Editing Eratosthenes (section)

===Measurement of Earth's circumference{{anchor|Earth's circumference|Arc measurement}}===
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{{main|Earth's circumference#Eratosthenes}}

[[File:Eratosthenes_measure_of_Earth_circumference.svg|thumb|upright=1.4|Measure of Earth's circumference according to Cleomedes' simplified version, based on the approximation that [[Syene]] is on the [[Tropic of Cancer]] and on the same meridian as [[Alexandria]].]]

The measurement of [[Earth's circumference]] is the most famous among the results obtained by Eratosthenes,<ref>{{cite book
 |last=Russo
 |first=Lucio
 |author-link=Lucio Russo
 |url=https://books.google.com/books?id=MOTpnfz7ZuYC
 |title=The Forgotten Revolution: How Science Was Born in 300 BC and Why It Had to Be Reborn
 |date=2004
 |publisher=Springer
 |isbn=3-540-20396-6
 |location=Berlin
 |page=68
 |oclc=52945835
 |access-date=2024-08-28
 |url-status=live
 |archive-url=https://web.archive.org/web/20240828024309/https://www.google.com/books/edition/The_Forgotten_Revolution/MOTpnfz7ZuYC
 |archive-date=2024-08-28
}}</ref> who estimated that the meridian has a length of 252,000 [[Stadion (unit)|stadia]] ({{convert|39060|to|40320|km|mi}}), with an error on the real value between −2.4% and +0.8% (assuming a value for the stadion between {{convert|155|and|160|m|ft}}).<ref name="russo273277" /> Eratosthenes described his [[arc measurement]] technique,<ref name="Torge Müller 2012 p. 5">{{cite book | last1=Torge | first1=W. | last2=Müller | first2=J. | title=Geodesy | publisher=De Gruyter | series=De Gruyter Textbook | year=2012 | isbn=978-3-11-025000-8 | url=https://books.google.com/books?id=RcfmBQAAQBAJ&pg=PA6 | access-date=2021-05-02 | page=5}}</ref> in a book entitled ''{{visible anchor|On the Measure of the Earth}}'', which has not been preserved. However, a simplified version of the method has been preserved, as described by [[Cleomedes]].<ref>Cleomedes, ''Caelestia'', i.7.49–52.</ref>  Modern day measurements of the actual circumference around the [[equator]] is {{cvt|40075.017|km|mi}}, and passing through the [[geographical pole|poles]] the circumference is {{cvt|40007.863|km|mi}}.<ref>{{cite web |first1=Sigurd |last1=Humerfelt |date=26 October 2010 |title=How WGS 84 defines Earth |url=http://home.online.no/~sigurdhu/WGS84_Eng.html |access-date=27 February 2025 |url-status=dead |archive-url=https://web.archive.org/web/20110424104419/http://home.online.no/~sigurdhu/WGS84_Eng.html |archive-date=24 April 2011 }}</ref>  

The simplified method works by considering two cities along the same [[meridian (geography)|meridian]] and measuring both the distance between them and the difference in angles of the shadows cast by the sun on a vertical rod (a [[gnomon]]) in each city at noon on the summer [[solstice]].  The two cities used were [[Alexandria]] and [[Syene]] (modern [[Aswan]]), and the distance between the cities was measured by professional [[bematist]]s.<ref>Martianus Capella, ''De nuptiis Philologiae et Mercurii'', VI.598.</ref> A geometric calculation reveals that the circumference of the Earth is the distance between the two cities divided by the difference in shadow angles expressed as a fraction of [[turn (angle)|one turn]].

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