{{Short description|Greek librarian, mathematician, geographer, and poet}}
{{about|the Greek scholar of the third century BC}}
{{good article}}
{{Infobox person
| name               = Eratosthenes
| image              = Portrait of Eratosthenes.png
| image_upright      = 0.9
| caption            = Eratosthenes
| birth_date         = 276 BC{{efn|The ''[[Suda]]'' states that he was born in the 126th [[Olympiad]], (276–272&nbsp;BC). [[Strabo]] (''Geography'', i.2.2), though, states that he was a "pupil" (γνωριμος) of [[Zeno of Citium]] (who died in 262&nbsp;BC), which would imply an earlier year of birth ({{nowrap|{{circa}}&nbsp;285 BC}}) since he is unlikely to have studied under him at the young age of 14. However, γνωριμος can also mean "acquaintance", and the year of Zeno's death is by no means definite.<ref name= "Dictionary Sci Bi IV" />}}
| birth_place        = [[Cyrene, Libya|Cyrene]] (in modern [[Libya]])
| death_date         = 194 BC (around age 82){{efn|The ''Suda'' states he died at the age of 80, [[Censorinus]] (''De die natali'', 15) at the age of 81, and [[Pseudo-Lucian]] (''Makrobioi'', 27) at the age of 82.}}
| death_place        = [[Alexandria]]
| occupation         = {{unbulleted list|Scholar|Librarian |Poet |Inventor}}
| known_for          = {{unbulleted list|[[Sieve of Eratosthenes]]|Founder of Geography}}
}}

'''Eratosthenes of Cyrene''' ({{IPAc-en|ɛr|ə|ˈ|t|ɒ|s|θ|ə|,|n|iː|z}} {{respell|err|ə|TOSS|thə|NEEZ}}; {{langx|grc|[[wikt:Ἐρατοσθένης|Ἐρατοσθένης]]}} {{IPA|el|eratostʰénɛːs|}}; {{nowrap|{{circa}}&nbsp;276 BC}}&nbsp;– {{nowrap|{{circa|195/194 BC|lk=no}}}}) was an Ancient Greek [[polymath]]: a philosopher, scholar, mathematician, geographer, poet, astronomer, and music theorist. Eratosthenes eventually became the chief librarian at the [[Library of Alexandria]]. His work was the precursor to the modern discipline of geography, and he introduced some of its terminology, coining the terms ''geography'' and ''geographer''.<ref name= Roller-2010>{{Cite book |url= https://books.google.com/books?id=8peKyWK_SWsC&pg=PA1 |title=Eratosthenes' Geography |author1=Eratosthenes|last2=Roller|first2=Duane W. |date=2010 |publisher=[[Princeton University Press]] |isbn=978-0-691-14267-8 |location= |oclc=373055686}}</ref>{{rp|ix, 1}}

He is best remembered as the first known person to calculate the [[Earth's circumference#Eratosthenes|Earth's circumference]]. He was also the first to calculate [[Earth's axial tilt]], which similarly proved to have remarkable accuracy.<ref name=":02">{{Cite book |last1=Spellman |first1=Frank R. |url=https://books.google.com/books?id=3IW56dcniuwC&pg=PA7 |title=The Handbook of Geoscience |last2=Stoudt |first2=Melissa L. |date=2013 |publisher= Scarecrow Press |isbn=978-0-8108-8614-8 |location= |pages=7}}</ref><ref name="cornell" /> He created the [[Eratosthenes' Map of the World|first global projection]] of the world incorporating [[Circle of latitude|parallels]] and [[Longitude|meridians]] based on the geographic knowledge of his era.<ref name=":02" /> Eratosthenes was the founder of scientific [[chronology]]; he used Egyptian and Persian records to estimate the dates of the main events of the [[Trojan War]], dating the sack of [[Troy]] to 1184&nbsp;BC.<ref name= Williams>{{Cite book |last1=Williams |first1=Henry Smith |author-link1=Henry Smith Williams |url=https://books.google.com/books?id=chNLAAAAYAAJ&pg=PA226 |title=A History of Science: The Beginnings of Science |last2=Williams |first2=Edward Huntington |publisher=Harper & Brothers |year=1904 |volume=I}}</ref>{{rp|226}} In [[number theory]], he introduced the [[sieve of Eratosthenes]], an efficient method of identifying [[prime number]]s and composite numbers.

His devotees nicknamed him ''Pentathlos'' after the Olympians who were well-rounded competitors, for he had proven himself to be knowledgeable in every area of learning. Yet, according to an entry in the ''[[Suda]]'' (a 10th-century Byzantine encyclopedia), some critics scorned him, calling him ''Beta'' (Second, or Number 2'')'' because he always came in second in all his endeavors.<ref name=":14">{{Cite book|title=Suidae lexicon|publisher=In aedibus B. G. Teubneri| year= 1967 |location=Stuttgart|isbn=978-3-519-04233-4|series=Lexicographi Graeci|editor-first=Ada|editor-last=Adler| pages=403| language= Greek |volume= 2 |url= https://www.cs.uky.edu/~raphael/sol/sol-entries/epsilon/2898}}</ref><ref name="asimov">{{cite book |last=Asimov |first=Isaac |chapter=Eratosthenes |title=Asimov's Biographical Encyclopedia of Science and Technology |issue=42| edition= New Revised |publisher=Pan Books Ltd |year=1975 |location=London |page=29 |isbn=0-330-24323-3}}</ref><ref>{{cite book |last=Sagan |first=Carl |title=Cosmos |publisher=Random House Publishing Group |year=2013 |location=US |pages=7–12}}</ref>

==Life==
The son of Aglaos, Eratosthenes was born in [[276 BC]] in [[Cyrene (city)|Cyrene]]. Now part of modern-day [[Libya]], Cyrene had been founded by Greeks during the second half of the 7th century BCE,<ref name= Roller-2010 />{{rp|2}} and its proximity to the sea, its defensible position, its abundant water sources and its rich soil all contributed to its status as the capital city of [[Cyrenaica]].<ref name="Jews Greeks">{{Cite book|title=Jews and Greeks in ancient Cyrene|publisher=Brill|date=1986|location=Leiden|isbn=978-90-04-05970-2|series=Studies in Judaism in late antiquity|first=Shim'on|last=Applebaum}}</ref>{{rp|12}} Cyrene came under the rule of [[Alexander the Great]] in [[332 BC]],<ref name="Jews Greeks" />{{rp|48}} and following his death in [[323 BC]], after a local civil war, it was seized by one of his generals, [[Ptolemy I Soter]], the founder of the [[Ptolemaic Kingdom]].<ref name="Jews Greeks" />{{rp|48}} When Cyrene came under Ptolemaic rule, it had a rich economy, based largely on the export of horses and [[Silphium (antiquity)|silphium]],{{efn|Silphium was a plant used for rich seasoning and medicine,<ref name= Roller-2010 />{{rp|8}} now extinct.<ref name= Matthew>{{Cite book |last= Matthew |first=Christopher Anthony |title=Eratosthenes and the measurement of the Earth's circumference (c. 230 bc) |date=2023 |publisher= Oxford University Press |isbn=978-0-19-887429-4 |location=Oxford}}</ref>{{rp|10}}}}<ref name= Roller-2010 />{{rp|8}} and was long known as a prosperous hub of Greek culture.<ref name= Roller-2010 />{{rp|8}}

