ref name=Boyer-229>{{Citation | first=Carl B. | last=Boyer | author-link=Carl Benjamin Boyer | title=A History of Mathematics | edition=Second | publisher=John Wiley & Sons, Inc. | year=1991 | isbn=978-0-471-54397-8 | chapter-url=https://archive.org/details/historyofmathema00boye/page/229 | chapter=The Arabic Hegemony | page=[https://archive.org/details/historyofmathema00boye/page/229 229] | quote=It is not certain just what the terms ''al-jabr'' and ''muqabalah'' mean, but the usual interpretation is similar to that implied in the translation above. The word ''al-jabr'' presumably meant something like "restoration" or "completion" and seems to refer to the transposition of subtracted terms to the other side of an equation, which is evident in the treatise; the word ''muqabalah'' is said to refer to "reduction" or "balancing"—that is, the cancellation of like terms on opposite sides of the equation. }}</ref> The name "[[algebra]]" comes from the "''al-jabr''" in the title of his book.