Editing Posidonius (section)

====Earth's circumference====
{{anchor|Circumference of the Earth|Calculation of Earth's circumference|Arc measurement}}
Posidonius calculated the [[Earth's circumference]] by the [[arc measurement]] method, by reference to the position of the star [[Canopus (star)|Canopus]].<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=978-3110250008 | url=https://books.google.com/books?id=RcfmBQAAQBAJ&pg=PA6 | access-date=2021-05-02 | page=5}}</ref> As explained by Cleomedes, Posidonius observed Canopus on but never above the horizon at Rhodes, while at [[Alexandria]] he saw it ascend as far as 7½ degrees above the horizon (the [[meridian arc]] between the latitude of the two locales is actually 5 degrees 14 minutes). Since he thought Rhodes was 5,000 [[stadion (unit of length)|stadia]] due north of Alexandria, and the difference in the star's elevation indicated the distance between the two locales was 1/48 of the circle, he multiplied 5,000 stadia by 48 to arrive at a figure of 240,000 stadia for the circumference of the Earth.<ref name="fragment 202">Posidonius, [http://www.attalus.org/translate/poseidonius.html#202.K fragment 202]</ref>

His estimate of the latitude difference of these two points, 360 degrees/48=7.5 degrees, is rather erroneous. (The modern value is approximately 5 degrees.) In addition, they are not quite on the same meridian as they were assumed to be. The longitude difference of the points, slightly less than 2 degrees, is not negligible compared with the latitude difference.

Translating stadia into modern units of distance can be problematic, but it is generally thought that the stadion used by Posidonius was almost exactly 1/10 of a modern statute mile. Thus Posidonius's measure of 240,000 stadia translates to {{cvt|24000|mi|km}} compared to the actual circumference of {{cvt|24901|mi|km}}.<ref name="fragment 202"/>

[[File:Posidonius earth circumference.svg|thumb|250px|Posidonius's method for calculating the circumference of the Earth, relied on the [[Horizontal coordinate system|altitude]] of the star [[Canopus]]]]
Posidonius was informed in his approach to finding the Earth's circumference by [[Eratosthenes]], who a century earlier arrived at a figure of 252,000 stadia; both men's figures for the Earth's circumference were uncannily accurate.

[[Strabo]] noted that the distance between Rhodes and Alexandria is 3,750 stadia, and reported Posidonius's estimate of the Earth's circumference to be 180,000 stadia or {{cvt|18000|mi|km}}.<ref>Cleomedes ([http://adsabs.harvard.edu/abs/1975QJRAS..16..152F in Fragment 202]) stated that if the distance is measured by some other number the result will be different, and using 3,750 instead of 5,000 produces this estimation: 3,750 x 48 = 180,000; see Fischer I., (1975), ''Another Look at Eratosthenes' and Posidonius' Determinations of the Earth's Circumference'', Ql. J. of the Royal Astron. Soc., Vol. 16, p. 152.</ref> [[Pliny the Elder]] mentions Posidonius among his sources and without naming him reported his method for estimating the Earth's circumference. He noted, however, that [[Hipparchus]] had added some 26,000 stadia to Eratosthenes's estimate. The smaller value offered by Strabo and the different lengths of Greek and Roman stadia have created a persistent confusion around Posidonius's result. [[Ptolemy]] used Posidonius's lower value of 180,000 stades (about 33% too low) for the Earth's circumference in his [[Geography (Ptolemy)|''Geography'']]. This was the number used by [[Christopher Columbus]] to underestimate the distance to India as 70,000 stades.<ref>[[John Freely]], [https://books.google.com/books?id=MfhjAAAAQBAJ ''Before Galileo: The Birth of Modern Science in Medieval Europe''] (2013), {{ISBN|978-1468308501}}</ref>