According to Roller, the rarity of both Eratosthenes' and his father's names are indicative of his humble origins, although due to the possibilities of upward mobility in the [[Hellenistic world]] he was not limited by them.<ref name= Roller-2010 />{{rp|8}} However, Matthew suggests that his name, meaning "lovely strength" suggests noble upbringing,<ref name= Matthew />{{rp|10}} as does his education from a young age, which could imply his belonging to the aristocracy of Cyrene.<ref name= Roller-2010 />{{rp|11}} Like any young Greek at the time, Eratosthenes would have [[Education in ancient Greece|studied]] in the local [[Gymnasium (ancient Greece)|gymnasium]], where he would have learned physical skills as well as reading, writing, arithmetic, poetry, and music.<ref>{{cite journal|page=110|journal=Self Culture; A Monthly Devoted to the Interests of the Home University League.|year=1896|title=Ancient Greek Athleticism}}</ref><ref>{{cite journal |url=https://muse.jhu.edu/article/654228 |last=Booth |first=A. D. |title=Douris' Cup and the Stages of Schooling in Classical Athens |journal=Echos du Monde Classique: Classical News and Views |volume=29 |issue=2 |year=1985 |pages=274–280 |access-date=2026-01-07}}</ref>

By the late [[260s BCE]], Eratosthenes went to [[Athens]] to further his studies.<ref name= Roller-2010 />{{rp|8}} According to [[Strabo]], he was taught [[Stoicism]] there by the school's founder, [[Zeno of Citium]], though their interaction would have been minimal, since Zeno died shortly after Eratosthenes arrived.<ref name= Roller-2010 />{{rp|9}} Strabo also lists the little-known Apelles of [[Chios]] among his teachers.<ref name= Roller-2010 />{{rp|9}} Eratosthenes is said to have studied under the [[Cynicism (philosophy)|cynic]] [[Aristo of Chios]],<ref name= "Dictionary Sci Bi IV">{{Cite encyclopedia| url= https://archive.org/details/dictionaryofscie0004unse |title= Eratosthenes|editor= Charles Coulston Gillispie | encyclopedia= [[Dictionary of Scientific Biography]] |volume= IV |year=1971 |location=New York |publisher= Charles Scribner's Sons |via=Internet Archive |isbn=978-0-684-16962-0}}</ref>{{rp|388}} and the eclectic [[Bion of Borysthenes]].<ref name= Roller-2010 />{{rp|9}} He was further taught by the recently appointed head of the [[Platonic Academy]], [[Arcesilaus of Pitane]].<ref name= Roller-2010 />{{rp|9}} Eratosthenes' later mathematical work implies that he received mathematical training there.<ref name= Roller-2010 />{{rp|9}} According to the ''Suda'' Eratosthenes was also a student of Lysanias of Cyrene, a philologist and grammarian who focused on [[Homer]].<ref name=":14" /> The poet, scholar, and librarian [[Callimachus]] is likely to have crossed paths with Eratosthenes in local debates and scholarly discourse,<ref name= Roller-2010 />{{rp|9}} even though it is unlikely he was ever formally his teacher.

[[File:Eratosthenes_Teaching_in_Alexandria_(Bernardo_Strozzi,_Montreal).jpg|thumb|''Eratosthenes teaching in Alexandria'' by [[Bernardo Strozzi]] (1635)]]

Strabo complained that Eratosthenes did not pay enough respect to Zeno<ref name= Roller-2010 />{{rp|9}} and criticized him for his association with such varied schools of thought. He believed Eratosthenes was unwilling to commit to philosophy and had learned only enough to appear as a philosopher, seeing it as nothing more than a distraction from his regular work.<ref name= Matthew />{{rp|13}}<ref name= Roller-2010 />{{rp|9}} Later authors may have shared this view to some extent: The ''Suda'' states that Eratosthenes was referred to as ''Beta'' (Second, or Number 2), because he was not seen as the leading expert in any given field.{{efn|Though this may have been because he was the second chief librarian in Alexandria.<ref name= "Dictionary Sci Bi IV" />{{rp|389}}}}<ref name= Roller-2010 />{{rp|9}}<ref name=":14" /> Others dubbed him ''Pentathlos'' (Πένταθλος - All-Rounded), given his various skills and areas of knowledge;<ref name= "Dictionary Sci Bi IV" />{{rp|389}}<ref name=":14" /> ''Pentathlos'', however, is also the title of an athlete who competes in many events but comes in second in all of them.<ref name= Heath-GMath />{{rp|104}} Strabo described Eratosthenes as a mathematician among geographers and a geographer among mathematicians.<ref name="Dicks1971" />

The majority of Eratosthenes' studies focused on philosophy; mathematics was less prominent, and philology even less so.<ref name= Roller-2010 />{{rp|9}} Despite his later contributions to the field, Eratosthenes could not formally study geography, as such a discipline did not exist at the time.<ref name= Roller-2010 />{{rp|9}} Eratosthenes was however exposed to extensive geographic literature, such as the works of Homer, whom he considered the first geographer, [[Hecataeus of Miletus]] (''Circuit of the Earth''), [[Aeschylus]], [[Herodotus]], and others.<ref name= Roller-2010 />{{rp|9}} Additionally, Eratosthenes was born forty years after the death of [[Alexander the Great]], and he would also have encountered the works of Alexander's travel companions [[Androsthenes of Thasos|Androsthenes]], [[Nearchus|Nearchos]], [[Onesicritus|Onesikratos]], [[Ptolemy I Soter|Ptolemy I]], and others, who wrote about their journeys with him, and whose conquests cleared the path for Hellenistic explorers.<ref name= Roller-2010 />{{rp|9}}

Eratosthenes remained in Athens for some twenty years, studying and writing.<ref name= Roller-2010 />{{rp|10}} During this period, he wrote ''Platonikos'', inquiring into the mathematics and music in Plato's philosophy, as well as the poetic works of ''Hermes'' and ''Erigone''. His ''Chronographies'' focused on the important dates of the [[Trojan War]], and his ''Olympic Victors'' compiled a list of the winners of the Olympic games.<ref name= Matthew />{{rp|10}} Little more is known about this period of his life.<ref name= Roller-2010 />{{rp|9}}

In [[246 BCE]], [[Ptolemy III Euergetes|Ptolemy III]] succeeded his father, [[Ptolemy II Philadelphus|Ptolemy II]]. Over the next twenty-five years, the [[Ptolemaic Kingdom|Ptolemaic Empire]] reached its greatest extent, and [[Alexandria]] attained its zenith as an intellectual center.<ref name= Roller-2010 />{{rp|10–11}} The post of [[Library of Alexandria|librarian]], which included the position of royal tutor to [[Ptolemy IV Philopator]],<ref name= Heath-GMath />{{rp|104}} became the most prestigious academic appointment.<ref name= Roller-2010 />{{rp|10–11}} The reigning librarian, [[Apollonius of Rhodes]], was forced into retirement by the new king (possibly through the influence of Callimachus), and Eratosthenes, who by this time was gaining fame as a scholar and a poet in the tradition of Callimachus, was summoned from Athens to replace him.<ref name= Roller-2010 />{{rp|12}} Roller suggests that Eratosthenes' roots in Cyrene, the native city of Callimachus, and more importantly Queen [[Berenice II|Berenike]], contributed favorably to his appointment.<ref name= Roller-2010 />{{rp|12}}

