Editing Mathematical analysis (section)

===Ancient===
Mathematical analysis formally developed in the 17th century during the [[Scientific Revolution]],<ref name=analysis>{{cite book|last=Jahnke|first=Hans Niels|title=A History of Analysis|series=History of Mathematics |url=https://books.google.com/books?id=CVRZEXFVsZkC&pg=PR7|date=2003|volume=24 |publisher=[[American Mathematical Society]]|isbn=978-0821826232|page=7|access-date=2015-11-15|archive-date=2016-05-17|archive-url=https://web.archive.org/web/20160517180439/https://books.google.com/books?id=CVRZEXFVsZkC&pg=PR7|url-status=live|doi=10.1090/hmath/024}}</ref> but many of its ideas can be traced back to earlier mathematicians. Early results in analysis were implicitly present in the early days of [[Greek mathematics|ancient Greek mathematics]]. For instance, an [[geometric series|infinite geometric sum]] is implicit in [[Zeno of Elea|Zeno's]] [[Zeno's paradoxes#Dichotomy paradox|paradox of the dichotomy]].<ref name="Stillwell_2004"/> (Strictly speaking, the point of the paradox is to deny that the infinite sum exists.) Later, [[Greek mathematics|Greek mathematicians]] such as [[Eudoxus of Cnidus|Eudoxus]] and [[Archimedes]] made more explicit, but informal, use of the concepts of limits and convergence when they used the [[method of exhaustion]] to compute the area and volume of regions and solids.<ref name="Smith_1958"/> The explicit use of [[infinitesimals]] appears in Archimedes' ''[[The Method of Mechanical Theorems]]'', a work rediscovered in the 20th century.<ref>{{cite book|last=Pinto|first=J. Sousa|title=Infinitesimal Methods of Mathematical Analysis|url=https://books.google.com/books?id=bLbfhYrhyJUC&pg=PA7|date=2004|publisher=Horwood Publishing|isbn=978-1898563990|page=8|access-date=2015-11-15|archive-date=2016-06-11|archive-url=https://web.archive.org/web/20160611045431/https://books.google.com/books?id=bLbfhYrhyJUC&pg=PA7|url-status=live}}</ref> In Asia, the [[Chinese mathematics|Chinese mathematician]] [[Liu Hui]] used the method of exhaustion in the 3rd century CE to find the area of a circle.<ref>{{cite book|series=Chinese studies in the history and philosophy of science and technology|volume=130|title=A comparison of Archimedes' and Liu Hui's studies of circles|first1=Liu|last1=Dun|first2=Dainian|last2=Fan|first3=Robert Sonné|last3=Cohen|publisher=Springer|date=1966|isbn=978-0-7923-3463-7|page=279|url=https://books.google.com/books?id=jaQH6_8Ju-MC|access-date=2015-11-15|archive-date=2016-06-17|archive-url=https://web.archive.org/web/20160617055211/https://books.google.com/books?id=jaQH6_8Ju-MC|url-status=live}}, [https://books.google.com/books?id=jaQH6_8Ju-MC&pg=PA279 Chapter, p. 279] {{Webarchive|url=https://web.archive.org/web/20160526221958/https://books.google.com/books?id=jaQH6_8Ju-MC&pg=PA279 |date=2016-05-26 }}</ref> From Jain literature, it appears that Hindus were in possession of the formulae for the sum of the [[arithmetic series|arithmetic]] and [[geometric series|geometric]] series as early as the 4th century BCE.<ref>{{cite journal | title = On the Use of Series in Hindu Mathematics | author = Singh, A. N. | journal  =    Osiris | volume = 1  |date = 1936  | pages = 606–628 | doi = 10.1086/368443 | jstor = 301627 | s2cid = 144760421 | url = https://www.jstor.org/stable/301627}}</ref>
[[Bhadrabahu|Ācārya Bhadrabāhu]] uses the sum of a geometric series in his Kalpasūtra in {{BCE|433}}.<ref>{{cite journal | title = Summation of Convergent Geometric Series and the concept of approachable Sunya | author = K. B. Basant, Satyananda Panda | journal = Indian Journal of History of Science | volume = 48  |date = 2013  | pages = 291–313 | url = https://insa.nic.in/writereaddata/UpLoadedFiles/IJHS/Vol48_2_7_KBBasant.pdf}}</ref>