Editing Analytic geometry (section)

===Persia===
The 11th-century Persian mathematician [[Omar Khayyam]] saw a strong relationship between geometry and algebra and was moving in the right direction when he helped close the gap between numerical and [[geometric algebra]]<ref name="Boyer Omar Khayyam positive roots"/> with his geometric solution of the general [[cubic equation]]s,<ref>{{cite journal
| last1=Cooper | first1=Glen M.
| date=2003
| title=Review: Omar Khayyam, the Mathmetician by R. Rashed, B. Vahabzadeh
| journal=[[The Journal of the American Oriental Society]]
| volume=123
| issue=1
| pages=248–249
| doi=10.2307/3217882
| jstor=3217882}}</ref> but the decisive step came later with Descartes.<ref name="Boyer Omar Khayyam positive roots">{{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=The Arabic Hegemony|pages=[https://archive.org/details/historyofmathema00boye/page/241 241–242]|isbn=9780471543978 |quote=Omar Khayyam (ca. 1050–1123), the "tent-maker," wrote an ''Algebra'' that went beyond that of al-Khwarizmi to include equations of third degree. Like his Arab predecessors, Omar Khayyam provided for quadratic equations both arithmetic and geometric solutions; for general cubic equations, he believed (mistakenly, as the sixteenth century later showed), arithmetic solutions were impossible; hence he gave only geometric solutions. The scheme of using intersecting conics to solve cubics had been used earlier by Menaechmus, Archimedes, and Alhazan, but Omar Khayyam took the praiseworthy step of generalizing the method to cover all third-degree equations (having positive roots). For equations of higher degree than three, Omar Khayyam evidently did not envision similar geometric methods, for space does not contain more than three dimensions, ... One of the most fruitful contributions of Arabic eclecticism was the tendency to close the gap between numerical and geometric algebra. The decisive step in this direction came much later with Descartes, but Omar Khayyam was moving in this direction when he wrote, "Whoever thinks algebra is a trick in obtaining unknowns has thought it in vain. No attention should be paid to the fact that algebra and geometry are different in appearance. Algebras are geometric facts which are proved."}}</ref> Omar Khayyam is credited with identifying the foundations of [[algebraic geometry]], and his book ''Treatise on Demonstrations of Problems of Algebra'' (1070), which laid down the principles of analytic geometry, is part of the body of Persian mathematics that was eventually transmitted to Europe.<ref>[[#refmathmaster|Mathematical Masterpieces: Further Chronicles by the Explorers]], p. 92</ref> Because of his thoroughgoing geometrical approach to algebraic equations, Khayyam can be considered a precursor to Descartes in the invention of analytic geometry.<ref name ="Cooper">Cooper, G. (2003). Journal of the American Oriental Society,123(1), 248-249.</ref>{{rp|248}}