The beginning of Eratosthenes' career in Alexandria was focused on mathematics. He was closely affiliated with [[Archimedes]], who sent him material for comment and praised him enthusiastically for his contributions;<ref name= Roller-2010 />{{rp|12}} his [[The Method of Mechanical Theorems|''Method of Mechanical Theorems'']] was written as a letter to Eratosthenes,<ref>{{Cite book |last1=Archimedes |url=http://archive.org/details/cu31924005730563 |title=The method of Archimedes, recently discovered by Heiberg; a supplement to the Works of Archimedes, 1897 |last2=Heiberg |first2=J. L. (Johan Ludvig) |last3=Heath |first3=Thomas Little |date=1912 |publisher=Cambridge University Press |others=Cornell University Library |pages=12}}</ref> and he sent Eratosthenes the famous ''[[Archimedes's cattle problem|Cattle Problem]]'' to be presented to the mathematicians of Alexandria.<ref name= "Dictionary Sci Bi IV" />{{rp|389}} <ref name= Heath-GMath />{{rp|104}} <ref>{{Cite web |title=Drucke des 18. Jahrhunderts (VD18) / Beytrag 2 [177] |url=http://digitale.bibliothek.uni-halle.de/vd18/content/pageview/4023090 |archive-url=https://web.archive.org/web/20180917182145/http://digitale.bibliothek.uni-halle.de/vd18/content/pageview/4023090 |archive-date=2018-09-17 |access-date=2025-12-04 |via= bibliothek.uni-halle.de |language=de}}</ref> Eratosthenes subsequently wrote compositions on [[geography]], [[philosophy]], [[rhetoric]], [[literary criticism]], [[grammar]], poetry and [[star lore]].<ref name= Matthew />{{rp|12}} <ref name= "Dictionary Sci Bi IV" />{{rp|389}} D. R. Dicks suggests that his astronomical contributions were hardly notable,{{efn|It appears that, outside of the geographical context, Eratosthenes did not contribute any original work in the field of astronomy. His name was not associated with any astronomical observations, nor was he cited as an authority in Ptolemy's works on astronomical calendars and ''[[Almanac|parapegmata]]''.<ref name= "Dictionary Sci Bi IV" />{{rp|391}} Additionally, doubt has been cast on the attribution of the measurement of the sun to him by Eusebius and Macrobius, and the one astronomical title associated with his name, ''Catasterismi'', is considered to be incorrectly attributed, and the lost work upon which it was possibly based can hardly be considered astronomical.<ref name= "Dictionary Sci Bi IV" />{{rp|391}}}}<ref name= "Dictionary Sci Bi IV" />{{rp|391}} and it was said that his poetry strangely contained the very [[Didacticism|didactic]] elements which he condemned.<ref name= Roller-2010 />{{rp|10–11}}

Toward the end of his days, he served as an advisor and companion to [[Arsinoe III|Arsinoe]], sister and wife of Ptolemy IV.<ref name= Matthew />{{rp|15}} According to the ''Suda'', as he aged his eyesight began to fail.<ref name= Matthew />{{rp|301}} <ref name=":14" /> Losing the ability to read and to observe nature plagued and depressed him, leading him to voluntarily starve himself to death.<ref name= Matthew />{{rp|301}} He died at the age of 80 in Alexandria<ref name= Matthew />{{rp|301}} around [[196 BCE]].<ref name= Matthew />{{rp|74}} Roller notes that Dionysios of Kyzikos recorded the genuine epitaph of Eratosthenes, bemoaning the fact that he was buried in a foreign land, with "the shore of Proteus" being a Homeric allusion to the land of Egypt:<ref name= Roller-2010 />{{rp|270}}

<blockquote>A softening old age with no darkening through disease quenched you and put you to deserved sleep pondering great things, Eratosthenes. Mother Kyrene did not receive you into the paternal tombs, son of Aglaos, but you are buried as a friend in a foreign land, here on the edge of the shore of Proteus.<ref name= Roller-2010 />{{rp|270}}</blockquote>

The ''Suda'' records four students of Eratosthenes: [[Aristophanes of Byzantium]], his successor as Librarian of Alexandria, the geographer [[Mnaseas|Mnaseus]] of [[Patara (Lycia)|Patara]] in [[Lycia]], the historian Menander, probably of Ephesos, and Aristis, who was otherwise unknown.<ref name=":14" /><ref name= Matthew />{{rp|14}}

== Contributions ==

=== Astronomy ===

==== Measurement of Earth's circumference{{anchor|Earth's circumference|Arc measurement}} ====
{{main|Earth's circumference#Eratosthenes}}
[[File:Eratosthenes_measure_of_Earth_circumference.svg|thumb|upright=1.5|Measure of Earth's circumference according to Cleomedes's simplified version, based on the approximation that [[Syene]] is on the [[Tropic of Cancer]] and on the same meridian as [[Alexandria]]]]

<!--[[History of physics]] links here -->
The [[Earth's circumference]] is the most famous measurement obtained by Eratosthenes.{{efn|There is much disagreement over the dimension of the unit of length Eratosthenes used, the stade, with the possibilities being {{cvt|160|m}} (Messenian), {{cvt|177|m}} (Delphic), {{cvt|180|m}} (Pan-Hellenic), {{cvt|185|m}} (Attic), {{cvt|191|m}} (Olympic) and {{cvt|210|m}} (Ptolemaic). The size of the stade has direct influence on the measurement of the circumference.<ref name= Matthew />{{rp|273, 280–281}} After a long discussion, Matthew concluded that Eratosthenes' original calculation resulted in a circumference of approximately 224,100 stadia, which, based on the use of the Pan-Hellenic stade of 180 m, is equivalent to {{cvt|40,338|km}} with a margin of error of less than 1%. An approximation extremely close to modern day measurements. Concluding the same discussion, Matthew suggested that one generation later Hipparchus adjusted Eratosthenes' result to 250,000 stadia, and an even later Cleomedes attributed this number to Eratosthenes. Due to an error in transmission, or the intent to match the measurement with the ideal of Platonic numerical perfection, Roman sources of the 1st century CE altered the distance to 252,000 stadia, which was altered again in the 4th century CE to 259,200 stadia, due to an error in transmission or because it divides evenly into degrees, minutes and seconds. Most modern studies follow Cleoemedes or the Roman period measurements of 250,000 and 252,000 stadia respectively.<ref name= Matthew />{{rp|280–281}}}}<ref name="russo273277" /> He described his [[arc measurement]] technique in his book ''{{visible anchor|On the Measure of the Earth}}'', which has not been preserved.<ref name="Torge Müller 2012 p. 52">{{cite book |last1=Torge |first1=W. |url= https://books.google.com/books?id=RcfmBQAAQBAJ&pg=PA6 |title=Geodesy |last2=Müller |first2=J. |publisher= De Gruyter |year=2012 |isbn=978-3-11-025000-8 |series=De Gruyter Textbook |page=5 |access-date= 2021-05-02}}</ref> However, a simplified version of the method as described by [[Cleomedes]] was preserved.<ref>Cleomedes, ''Caelestia'', i.7.49–52.</ref>

The simplified method works by considering two cities along the same [[Meridian (geography)|meridian]], and the difference in angles of the shadows cast by the sun on a vertical rod (a [[gnomon]]). The two cities used by Eratosthenes were [[Alexandria]] and [[Syene]] (modern Aswan). At noon on the summer [[solstice]], there were still shadows in Alexandria.  However, in Syene, rods cast no shadows, and the Sun's rays shone straight down into the city-center well.<ref name=":16">{{Cite web |title=Eratosthenes of Cyrene |url=https://www.khanacademy.org/partner-content/big-history-project/solar-system-and-earth/knowing-solar-system-earth/a/eratosthenes-of-cyrene |access-date=2019-11-19 |website=Khan Academy |language=en}}</ref>

According to Cleomedes, Eratosthenes then measured the shadow's angle to be about 7.2 degrees, which is 1/50 of a full circle, and reasoned using [[Transversal (geometry)|alternate interior angles]] that this angle represented the portion of Earth's curvature between the two cities. The distance between Alexandria and Syene was reported to be about 5,000 stadia, as measured by professional [[bematist]]s.<ref>Martianus Capella, ''De nuptiis Philologiae et Mercurii'', VI.598.</ref>  Eratosthenes multiplied this number by 50 and arrived at a total of roughly 250,000 stadia for the Earth's circumference.<ref name= Heath-GMath />{{rp|106–07}}

This calculation is expressed algebraically as <math>C = \frac{360^\circ d}{\Delta\theta}</math>

where <math>C</math> is the Earth's circumference, <math>d</math> is the distance between the two cities, and <math>{\Delta\theta}</math> is the difference in the two cities' shadow angles.

