Editing Diophantus (section)

===Fermat===
[[File:Diophantus-II-8-Fermat.jpg|right|thumb|200px|[[Diophantus_II.VIII|Problem II.8]] in the ''Arithmetica'' (edition of 1670), annotated with Fermat's comment which became [[Fermat's Last Theorem]].]]
The Latin translation of ''Arithmetica'' by [[Bachet]] in 1621 became the first Latin edition that was widely available. [[Pierre de Fermat]] owned a copy, studied it and made notes in the margins. The 1621 edition of ''Arithmetica'' by [[Bachet]] gained fame after [[Pierre de Fermat]] wrote his famous "[[Fermat's Last Theorem|Last Theorem]]" in the margins of his copy: <blockquote>If an integer {{math|''n''}} is greater than 2, then {{math|''a''{{sup|''n''}} + ''b''{{sup|''n''}} {{=}} ''c''{{sup|''n''}}}} has no solutions in non-zero integers {{math|''a''}}, {{math|''b''}}, and {{math|''c''}}. I have a truly marvelous proof of this proposition which this margin is too narrow to contain.</blockquote>Fermat's proof was never found, and the problem of finding a proof for the theorem went unsolved for centuries. A proof was finally found in 1994 by [[Andrew Wiles]] after working on it for seven years.  It is believed that Fermat did not actually have the proof he claimed to have. Although the original copy in which Fermat wrote this is lost today, Fermat's son edited the next edition of Diophantus, published in 1670. Even though the text is otherwise inferior to the 1621 edition, Fermat's annotations—including the "Last Theorem"—were printed in this version.

Fermat was not the first mathematician so moved to write in his own marginal notes to Diophantus; the Byzantine scholar [[John Chortasmenos]] (1370–1437) had written "Thy soul, Diophantus, be with Satan because of the difficulty of your other theorems and particularly of the present theorem" next to the same problem.<ref>{{Cite book|url=https://books.google.com/books?id=-zrGDDwQLo8C&pg=PA322|title=Margins and Metropolis: Authority across the Byzantine Empire|last=Herrin|first=Judith|date=2013-03-18|publisher=Princeton University Press|isbn=978-1400845224|page=322|language=en}}</ref>

Diophantus was among the first to recognise positive [[rational number]]s as numbers, by allowing fractions for coefficients and solutions. He coined the term παρισότης (''parisotēs'') to refer to an approximate equality.<ref>{{citation |last1=Katz |first1=Mikhail G. |title=Almost Equal: The Method of [[Adequality]] from Diophantus to Fermat and Beyond |journal=[[Perspectives on Science]] |volume=21 |issue=3 |pages=283–324 |year=2013 |arxiv=1210.7750 |bibcode=2012arXiv1210.7750K |doi=10.1162/POSC_a_00101 |s2cid=57569974 |last2=Schaps |first2=David |last3=Shnider |first3=Steve |author1-link=Mikhail Katz |author3-link=Steve Shnider}}</ref> This term was rendered as ''adaequalitas'' in Latin, and became the technique of [[adequality]] developed by [[Pierre de Fermat]] to find maxima for functions and tangent lines to curves.