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=== History === The ancient Greeks had good measurements of the obliquity since about 350 BCE, when [[Pytheas]] of Marseilles measured the shadow of a [[gnomon]] at the summer solstice.<ref> {{cite book |last=Gore |first=J. E. |date=1907 |title=Astronomical Essays Historical and Descriptive |publisher=Chatto & Windus |url=https://archive.org/details/astronomicaless00goregoog |page=[https://archive.org/details/astronomicaless00goregoog/page/n78 61] }}</ref> About 830 CE, the Caliph [[Al-Mamun]] of Baghdad directed his astronomers to measure the obliquity, and the result was used in the Arab world for many years.<ref> {{cite book |last=Marmery |first=J. V. |date=1895 |title=Progress of Science |publisher=Chapman and Hall, ld. |url=https://archive.org/details/in.ernet.dli.2015.45033 |page=[https://archive.org/details/in.ernet.dli.2015.45033/page/n67 33] }}</ref> In 1437, [[Ulugh Beg]] determined the Earth's axial tilt as 23°30′17″ (23.5047°).<ref>{{cite book |first=L.P.E.A. |last=Sédillot |title=Prolégomènes des tables astronomiques d'OlougBeg: Traduction et commentaire |location=Paris |publisher=Firmin Didot Frères |year=1853 |pages=87 & 253}}</ref> During the [[Middle Ages]], it was widely believed that both precession and Earth's obliquity oscillated around a mean value, with a period of 672 years, an idea known as ''[[trepidation (astronomy)|trepidation]]'' of the equinoxes. Perhaps the first to realize this was incorrect (during historic time) was [[Ibn al-Shatir]] in the fourteenth century<ref>{{cite book |last=Saliba |first=George |date=1994 |title= A History of Arabic Astronomy: Planetary Theories During the Golden Age of Islam |page=235 }}</ref> and the first to realize that the obliquity is decreasing at a relatively constant rate was [[Fracastoro]] in 1538.<ref> {{cite book |last=Dreyer |first=J. L. E. |date=1890 |url=https://archive.org/details/tychobraheapict00dreygoog |title=Tycho Brahe |publisher=A. & C. Black |page=[https://archive.org/details/tychobraheapict00dreygoog/page/n387 355] }}</ref> The first accurate, modern, western observations of the obliquity were probably those of [[Tycho Brahe]] from [[Denmark]], about 1584,<ref>Dreyer (1890), p. 123</ref> although observations by several others, including [[al-Ma'mun]], [[Sharaf al-Dīn al-Tūsī|al-Tusi]],<ref> {{cite book |last=Sayili |first=Aydin |date=1981 |title= The Observatory in Islam |page=78 }}</ref> [[Georg Purbach|Purbach]], [[Regiomontanus]], and [[Bernhard Walther|Walther]], could have provided similar information.
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