According to Matthew, the result of Eratosthenes calculation is approximately {{cvt|40338|km|mi}},<ref name= Matthew />{{rp|280}} while the modern day measurement of the circumference around the [[equator]] is {{cvt|40075.017|km|mi}}; passing through the [[Geographical pole|poles]] the circumference is {{cvt|40007.863|km|mi}}.<ref>{{cite web |last1=Humerfelt |first1=Sigurd |date=26 October 2010 |title=How WGS 84 defines Earth |url= http://home.online.no/~sigurdhu/WGS84_Eng.html |url-status=dead |archive-url= https://web.archive.org/web/20110424104419/http://home.online.no/~sigurdhu/WGS84_Eng.html |archive-date=24 April 2011 |access-date=27 February 2025}}</ref>

While Eratosthenes' method was sound he made two false assumptions which fortuitously cancelled each other out. The first was that Syene was on the [[Tropic of Cancer]] and the second was that it lay on the same meridian of longitude (directly south) of Alexandria.  In fact Syene is 1° north of the Tropic and 3° east of Alexandria.<ref>{{Cite book |last=Mercier |first=Hugo |title=The Enigma of Reason |last2=Sperber |first2=Dan |publisher=[[Harvard University Press]] |year=2017 |isbn=978-0674-368309 |location=Cambridge Massachusets |publication-date=2017 |pages=113}}</ref>

==== Sun measurements ====

[[Eusebius of Caesarea]] in his ''[[Preparatio Evangelica]]'' includes a brief chapter of three sentences on celestial distances.<ref name= EoC-Gifford>{{cite book |author= [[Eusebius of Caesarea]] |trans-title=Praeparatio Evangelica |title= Preparation for the Gospel| language= en| translator= [[Edwin Hamilton Gifford]] |year= 1903| chapter= Book 15, Chapter 53 |publisher= Clarendon Press| place= Oxford |url= https://www.tertullian.org/fathers/eusebius_pe_15_book15.htm |via= tertullian.org |access-date=2025-12-08}}</ref> He states simply that Eratosthenes found the distance to the Sun to be "{{lang|grc|σταδίων μυριάδας τετρακοσίας καὶ ὀκτωκισμυρίας}}" (literally "of [[Stadia (length)|stadia]] [[myriad]]s 400 and 80,000") and the distance to the Moon to be 780,000 stadia. The expression for the distance to the Sun has been translated either as 4,080,000 stadia<ref name= EoC-Gifford /> or as 804,000,000 stadia.<ref>{{cite book |author= Eusebius of Caesarea |title= La Préparation Évangélique |trans-title= Preparation for the Gospel| language= fr | editor1= [[Édouard des Places]] |editor2= Jean Sirinelli |translator= Édouard des Places |orig-year= 1974| year= 1980| place= Paris |publisher= Éditions du Cerf| url= |via= |access-date= }}</ref> The meaning depends on whether Eusebius meant 400 myriad plus 80,000 or "400 and 80,000" myriad. With a stade of {{cvt|185|m|||}}, 804,000,000 stadia is {{cvt|149000000|km|||}}, approximately the distance from the Earth to the Sun.

Eratosthenes also calculated the Sun's diameter. According to [[Macrobius]], Eratosthenes made the diameter of the Sun to be about 27 times that of the Earth.<ref name="Smith2005" /> The actual figure is approximately 109 times.<ref name="caltech" />

==== Obliquity of the ecliptic ====

Eratosthenes determined the [[Axial tilt|obliquity of the ecliptic]].<ref name=":42">{{Cite journal |last=Jones |first=Alexander |date=2002-02-01 |title=Eratosthenes, Hipparchus, and the Obliquity of the Ecliptic |url=https://doi.org/10.1177/002182860203300103 |journal=Journal for the History of Astronomy |language=EN |volume=33 |issue=1 |pages=15–19 |doi=10.1177/002182860203300103 |bibcode=2002JHA....33...15J |issn=0021-8286|url-access=subscription }}</ref> The [[ecliptic]] is the apparent circular orbit of the sun projected onto the imaginary celestial sphere over the course of a year; its obliquity is the inclination of its plane relative to the plane of the equator.<ref name=":42" /> The value of this angle is not constant; at the time of Eratosthenes, it was 23° 43′ 40″. As early as the 5th century BC, [[Oenopides|Oenopides of Chios]] had determined 24°; Eratosthenes improved the accuracy of the measurement.<ref name=":42" /> He determined the angular distance between the two tropics as of the full circle (360°), i.e., 47° 42′ 40″, which, when halved, yields a value of 23° 51′ 20″.<ref name=":42" /> How he arrived at this result is unknown; the hypotheses considered in research are speculative. While at the Library of Alexandria, Eratosthenes devised a calendar using his predictions about the ecliptic of the Earth. He calculated that there are 365 days in a year and that every fourth year there would be 366 days.<ref name="manawatu" /> The [[Greek astronomy|Greek astronomer]] [[Hipparchus]] ({{Circa|190|120 BC}}) credited Eratosthenes (276{{snd}}194 BC) as the inventor of the armillary sphere,<ref name= Williams/>{{rp|131}} <ref>{{cite book |last=Bryant |first=Walter William |title= [[iarchive:AHistoryOfAstronomy/page/n33/mode/2up|A History of Astronomy]] |year=1907 |page=18}}</ref><ref>{{cite book |last=Ferguson |first=John |title=Callimachus |year=1980 |page=18 |isbn=978-0-8057-6431-4}}</ref><ref>{{cite book |last=King |first=Henry C. |title=The History of the Telescope |year=2003 |page=7 |publisher=Courier Corporation |isbn=978-0-486-43265-6}}</ref><ref>{{cite book |last1=Couprie |first1=Dirk L. |last2=Hahn |first2=Robert |last3=Naddaf |first3=Gerard |title=Anaximander in Context: New Studies in the Origins of Greek Philosophy |year=2003 |page=179 |publisher=SUNY Press |isbn=978-0-7914-5537-1}}</ref> a model of [[Astronomical object|objects]] in the sky (on the [[celestial sphere]]), consisting of a spherical framework of [[wikt:ring|rings]], centered on [[Earth]] or the [[Sun]], that represent lines of [[Celestial coordinate system|celestial longitude and latitude]] and other astronomically important features, such as the ecliptic.<ref>{{Cite web |title=Armillary sphere {{!}} Navigation, Celestial, Celestial Sphere |url=https://www.britannica.com/science/armillary-sphere |website= britannica.com |language=en |access-date=2025-11-13}}</ref>

{{anchor|Geography}}<!--linked-->

=== Geography ===
[[File:Mappa_di_Eratostene.jpg|alt=Eratosthenes's map of the world (194 BC)|right|thumb|19th-century reconstruction of [[Eratosthenes' Map of the World|Eratosthenes's map of the (for the Greeks) known world]], {{nowrap|{{circa}} 194 BC}}]]

