Editing History of calculus (section)

=== Integrals ===
[[Johannes Kepler]]'s work ''Stereometrica Doliorum'' published in 1615 formed the basis of integral calculus.<ref>{{cite web |title=Johannes Kepler: His Life, His Laws and Times |date=24 September 2016 |url=https://www.nasa.gov/kepler/education/johannes |accessdate=2021-06-10 |publisher=NASA |archive-date=2021-06-24 |archive-url=https://web.archive.org/web/20210624003856/https://www.nasa.gov/kepler/education/johannes/ |url-status=dead }}</ref> Kepler developed a method to calculate the area of an ellipse by adding up the lengths of many radii drawn from a focus of the ellipse.<ref name=EB1911>{{cite EB1911 |wstitle=Infinitesimal Calculus/History |display=Infinitesimal Calculus § History |volume=14 |page=537}}</ref>

A significant work was a treatise inspired by Kepler's methods<ref name=EB1911/> published in 1635 by [[Bonaventura Cavalieri]] on his [[method of indivisibles]]. He argued that volumes and areas should be computed as the sums of the volumes and areas of infinitesimally thin cross-sections. He discovered [[Cavalieri's quadrature formula]] which gave the area under the curves ''x''<sup>''n''</sup> of higher degree. This had previously been computed in a similar way for the parabola by Archimedes in ''[[The Method of Mechanical Theorems|The Method]]'', but this treatise is believed to have been lost in the 13th century, and was only rediscovered in the early 20th century, and so would have been unknown to Cavalieri. Cavalieri's work was not well respected since his methods could lead to erroneous results, and the infinitesimal quantities he introduced were disreputable at first.

[[Evangelista Torricelli|Torricelli]] extended Cavalieri's work to other curves such as the [[cycloid]], and then the formula was generalized to fractional and negative powers by Wallis in 1656. In a 1659 treatise, Fermat is credited with an ingenious trick for evaluating the integral of any power function directly.<ref name=quadrature>{{Cite web | last1 = Paradís | first1 = Jaume | last2 = Pla | first2 = Josep | last3 = Viader | first3 = Pelagrí | title = Fermat's Treatise On Quadrature: A New Reading | url = http://www.econ.upf.edu/docs/papers/downloads/775.pdf | access-date = 2008-02-24 | archive-date = 2007-01-07 | archive-url = https://web.archive.org/web/20070107221624/http://www.econ.upf.edu/docs/papers/downloads/775.pdf | url-status = dead }}</ref> Fermat also obtained a technique for finding the centers of gravity of various plane and solid figures, which influenced further work in quadrature.