Editing Plus and minus signs (section)

== History ==
Though the signs now seem as familiar as the [[alphabet]] or the [[Arabic numerals]], they are not of great antiquity. The [[Egyptian hieroglyph]]ic sign for addition, for example, resembles a pair of legs walking in the direction in which the text was written ([[Egyptian language|Egyptian]] could be written either from right to left or left to right), with the reverse sign indicating subtraction:<ref>
{{cite journal
 | last = Karpinski | first = Louis C.
 | doi = 10.2307/2973180
 | issue = 6
 | journal = [[The American Mathematical Monthly]]
 | mr = 1518824
 | pages = 257–265
 | title = Algebraical Developments Among the Egyptians and Babylonians
 | volume = 24
 | year = 1917| jstor = 2973180
 }}</ref>
{| align="center"
|<hiero>D54</hiero> or <hiero>D55</hiero>
|}

[[Nicole Oresme]]'s [[manuscript]]s from the 14th century show what may be one of the earliest uses of {{char|+}} as a sign for plus.<ref>[http://educ.ubc.ca/courses/etec540/Sep02/ResearchAssignment/LustigovaZ/ra-LustigovaZ.htm The birth of symbols – Zdena Lustigova, Faculty of Mathematics and Physics Charles University, Prague] {{webarchive|url=https://archive.today/20130708153352/http://educ.ubc.ca/courses/etec540/Sep02/ResearchAssignment/LustigovaZ/ra-LustigovaZ.htm |date=2013-07-08 }}</ref>

In early 15th century Europe, the letters "P" and "M" were generally used.<ref name="ley196504">{{Cite magazine
 |last=Ley
 |first=Willy
 |date=April 1965
 |title=Symbolically Speaking
 |department=For Your Information
 |url=https://archive.org/stream/Galaxy_v23n04_1965-04#page/n57/mode/2up
 |magazine=Galaxy Science Fiction
 |pages=57–67
}}</ref><ref>{{cite journal|last=Stallings|first=Lynn|date=May 2000|title=A brief history of algebraic notation|journal=School Science and Mathematics|volume=100|issue=5|pages=230–235|doi=10.1111/j.1949-8594.2000.tb17262.x|url=https://dx.doi.org/10.1111/j.1949-8594.2000.tb17262.x|access-date=13 April 2009}}</ref> The symbols (P with overline, {{char|p̄}}, for {{lang|IT|più}} (more), i.e., plus, and M with overline, {{char|m̄}}, for {{lang|IT|meno}} (less), i.e., minus) appeared for the first time in [[Luca Pacioli]]'s mathematics [[compendium]], {{lang|IT|[[Summa de arithmetica|Summa de arithmetica, geometria, proportioni et proportionalità]]}}, first printed and published in [[Venice]] in 1494.<ref>{{cite journal |first1=Alan |last1=Sangster |first2=Greg |last2=Stoner |first3=Patricia |last3=McCarthy |title=The market for Luca Pacioli's Summa Arithmetica |journal=Accounting Historians Journal |volume=35 |issue=1 |year=2008 |pages=111–134 [p. 115] |url=http://eprints.mdx.ac.uk/3201/1/final_final_proof_Market_paper_050308.pdf |doi=10.2308/0148-4184.35.1.111 |s2cid=107010686 |access-date=2012-04-29 |archive-date=2018-01-26 |archive-url=https://web.archive.org/web/20180126012523/http://eprints.mdx.ac.uk/3201/1/final_final_proof_Market_paper_050308.pdf |url-status=live }}</ref>

The {{char|+}} sign is a simplification of the {{langx|la|et}} (comparable to the evolution of the [[ampersand]] {{char|&}}).<ref>{{cite book|last=Cajori|first=Florian|title=A History of Mathematical Notations, Vol. 1|title-link=A History of Mathematical Notations|year=1928|publisher=The Open Court Company, Publishers|chapter=Origin and meanings of the signs + and -}}</ref> The {{char|−}} may be derived from a [[Macron (diacritic)|macron]] <span style="font-family: serif">{{char|◌̄}}</span> written over {{angbr|m}} when used to indicate subtraction; or it may come from a shorthand version of the letter {{angbr|m}} itself.<ref>{{cite book|title=Intermediate Algebra|edition=4th|year=2000|first1=D. Franklin|last1=Wright|first2=Bill D.|last2=New|publisher=Thomson Learning|page=1|quote=The minus sign or bar, — , is thought to be derived from the habit of early scribes of using a bar to represent the letter m}}</ref>

[[File:Johannes_Widmann-Mercantile_Arithmetic_1489.jpg|thumb|alt=A page from Johannes Widmann's book |From [[Johannes Widmann]]'s book on "handy and pretty [[arithmetic]] for all [[merchant]]s"<ref name="widmann1489">{{cite web |last1=Widmann |first1=Johannes |title=Behe[n]de vnd hubsche Rechenung auff allen kauffmanschafft |year=1489 |url=https://www.digitale-sammlungen.de/en/view/bsb00035102?page=176,177 |page=176 |publisher=Leipzig : Konrad Kachelofen |access-date=2022-05-03 |archive-date=2022-05-03 |archive-url=https://web.archive.org/web/20220503161118/https://www.digitale-sammlungen.de/en/view/bsb00035102?page=176,177 |url-status=live }}</ref><ref name="widmann1508">{{cite web |last1=Widmann |first1=Johannes |title=Behend vnd hüpsch Rechnung vff allen Kauffmanschafften |year=1508 |url=https://www.digitale-sammlungen.de/en/view/bsb00003523?page=122,123 |page=122 |publisher=Kolophon: Gedruck zů Pfhortzheim von Thoman Anßhelm |access-date=2022-05-03 |archive-date=2022-05-03 |archive-url=https://web.archive.org/web/20220503161116/https://www.digitale-sammlungen.de/en/view/bsb00003523?page=122,123 |url-status=live }}</ref>]]
In his 1489 treatise, [[Johannes Widmann]] referred to the symbols {{char|−}} and {{char|+}} as ''minus'' and ''mer'' (Modern German {{lang|DE|mehr}}; "more"): {{lang|DE|"[...] was − ist das ist minus [...] und das + das ist mer das zu addirst"}}.{{R|widmann1489}}{{R|widmann1508}}<ref name="OED">{{OED|plus}}</ref> They were not used for addition and subtraction in the treatise, but were used to indicate surplus and deficit; usage in the modern sense is attested in a 1518 book by [[Henricus Grammateus]].<ref>{{cite book|last=Smith|author-link=David Eugene Smith|first=D.E.|title=History of Mathematics|isbn=0486204308 |publisher=Courier Dover Publications|year=1951|volume=1|pages=258, 330}}</ref><ref>{{Cite web |url=https://jeff560.tripod.com/operation.html |title=Earliest Uses of Symbols of Operation |access-date=2022-05-03 |archive-date=2022-04-29 |archive-url=https://web.archive.org/web/20220429221229/https://jeff560.tripod.com/operation.html |url-status=live }}</ref>

[[Robert Recorde]], the designer of the [[equals sign]], introduced plus and minus to Britain in 1557 in ''[[The Whetstone of Witte]]'':<ref>{{citation|title=A History of Mathematical Notations|first=Florian|last=Cajori|author-link=Florian Cajori|publisher=Cosimo|year=2007|isbn=9781602066847|page=164|url=https://books.google.com/books?id=rhEh8jPGQOcC&pg=PA164}}.</ref> "There be other 2 signes in often use of which the first is made thus + and betokeneth more: the other is thus made − and betokeneth lesse."