{{see also|History of geodesy|History of longitude}}

Eratosthenes continued to study the Earth, and began to sketch it. In the Library of Alexandria he had access to travel books, which contained information and representations of the world that needed to be pieced together in some organized format.<ref name="Smith2005" /> In his three-volume work ''Geography'' ({{langx|grc-Latn|Geographika}}), he described and mapped his entire known world, even dividing the Earth into five [[Climate classification|climate zones]]:<ref name="Morris" /> two freezing zones around the poles, two [[temperate zones]], and a zone encompassing the equator and the [[tropics]].<ref name="Hutchinson">{{cite encyclopedia |title=Eratosthenes |encyclopedia=Hutchinson's Biography Database |volume=1 |year=2011}}</ref> He placed grids of overlapping lines over the surface of the Earth. He used parallels and meridians to link together every place in the world. It was then possible to estimate the distance from remote locations with this network over the surface of the Earth. In the ''Geography'' he recorded the names of over 400 cities and their locations were shown, a feat without precedent.<ref name= Roller-2010 />

According to Strabo, Eratosthenes argued against the Greek-[[Barbarian]] dichotomy and said Alexander ignored his advisers by his regard for all people with law and government.{{efn|Plutarch's similar discussion claiming that Alexander ignored [[Aristotle]]'s advice in this matter may have been influenced by Eratosthenes, but Plutarch does not confirm his sources.}} Though he argued that Eratosthenes was wrong to claim that Alexander had disregarded the counsel of his advisers asserting that it was Alexander's interpretation of their "real intent" in recognizing that "in some people there prevail the law-abiding and the political instinct, and the qualities associated with education and powers of speech".<ref>{{cite book |last=Isaac |first=Benjamin |title=Invention of Racism in Classical Antiquity |publisher=Princeton University Press |year=2013}}</ref>

=== Mathematics, music theory and metaphysics ===

{{See also|Sieve of Eratosthenes|Primality test}}

In ''Platonikos'', primarily mathematical questions were dealt with; the concepts discussed included distance, ratio, continuous and discontinuous proportion, mathematical mean, prime number and point. The focus was on the theory of proportions, in which Eratosthenes saw the key to [[Platonism|Platonic philosophy.]]  He applied the tool of the ratio equation ("a is to b as c is to d"), which he called "analogy", to both mathematics and philosophy.<ref>{{cite book |editor-last=Dörrie |editor-first=Heinrich |title=Der Platonismus in der Antike |volume=1 |publisher=Stuttgart-Bad Cannstatt |year=1987 | language= de |pages=351, 355, 361f., 367–386}}</ref> Friedrich Solmsen states that in proportion, he believed he had found the unifying bond of the "mathematical" sciences ([[arithmetic]], [[geometry]], [[astronomy]], [[music theory]]), since all statements of these sciences could ultimately be traced back to statements about proportions.<ref>{{Cite journal |last=Solmsen |first=Friedrich |date=1942 |title=Eratosthenes as Platonist and Poet |url= https://www.jstor.org/stable/283547 |journal=Transactions and Proceedings of the American Philological Association |volume=73 |pages=194 |doi=10.2307/283547|jstor=283547 |url-access=subscription }}</ref>

According to Theon of Smyrna, he perceived ratio as the foundational principle which underlies proportion, as well as the "primary cause of the creation of all orderly things",<ref name= "Theon useful">{{Cite book |author1=Theon of Smyrna |title=Mathematics useful for understanding Plato |last2=Lawlor |first2=Robert |last3=Lawlor |first3=Deborah |last4=Toulis |first4=Christos |date=1979 |publisher=Wizards Bookshelf |isbn=978-0-913510-24-7 |series=Secret doctrine reference series |location=San Diego}}</ref>{{rp|54}} while he saw the number one as the starting point ''([[first principle|archḗ]])'' and the primary element ''(stoicheíon)'' of numbers and quantity.<ref name= "Theon useful" /><ref>{{cite journal |last=Solmsen |first=Friedrich |title=Eratosthenes as Platonist and Poet |journal=Transactions and Proceedings of the American Philological Association |volume=73 |publisher=American Philological Association |year=1942 |pages=192–213 |doi=10.2307/283547 |jstor=283547 }}</ref>

For Eratosthenes, numbers are unproblematic; but lines, on the other hand, are curious, as they cannot be produced by the combination of individual points, since the individual point has no extension. Eratosthenes contends rather it arises from the continuous movement of a point.<ref name=":12">{{Cite book |author1= Sextus Empiricus |title=Against those in the disciplines |last2=Bett |first2=Richard |date=2018 |publisher=Oxford University Press |isbn=978-0-19-871270-1 |location=Oxford |pages=161–163}}</ref> This view was later criticized by the skeptic [[Sextus Empiricus]].<ref name=":12" />

[[File:Sieve of Eratosthenes animation.gif|right|frame|Sieve of Eratosthenes: algorithm steps for primes below 121 (including optimization of starting from the prime's square)]]

Eratosthenes proposed a mathematical approximate solution to the problem of [[doubling the cube]],{{efn|It was called the "Delian problem" because the [[oracle of Delphi]] said the way to defeat a plague in [[Delos]] was by doubling the size of a cube-shaped altar to [[Apollo]].<ref name= Heath-GMath />{{rp|104}}}}  which was unsolvable with compass and ruler. In order to solve this problem, he constructed a mechanical line drawing device to calculate the cube, called the [[Mesolabio]].<ref>{{Cite web |date=2023-09-23 |title=The Eratosthenes' mesolabio (mean-taker) |url=https://kotsanas.com/en/the-eratosthenes-mesolabio-mean-taker/ |access-date=2025-11-13 |website=Museum of the Ancient Greek Technology |language=en-GB |archive-date=2025-12-01 |archive-url=https://web.archive.org/web/20251201061140/https://kotsanas.com/en/the-eratosthenes-mesolabio-mean-taker/ |url-status=dead }}</ref> He dedicated his solution to King Ptolemy, presenting a model in bronze, with a letter and an epigram.<ref>{{cite book |last=Eutocius |chapter=Eutocii commentarii in libros de sphaera et cylindro |title=Archimedes opera omnia |volume=II |issue=1}}</ref><ref name="zhumud" />

Eratosthenes used an [[algorithm]] that allows one to separate all prime numbers from the set of all odd natural numbers that are less than or equal to a given number. This method is known as the ''[[Sieve of Eratosthenes]]'' (Greek: κόσκινον Ἐρατοσθένους). However, according to Hans-Joachim Waschkies, he did not invent it - as was previously believed; rather, it was already known, and he only coined the term "sieve".<ref>{{cite book |last=Waschkies |first=Hans-Joachim |title=Anfänge der Arithmetik im Alten Orient und bei den Griechen |language= de| place= Amsterdam |year=1989 |pages=280–288}}</ref><ref name= Geus-2002>{{cite book |last=Geus |first=Klaus |title=Eratosthenes von Kyrene. Studien zur hellenistischen Kultur- und Wissenschaftgeschichte |publisher=Munich |year=2002 |language= de| url= https://www.academia.edu/attachments/12860252/download_file | access-date= }}</ref>{{rp|189}}

Eratosthenes' sieve is one of a number of [[prime number sieve]]s, and is a simple, ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite, ''i.e.'', not prime, the multiples of each prime, starting with the multiples of 2. The multiples of a given prime are generated starting from that prime, as a sequence of numbers with the same difference, equal to that prime, between consecutive numbers. This is the sieve's key distinction from using trial division to sequentially test each candidate number for divisibility by each prime.

