Editing Commutative property (section)

== History and etymology ==
Records of the implicit use of the commutative property go back to ancient times. The [[Egypt|Egyptians]] used the commutative property of [[multiplication]] to simplify computing [[Product (mathematics)|products]].{{sfn|Gay|Shute|1987|p=[https://archive.org/details/rhindmathematica0000robi_h8l4/page/16 16&dash;17]}} [[Euclid]] is known to have assumed the commutative property of multiplication in his book [[Euclid's Elements|''Elements'']].<ref>{{harvnb|Barbeau|1968|p=183}}. See [http://aleph0.clarku.edu/~djoyce/elements/bookVII/propVII5.html Book VII, Proposition 5], in [[David E. Joyce]]'s online edition of Euclid's ''Elements''</ref> Formal uses of the commutative property arose in the late 18th and early 19th centuries when mathematicians began to work on a theory of functions. Nowadays, the commutative property is a well-known and basic property used in most branches of mathematics.{{sfn|Saracino|2008|p=[https://books.google.com/books?id=GW4fAAAAQBAJ&pg=PA11 11]}}

[[File:Commutative Word Origin.PNG|right|thumb|250px|The first known use of the term was in a French Journal published in 1814]]
The first recorded use of the term ''commutative'' was in a memoir by [[François-Joseph Servois|François Servois]] in 1814, which used the word ''commutatives'' when describing functions that have what is now called the commutative property.{{sfn|Allaire|Bradley|2002}} ''Commutative'' is the feminine form of the French adjective ''commutatif'', which is derived from the French noun ''commutation'' and the French verb ''commuter'', meaning "to exchange" or "to switch", a cognate of ''to commute''. The term then appeared in English in 1838. in [[Duncan Gregory]]'s article entitled "On the real nature of symbolical algebra" published in 1840 in the [[Royal Society of Edinburgh|Transactions of the Royal Society of Edinburgh]].{{sfnm
 | 1a1 = Rice | 1y = 2011 | 1p = [https://books.google.com/books?id=YruifIx88AQC&pg=PA4 4]
 | 2a1 = Gregory | 2y = 1840
}}
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