Editing Equals sign (section)

==History==
[[Image:First Equation Ever.png|thumb|The first use of an equals sign, equivalent to 14''x''+15=71 in modern notation. From ''[[The Whetstone of Witte]]'' (1557) by [[Robert Recorde]].]]
[[Image:Recorde - The Whetstone of Witte - equals.jpg|thumb|Recorde's introduction of "="]]

Prior to 16th century there was no common symbol for equality, and equality was usually expressed with a word, such as ''aequales, aequantur, esgale, faciunt, ghelijck'' or ''gleich,'' and sometimes by the abbreviated form ''aeq'', or simply {{angbr|æ}} and {{angbr|œ}}.<ref name=":0">{{cite encyclopedia |year=2002 |title=Robert Recorde |encyclopedia=[[MacTutor History of Mathematics Archive]] |url=https://mathshistory.st-andrews.ac.uk/Biographies/Recorde/ |access-date=19 October 2013 |url-status=live |archive-url=https://web.archive.org/web/20131129160351/http://www-history.mcs.st-and.ac.uk/Mathematicians/Recorde.html |archive-date=29 November 2013 |last2=Robertson |first2=E. F. |first1=J. J. |last1=O'Connor}}</ref> [[Diophantus]]'s use of {{angbr|ἴσ}}, short for {{lang|grc|ἴσος}} ({{tlit|grc|ísos}} 'equals'), in ''[[Arithmetica]]'' ({{circa|AD&nbsp;250}}) is considered one of the first uses of an equals sign.<ref>{{cite book |last=Derbyshire |first=John |author-link=John Derbyshire |url=https://archive.org/details/isbn_9780309096577/page/34/mode/2up?q=Equals |title=Unknown Quantity: A Real And Imaginary History of Algebra |publisher=Joseph Henry Press |year=2006 |isbn=0-309-09657-X |page=35}}</ref>

The {{char|1==}} symbol, now universally accepted in mathematics for equality, was first recorded by the Welsh mathematician [[Robert Recorde]] in ''[[The Whetstone of Witte]]'' (1557).<ref>{{Cite web |title=The History of Equality Symbols in Math |url=https://sciencing.com/history-equality-symbols-math-8143072.html |access-date=2020-08-09 |website=Sciencing |date=24 April 2017 |language=en |archive-date=2020-09-14 |archive-url=https://web.archive.org/web/20200914232611/https://sciencing.com/history-equality-symbols-math-8143072.html |url-status=live }}</ref> The original form of the symbol was much wider than the present form. In his book Recorde explains his design of the "Gemowe lines" (meaning ''twin'' lines, from the [[Latin]] {{wikt-lang|la|gemellus}})<ref name="gemellus">See also [[wiktionary:geminus|geminus]] and [[Gemini (constellation)|Gemini]].</ref>
{{blockquote|
{{lang|en-emodeng|italics=yes|And to auoide the tediouſe repetition of theſe woordes : is equalle to : I will ſette as I doe often in woorke vſe, a paire of paralleles, or [[wikt:Gemini|Gemowe]] lines of one lengthe, thus: {{=}}, bicauſe noe .2. thynges, can be moare equalle.}} <br> And to avoid the tedious repetition of these words: "is equal to" I will set as I do often in work use, a pair of parallels, or [[twin|duplicate]] lines of one [the same] length, thus: {{=}}, because no 2 things can be more equal.
|multiline=yes
|source={{cite book |last=Recorde |first=Robert |title=The Whetstone of Witte |location=London |publisher=John Kyngstone |date=1557 }} [https://archive.org/stream/TheWhetstoneOfWitte#page/n237/mode/2up the third page of the chapter "The rule of equation, commonly called Algebers Rule."]
}}
The symbol {{char|1==}} was not immediately popular. After its introduction by Recorde, it was not used again in print until 1618 (61 years later), in an anonymous Appendix in [[Edward Wright (mathematician)|Edward Wright's]] English translation of ''[[Mirifici Logarithmorum Canonis Descriptio|Descriptio]]'', by [[John Napier]]. It was not until 1631 that it received more than general recognition in England, being adopted as the symbol for equality in three influential works, [[Thomas Harriot]]'s [[Artis analyticae praxis|''Artis analyticae praxis'']], [[William Oughtred]]'s ''[[Clavis mathematicae]]'' and [[Richard Norwood]]'s ''[[Trigonometria]]''.<ref>{{Cite book |last=Cajori |first=Florian |url=https://archive.org/details/historyofmathema031756mbp/page/n319/mode/2up |title=A History Of Mathematical Notations Vol I |date=1928 |publisher=The Open Court Company, Publishers |others=Osmania University, Digital Library Of India}}</ref> Later used by [[John Wallis]], [[Isaac Barrow]] and [[Isaac Newton]], which helped it to spread to continental Europe.

=== Competing symbols ===
There were several other competing symbols for equality, especially outside of England around the 16th and 17th centuries, and Recorde's version made no significant influence in the European continent until 1650 or 1660. In 1559 the French monk [[Johannes Buteo]] published his ''Logistica'' using the symbol<math>\ [  </math> for equality. In 1571 [[Wilhelm Xylander]] published an edition of [[Arithmetica|Diophantus' ''Arithmetica'']] in which two parallel vertical lines {{char|{{!}}{{!}}}} were used for equality.{{Efn|He gives no clue as to the origin of the symbol. Moritz Cantor suggests that perhaps the Greek word ίσοι ("equal") was abbreviated in the manuscript used by Xylander, by the writing of only the two letters ίι.}} This version was adopted by several prominent writers, including [[Giovanni Camillo Glorioso|Giovanni Glorioso]], Cardinal [[Michelangelo Ricci]], and many French and Dutch mathematicians in the hundred years after, including [[René Descartes]] in 1621. 

A major competitor to Recorde's sign was Descartes' own symbol, introduced in his [[La Géométrie|''La Géométrie'']] (1637). In fact, Descartes himself used the sign {{char|1==}} for equality in a letter in 1640. Descartes does not give any reason for introducing his new symbol; however, [[Florian Cajori]] suggests it is because {{char|1==}} was also being used for a difference operation at the time. Due to the prominence of ''La Géométrie'', by 1675, Descartes' symbol gained favour over Recorde's in Europe, and most 17th-century writers on the continent either used Descartes' notation for equality or none at all. Around the turn of the 18th century, Recorde's notation gained favour rapidly. The dominating trend in mathematics of the time was [[History of calculus#Newton and Leibniz|differential and integral calculus]]. The fact that both Newton and [[Gottfried Wilhelm Leibniz]] used Recorde's symbol led to its general adoption.