A secondary subject of ''Platonikos'' was [[music theory]], in which Eratosthenes applied the theory of proportions to music,<ref name=":22">{{cite book |last=Panteri |first=Sara |chapter=Eratosthenes' Πλατωνικός between Philosophy and Mathematics |date=2019-06-17 |title =On the Track of the Books: Scribes, Libraries and Textual Transmission |pages=143–166 |editor-last=Berardi |editor-first=Roberta |url= https://www.degruyterbrill.com/document/doi/10.1515/9783110632590-011/html |access-date=2025-10-27 |publisher=De Gruyter |language=en |doi= 10.1515/9783110632590-011 |isbn=978-3-11-063259-0 |editor2-last=Bruno |editor2-first=Nicoletta |editor3-last=Fizzarotti |editor3-first=Luisa}}</ref> Since antiquity, he is considered an authority in the field of music.<ref name=":22" /> The scholar [[Ptolemy]] preserved Eratosthenes' calculations for the tetrachord, which show that he used the "Pythagorean" tuning, which he then refined.<ref name="Chalmers divisions">{{Cite book |last1=Chalmers |first1=John H. |title=The divisions of the tetrachord: = Peri tōn toy tetrachordoy katatomōn = Sectiones tetrachordi; a prolegomenon to the construction of musical scales |last2=Polansky |first2=Larry |date=1993 |publisher=Frog Peak Music |isbn=978-0-945996-04-0 |location=Hanover, New Hampshire |pages=10}}</ref> Eratosthenes knew and considered the system of the music theorist [[Aristoxenus]].<ref name="Chalmers divisions" />{{rp|48}} However, Ptolemy does not disclose how he proceeded with his calculations.

Eratosthenes addressed metaphysics such as the doctrine of the [[soul]] in the ''Platonikos''. Like the Platonist [[Crantor]], by whom he was probably influenced, he held the view that the soul could not be purely immaterial, but must have something corporeal about it, for it exists in the world of sensible things; moreover, it is always in a body.<ref>{{cite book |last=Krämer |first=Hans |editor-last=Flashar |editor-first=Hellmut |editor-link=Hellmut Flashar |chapter=Eratosthenes |title=Grundriss der Geschichte der Philosophie. Die Philosophie der Antike |language=de |edition=2nd |volume=3: Ältere Akademie – Aristoteles – Peripatos |publisher=Basel |year=2004 |page=126}}</ref><ref>{{cite book |last=Solmsen |first=Friedrich |chapter=Eratosthenes as Platonist and Poet |title= Kleine Schriften |trans-title= Small Writings |language=de |volume=1 |publisher= |location= Hildesheim |year=1968 |pages=212–216}}</ref> This is based on the idea that the soul can only grasp sensible objects if it has a corresponding disposition in its own structure. Accordingly, it is a mixture of two components, one incorporeal and one corporeal.<ref name= Geus-2002/>{{rp|185f}}

== Works ==
[[File:Eratosthenes profile.png|thumb|alt=An etching of a man's head and neck in profile, looking to the left. The man has a beard and is balding|Etching by {{ill|Philipp Daniel Lippert|de}}, ''Dactyliothec'', 1767]]

Eratosthenes was one of the most eminent scholars of his time, and produced works covering a vast area of knowledge before and during his time at the Library. There are no documents left of his work after the [[destruction of the Library of Alexandria]].

===Athenian period===
* ''Platonikos'' - Most probably Eratosthenes' main mathematical treatise, of which only few extracts remain, found in the ''Expositio rerum mathematicarum ad legendum Platonem utilium'', by [[Theon of Smyrna]].<ref name= "Dictionary Sci Bi IV" />{{rp|391}} It is unclear whether the work was a commentary on [[Plato]]'s ''[[Timaeus (dialogue)|Timaeus]]'' or a dialogue with Plato as the principal speaker.<ref name= Heath-GMath />{{rp|104}} It is suggested that it served as a handbook intended to make Plato's works easier for a wider audience to access by clarifying terms and explaining difficult passages.<ref name= Geus-2002/>{{rp|142, 192–194}}
* ''On the Old Comedy'' - A work of literary criticism consisting of twelve books, which attempted to derive the authorship of plays from the dates they were performed, included discussions of textual criticism and contained a section on the meaning and usage of words.<ref name= "Dictionary Sci Bi IV" />{{rp|391}} The latter was highly praised and often cited by ancient authors.<ref name= "Dictionary Sci Bi IV" />{{rp|391}}
* ''Anterinys/Hesiod'' - A poetic work, now lost, the contents of which are unknown.<ref name= "Dictionary Sci Bi IV" />{{rp|392–93}}
* ''Erigone'' - A poetic work depicting the star legend of [[Icarius]], his daughter [[Erigone (daughter of Icarius)|Erigone]] and her dog [[Maera (hound)|Maera]],<ref name= "Dictionary Sci Bi IV" />{{rp|392–93}} according to which Erigone committed suicide upon hearing about the death of her father.<ref name= Roller-2010 />{{rp|115}} The work contained astronomical elements, as the characters were translated as the heavenly bodies of [[Boötes]], [[Virgo Cluster|Virgo]], and [[Sirius]].<ref name= "Dictionary Sci Bi IV" />{{rp|392–93}}
* ''Hermes'' - A poetic work, of which some sixteen lines have survived.<ref name= "Dictionary Sci Bi IV" />{{rp|392–93}} It paralleled the beginning of the [[Homeric hymn]], but added to it the heavenward ascent of Hermes which included a vivid description of the different climate zones of the inhabited world,<ref name= Roller-2010 />{{rp|115}}<ref name= "Dictionary Sci Bi IV" />{{rp|392–93}} and contained "a good deal of descriptive astronomy" in the words of Thomas Heath.<ref name= Heath-GMath />

