Editing Calculus (section)

==== Greece ====
{{See also|Greek mathematics}}
[[File:Parabolic segment and inscribed triangle.svg|thumb|upright|right|Archimedes used the [[method of exhaustion]] to calculate the area under a parabola in his work ''[[Quadrature of the Parabola]]''.]]
Laying the foundations for integral calculus and foreshadowing the concept of the limit, ancient Greek mathematician [[Eudoxus of Cnidus]] ({{circa|390–337{{nbsp}}BC|lk=no}}) developed  the [[method of exhaustion]] to prove the formulas for cone and pyramid volumes.

During the [[Hellenistic period]], this method was further developed by [[Archimedes]] ({{c.|lk=no|287|212}}{{nbsp}}BC), who combined it with a concept of the [[Cavalieri's principle|indivisibles]]—a precursor to [[Archimedes use of infinitesimals|infinitesimals]]—allowing him to solve several problems now treated by integral calculus. In ''[[The Method of Mechanical Theorems]]'' he describes, for example, calculating the [[center of gravity]] of a solid [[Sphere|hemisphere]], the center of gravity of a [[frustum]] of a circular [[paraboloid]], and the area of a region bounded by a [[parabola]] and one of its [[secant line]]s.<ref>See, for example:
* {{Cite web |last=Powers |first=J. |date=2020 |title="Did Archimedes do calculus?" |url=https://www.maa.org/sites/default/files/images/upload_library/46/HOMSIGMAA/2020-Jeffery%20Powers.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.maa.org/sites/default/files/images/upload_library/46/HOMSIGMAA/2020-Jeffery%20Powers.pdf |archive-date=9 October 2022 |url-status=live |website=[[Mathematical Association of America]] }}
* {{cite book |last=Jullien |first=Vincent |chapter=Archimedes and Indivisibles |date=2015 |doi=10.1007/978-3-319-00131-9_18 |title=Seventeenth-Century Indivisibles Revisited |pages=451–457 |place=Cham |publisher=Springer International Publishing |series=Science Networks. Historical Studies |volume=49 |isbn=978-3-319-00130-2  |issn = 1421-6329}}
* {{Cite web |last=Plummer |first=Brad |date=9 August 2006 |title=Modern X-ray technology reveals Archimedes' math theory under forged painting |url=http://news.stanford.edu/news/2006/august9/arch-080906.html |access-date=28 February 2022 |website=Stanford University |language=en |archive-date=20 January 2022 |archive-url=https://web.archive.org/web/20220120065134/https://news.stanford.edu/news/2006/august9/arch-080906.html |url-status=live }}
* {{cite book|author=Archimedes |title=The Works of Archimedes, Volume 1: The Two Books On the Sphere and the Cylinder |isbn=978-0-521-66160-7 |translator-first=Reviel |translator-last=Netz |publisher=Cambridge University Press |year=2004}}
* {{Cite journal |last1=Gray |first1=Shirley |last2=Waldman |first2=Cye H. |date=20 October 2018 |title=Archimedes Redux: Center of Mass Applications from The Method |journal=The College Mathematics Journal |volume=49 |issue=5 |pages=346–352 |doi=10.1080/07468342.2018.1524647 |issn=0746-8342 |s2cid=125411353}}</ref>