Editing Mathematical analysis (section)

===Medieval===
[[Zu Chongzhi]] established a method that would later be called [[Cavalieri's principle]] to find the volume of a [[sphere]] in the 5th century.<ref>{{cite book|title=Calculus: Early Transcendentals|edition=3|first1=Dennis G.|last1=Zill|first2=Scott|last2=Wright|first3=Warren S.|last3=Wright|publisher=Jones & Bartlett Learning|date=2009|isbn=978-0763759957|page=xxvii|url=https://books.google.com/books?id=R3Hk4Uhb1Z0C&pg=PR27|access-date=2015-11-15|archive-date=2019-04-21|archive-url=https://web.archive.org/web/20190421114230/https://books.google.com/books?id=R3Hk4Uhb1Z0C&pg=PR27|url-status=live}}</ref> In the 12th century, the [[Indian mathematics|Indian mathematician]] [[Bhāskara II]] used infinitesimal and used what is now known as [[Rolle's theorem]].<ref>{{citation|title=The positive sciences of the ancient Hindus|journal=Nature|volume=97|issue=2426|page=177|first=Sir Brajendranath|last=Seal|date=1915|bibcode=1916Natur..97..177.|doi=10.1038/097177a0|hdl=2027/mdp.39015004845684|s2cid=3958488|hdl-access=free}}</ref>

In the 14th century, [[Madhava of Sangamagrama]] developed [[series (mathematics)|infinite series]] expansions, now called [[Taylor series]], of functions such as [[Trigonometric functions|sine]], [[Trigonometric functions|cosine]], [[trigonometric functions|tangent]] and [[Inverse trigonometric functions|arctangent]].<ref name=rajag78>
{{cite journal
 | title =       On an untapped source of medieval Keralese Mathematics
 | first1=      C. T.
 | last1=      Rajagopal
 | first2 =      M. S.
 | last2=      Rangachari
 | journal  =    Archive for History of Exact Sciences
 | volume =      18 | number=2
 |date=June 1978
 | pages =       89–102 | doi = 10.1007/BF00348142
| s2cid= 51861422
 }}</ref> Alongside his development of Taylor series of [[trigonometric functions]], he also estimated the magnitude of the error terms resulting of truncating these series, and gave a rational approximation of some infinite series.  His followers at the [[Kerala School of Astronomy and Mathematics]] further expanded his works, up to the 16th century.