===Alexandrian period===
* ''On Intermediate Terms (Peri mesotḗtōn)'' - A work attributed to Eratosthenes by [[Pappus of Alexandria|Pappus]], of the late [[third century]] CE.<ref name= Heath-GMath>{{Cite book |last=Heath |first=Thomas Little |url=http://archive.org/details/historyofgreekm02heat |title=A history of Greek mathematics |date=1921 |location=Oxford |publisher= Clarendon Press |others=PIMS - University of Toronto |pages=105}}</ref> Its contents were lost, but it can be said that it consisted of two books, and was of enough importance to be included in what Pappus called the "Treasury of Analysis" together with the writings of [[Euclid]], [[Apollonius of Perga|Apollonius]], and [[Aristaeus the Elder|Aristaeus]], thus implying that it was a systematic geometrical composition.<ref name= Heath-GMath /> In another passage, Pappus refers to "loci with reference to means" which were discussed by Eratosthenes, supposedly in the work mentioned, the nature of these loci in unknown.<ref name= Heath-GMath /> Since this work is not mentioned anywhere else in ancient sources, some have suggested that it is identical with ''Platonikos''.<ref name= Geus-2002/>{{rp|190f.}} In 1981, a medieval Arabic translation of a text by "Aristanes" (Eratosthenes) on mean proportionals was published. However, this is not the lost work ''On Intermediate Terms'' mentioned by Pappus, but an alleged letter from Eratosthenes to [[Ptolemy III Euergetes|King Ptolemy III]] about the doubling of a cube, which is preserved in the original Greek text. The authenticity of the letter is disputed.{{efn|<ref name=Geus-2002 />{{rp|133–135, 195–205}} Geus argues for the authenticity of the letter, which is usually considered a forgery, and provides a German translation on pages 196–200.}}
* ''The Catasterismi'' ("Placings among stars"), cited in the ''Suda'' under the title ''Astronomy''.<ref name=":53">{{Cite web |title=Early Astronomy in the University of Michigan Collections {{!}} Star Mythology: Eratosthenes' Catasterismi |url=https://www.early-astronomy-um.org/ancient_eratosthenes.php |access-date=2025-10-27 |website= early-astronomy-um.org}}</ref> The extant work by this name in its current form cannot be attributed to Eratosthenes, however it is rooted in a genuine work by him with the same name.<ref name= Heath-GMath />{{rp|108}} The ''Catasterismi'' contained a [[star catalogue]], which references the writings of Aratus, but as opposed to the largely technical descriptions of Aratus, it includes a collection of legends relating to individual stars and constellations.<ref name=":53" /> The catalogue contains 42 entries covering all the constellations, one entry on the planets and one entry on the milky way; it includes a list of stars belonging to each constellation, with their locations within the constellation, all together number 736,<ref name=":53" /> (though Hipparchus has approximately 1,000).<ref>{{Cite book |url=https://www.cambridge.org/core/books/cambridge-history-of-science/3916E2283F38CD8E83BD10774C1A5D4A |title=The Cambridge History of Science: Volume 1: Ancient Science |date=2018 |publisher=Cambridge University Press |isbn=978-0-521-57162-3 |editor-last=Jones |editor-first=Alexander |volume=1 |location=Cambridge |doi=10.1017/9780511980145 |editor-last2=Taub |editor-first2=Liba}}</ref> It has been pointed out, that Eratosthenes did not invent the myths, which had been transmitted over centuries through Greek traditions, rather he connected these tales to the constellations and attributed the different mythical characters to them.<ref name=":53" />
* ''Arsinoe'' (a memoir of queen [[Arsinoe III of Egypt|Arsinoe]]; lost; quoted by [[Athenaeus]] in the ''[[Deipnosophistae]]'') - A biography or eulogy of Arsinoe III, wife and sister of Ptolemy IV, who was murdered at the age of 30 after her husband's death.<ref name= Matthew />{{rp|15}} Eratosthenes had been her advisor and companion in public events.<ref name= Matthew />{{rp|15}} The writing of the work is the last datable event in the life of Eratosthenes, and the work itself is likely the last that he wrote, as Arsinoe's death occurred in 204 BCE, Eratosthenes was about eighty years old at the time, and he did not live for much longer.<ref name= Matthew />{{rp|15}}
* ''On the Measurement of the Earth (Περὶ τῆς ἀναμετρήσεως τῆς γῆς)'' - Described as a separate work by Heron in his Dioptra, and according to Galen it dealt with astronomical or mathematical geography.<ref name= Heath-GMath />{{rp|107}} Among the topics discussed were the size of the equator, the distance of the tropic and polar circles, the size of the polar area, the sizes of the sun and the moon and the distances from them and their total and partial eclipses and the changes in the length of the day according to location and date.
* ''Geographica (ГεωγραΦικά)'' - The work was the first attempt at providing a mathematical foundation for geographical studies, as well as the first recorded instance of many terms still in use, including the name of the science [[geography]].<ref name="intro12">{{cite book |last1=Dahlman |first1=Carl |url=https://www.pearson.com/store/en-us/pearsonplus/p/9780137504510.html?creative=545445680380&keyword=&matchtype=&network=g&device=c&gclid=CjwKCAjwpKyYBhB7EiwAU2Hn2QPXxmu7Nqnx04A__xcaDqM3GuPh2cbR2wI7G7ihOs2cQpV7CUFAxxoCzLEQAvD_BwE&gclsrc=aw.ds |title=Introduction to Geography: People, Places & Environment |last2=Renwick |first2=William |date=2014 |publisher=Pearson |isbn=978-0-13-750451-0 |edition=6 |access-date=28 August 2022}}</ref> It is now lost, but 155 [[literary fragment|fragments]] survive, 105 in the writings of Strabo, 16 in the writings of [[Pliny the Elder]], and the rest scattered in Byzantine sources.<ref name= Matthew />{{rp|15}} According to Strabo, who is the primary source for its form and content, it consisted of three parts.<ref name= "Dictionary Sci Bi IV" />{{rp|389}} For a long time it was the main authority on geographical matters, and was referred to by [[Julius Caesar]] in ''De Bello Gallico'', when he mentioned that Eratosthenes knew of the [[Hercynian Forest]].<ref name= "Dictionary Sci Bi IV" />{{rp|389}} Even the critical Strabo admitted that Eratosthenes was the leading authority on the southeastern quarter of the inhabited world.<ref name= "Dictionary Sci Bi IV" />{{rp|389}} The work described the global landmass as a whole, discussed its division into regions, estimated distances, landscape alterations, the location of the inhabited world, and included limited descriptions of lands and peoples.<ref name= "Dictionary Sci Bi IV" />{{rp|389}} The work was criticized by Strabo, who complained that Eratosthenes' approach was too mathematical, and by Hipparchus, who argued that it was not mathematical enough, as Eratosthenes did not make sufficient use of astronomical data in establishing the reference lines of his map.<ref name= "Dictionary Sci Bi IV" />{{rp|390}} It is possible that the circumference of the Earth was written as part of the ''Geographica'', though if it wasn't, it was most likely mentioned in it.<ref name= "Dictionary Sci Bi IV" />{{rp|390}} Its detailed description is now known only through ''De Motu Circulari'' by Cleomedes.<ref name= "Dictionary Sci Bi IV" />{{rp|390}} The first book was something of an introduction and gave a review of his predecessors, recognizing their contributions that he compiled in the library. In this book Eratosthenes denounced [[Homer]] as not providing any insight into what he described as geography. His disapproval of Homer's topography angered many who believed the world depicted in the ''Odyssey'' to be legitimate.<ref name="chambers">{{cite encyclopedia |last=Chambers |first=James T. |chapter=Eratosthenes of Cyrene |title=Dictionary of World Biography: The Ancient World |year=1998 |pages=1–3}}</ref><ref name="Eckerman" /> He commented on the ideas of the nature and origin of the Earth: he thought of Earth as an immovable globe while its surface was changing. He hypothesized that at one time the [[Mediterranean]] had been a vast lake that covered the countries that surrounded it and that it only became connected to the ocean to the west when a passage opened up sometime in its history. The second book contains his calculation of the circumference of the Earth. This is where, according to Pliny, "The world was grasped." Here Eratosthenes described his famous story of the well in Syene.<ref name=":16" /> This book would later be considered a text on [[mathematical geography]]. His third book of the ''Geography'' contained [[political geography]]. He cited countries and used parallel lines to divide the map into sections, to give accurate descriptions of the realms. This was a breakthrough that can be considered the beginning of geography. For this, Eratosthenes was named the "Father of Modern Geography".<ref name="Smith2005" />
* ''Chronographies and Olympic Victors'' - Two works that represent the first systematic, scientific treatment of chronological questions by a Greek author<ref name= "Dictionary Sci Bi IV" />{{rp|391}} and that established a dating system based on the Olympiads.<ref name= "Dictionary Sci Bi IV" />{{rp|389}} ''Olympic Victors'' was likely a popularizing work and included numerous anecdotes, some preserved by Plutarch.<ref name= "Dictionary Sci Bi IV" />{{rp|391}} Clement of Alexandria summarized its main results.<ref name= Heath-GMath />{{rp|109}} It provides dates for several events: the fall of Troy (1184/1183 BCE), the Dorian migration (1104/1103 BCE), the first Olympiad (777/776 BCE), Xerxes' invasion (480/479 BCE), and the outbreak of the Peloponnesian War (432/431 BCE), Eratosthenes' dates are still considered authoritative.<ref name= "Dictionary Sci Bi IV" />{{rp|391}}

