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===Greek mathematics=== [[File:Oxyrhynchus papyrus with Euclid's Elements.jpg|thumb|One of the oldest surviving fragments of Euclid's ''Elements'', found at [[Oxyrhynchus]] and dated to c. 100 CE.<ref>{{cite web |url=http://www.math.ubc.ca/~cass/Euclid/papyrus/papyrus.html |title=One of the Oldest Extant Diagrams from Euclid |author=Casselman, Bill |author-link=Bill Casselman (mathematician) |publisher=University of British Columbia |access-date=26 September 2008 |url-status=live |archive-date=4 June 2012 |archive-url=https://archive.today/20120604095737/http://www.math.ubc.ca/~cass/Euclid/papyrus/papyrus.html}}</ref>]] [[File:Archimedes pi.svg|thumb|right|upright=1.5<!--fmt low-aspect image-->|Archimedes used the [[method of exhaustion]] to approximate the value of [[pi|Ο]].]] In [[Ptolemaic Kingdom|Hellenistic Egypt]], the mathematician [[Euclid]] laid down the foundations of [[mathematical rigor]] and introduced the concepts of definition, axiom, theorem and proof still in use today in his [[Euclid's elements|''Elements'']], considered the most influential textbook ever written.<ref name="Boyer Influence of the Elements">{{cite book |last=Boyer |author-link=Carl Benjamin Boyer |title=A History of Mathematics |chapter-url=https://archive.org/details/historyofmathema00boye |chapter-url-access=registration |year=1991|chapter=Euclid of Alexandria|page=[https://archive.org/details/historyofmathema00boye/page/119 119]|publisher=John Wiley & Sons |isbn=978-0471543978 |quote=The ''Elements'' of Euclid not only was the earliest major Greek mathematical work to come down to us, but also the most influential textbook of all times. [...]The first printed versions of the ''Elements'' appeared at Venice in 1482, one of the very earliest of mathematical books to be set in type; it has been estimated that since then at least a thousand editions have been published. Perhaps no book other than the Bible can boast so many editions, and certainly no mathematical work has had an influence comparable with that of Euclid's ''Elements''.}}</ref> [[Archimedes]], considered one of the greatest mathematicians of all time,<ref>{{cite book |last=Calinger |first=Ronald |title=A Contextual History of Mathematics |year=1999 |publisher=Prentice-Hall |isbn=978-0-02-318285-3 |page=150 |quote=Shortly after Euclid, compiler of the definitive textbook, came Archimedes of Syracuse (c. 287β212 BC.), the most original and profound mathematician of antiquity. }}</ref> is credited with using the [[method of exhaustion]] to calculate the [[area]] under the arc of a [[parabola]] with the [[Series (mathematics)|summation of an infinite series]], and gave a remarkably accurate approximation of [[pi]].<ref>{{cite web |title=A history of calculus |author1=O'Connor, J.J. |author2=Robertson, E.F. |publisher=[[University of St Andrews]] |url=http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/The_rise_of_calculus.html |date=February 1996 |access-date=7 August 2007 |archive-date=15 July 2007 |archive-url=https://web.archive.org/web/20070715191704/http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/The_rise_of_calculus.html |url-status=live }}</ref> He is also known in physics for laying the foundations of [[Fluid statics|hydrostatics]], [[statics]], and the explanation of the principle of the [[lever]].
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