===Additional works===
* ''A means of determining prime numbers (the Sieve of Eratosthenes)''
* ''A work on instrumentation''
* ''The calculation of harmonics''
* ''A treatise on philosophy (On Good and Bad)''
* ''A work on rhetoric (On Declamation)''
* ''A literary critique of the works of the poet Homer''
* ''An extensive discussion of the nature of old comedy''
* ''A correction of the calendar (On the 8-Year Cycle)''
* ''An examination of planetary orbits''
* ''An examination of the winds''
* ''Philosophical analyses (On the Philosophical Sects and On Freedom from Pain)''
* ''Dialogues and grammatical works''
* ''A discussion of wealth and poverty''
* ''A history of the campaigns of Alexander the Great (uncertain)''<ref name= Roller-2010 />{{rp|12–13}}

==See also==
* [[Aristarchus of Samos]] ({{circa|310|230&nbsp;BC|lk=on}}), a Greek mathematician who [[On the Sizes and Distances (Aristarchus)|calculated]] the distance from the Earth to the Sun.
* [[Eratosthenes (crater)]] on the [[Moon]].
* [[Eratosthenian]] period in the [[lunar geologic timescale]].
* [[Eratosthenes Seamount]] in the eastern Mediterranean Sea.
* [[Eratosthenes Point]] in [[Antarctica]].
* [[Hipparchus]] ({{circa|190|120&nbsp;BC|lk=on}}), a Greek mathematician who [[On Sizes and Distances (Hipparchus)|measured]] the radii of the Sun and the Moon as well as their distances from the Earth.
* [[Posidonius]] ({{circa|135|51&nbsp;BC|lk=on}}), a Greek astronomer and mathematician who [[Posidonius#Calculation of Earth's circumference|calculated]] the circumference of the Earth.

==Notes==
{{notelist}}

==References==
{{Reflist|refs=<ref name="cornell">[https://hosting.astro.cornell.edu/academics/courses/astro201/eratosthenes.htm "Eratosthenes (276–195 B.C.)"] {{Webarchive|url=https://web.archive.org/web/20210224112430/http://hosting.astro.cornell.edu/academics/courses/astro201/eratosthenes.htm |date=2021-02-24 }}. Cornell University. Accessed 28 July 2019.</ref>
<ref name="Smith2005">Smith, Sir William. "Eratosthenes", in ''A Dictionary of Greek and Roman Biography and Mythology''. Ann Arbor, Michigan: University of Michigan Library, 2005.</ref>
<ref name="Morris">Morris, Terry R. "Eratosthenes of Cyrene." in ''Encyclopedia Of The Ancient World''. November 2001.</ref>
<ref name="Eckerman">Eckerman, Chris. Review of (D.W.) Roller 'Eratosthenes' Geography. Fragments Collected and Translated, with Commentary and Additional Material. The Classical Review. 2011.</ref>
<ref name="caltech">{{cite web|url=http://coolcosmos.ipac.caltech.edu/ask/5-How-large-is-the-Sun-compared-to-Earth-|title=Ask an Astronomer|website=Cool Cosmos|archive-url=https://web.archive.org/web/20140730214334/http://coolcosmos.ipac.caltech.edu/ask/5-How-large-is-the-Sun-compared-to-Earth-|archive-date=2014-07-30}}</ref>
<ref name="russo273277">{{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>
<ref name="manawatu">{{cite magazine |title=Greek Scholar's Work Shows Usefulness of Measurement |magazine=Manawatu Standard |issue=7 |date=2012-06-19 |via=Newspaper Source Plus}}</ref>
<ref name="zhumud">{{cite magazine |last=Zhumud |first=Leonid |title=Plato as 'Architect of Science' |magazine=Phonesis |volume=43 |issue= 3| pages= 211–244 |year=1998}}</ref>
<!-- <ref name="chondros">{{cite journal |last=Chondros |first=Thomas G. |title=Archimedes Life Works and Machines |volume=45 |issue=11 |pages=1766–1775}}</ref> -->
<ref name="Dicks1971">Dicks, D.R. "Eratosthenes", in ''Complete Dictionary of Scientific Biography''. New York: Charles Scribner's Sons, 1971.</ref>
}}

==Further reading==
{{refbegin|30em}}
* {{cite book |last=Aujac |first=G. |title=Eratosthène de Cyrène, le pionnier de la géographie |publisher=Édition du CTHS |year=2001 |location=Paris| language= fr}}
* {{cite book |last=Bulmer-Thomas |first=Ivor |title=Selections Illustlating the History of Greek Mathematics |date=1939–1940 |publisher=Harvard University Press |location=Cambridge, Massachusetts}}
* {{cite book |last=Dicks |first=D. R. |title=Biographical Dictionary of Mathematicians |publisher=Scribner |year=1991 |volume=2 (Dickson–Khwārizmī) |location=New York |pages=681–686 |chapter=Eratosthenes |chapter-url=https://archive.org/details/biographicaldict0002unse_k8v0/page/681/mode/1up |chapter-url-access=limited}}
* {{cite journal |last1=Diller |first1=A |year=1934 |title=Geographical Latitudes in Eratosthenes, Hipparchus and Posidonius |journal=Klio |volume=27 |issue=3 |pages=258–269 |doi=10.1524/klio.1934.27.27.258 |s2cid=194449299}}
* {{cite journal |last=Dorofeeva |first=A. V. |date=1988 |title=Eratosthenes (ca. 276–194 B.C.) |journal=Mat. V Shkole |language=ru |issue=4 |page=i}}
* {{cite journal |last=Dutka |first=J. |date=1993 |title=Eratosthenes' measurement of the Earth reconsidered |journal=Arch. Hist. Exact Sci. |volume=46 |issue=1 |pages=55–66 |bibcode=1993AHES...46...55D |doi=10.1007/BF00387726 |s2cid=119522892}}
* {{cite journal |last=El'natanov |first=B. A. |date=1983 |title=A brief outline of the history of the development of the sieve of Eratosthenes |journal=Istor.-Mat. Issled. |language=ru |volume=27 |pages=238–259}}
* {{cite journal |last1=Fischer |first1=I |year=1975 |title=Another look at Eratosthenes' and Posidonius' determinations of the Earth's circumference |journal=Quarterly Journal of the Royal Astronomical Society |volume=16 |pages=152–167 |bibcode=1975QJRAS..16..152F}}
* {{cite journal |last1=Fowler |first1=D. H. |last2=Rawlins |first2=Dennis |date=1983 |title=Eratosthenes' ratio for the obliquity of the ecliptic |journal=Isis |volume=74 |issue=274 |pages=556–562 |doi=10.1086/353361 |s2cid=144617495}}
* {{cite journal |last=Fraser |first=P. M. |date=1970 |title=Eratosthenes of Cyrene |journal=Proceedings of the British Academy |volume=56 |pages=175–207}}
* {{cite book |last=Fraser |first=P. M. |title=Ptolemaic Alexandria |date=1972 |publisher=Clarendon Press |location=Oxford}}
* {{cite encyclopedia |url=http://hdl.handle.net/10481/27536 |last=Fuentes González |first=P. P. |editor-last=Goulet |editor-first=R. |chapter= |title=Ératosthène de Cyrène |encyclopedia=Dictionnaire des Philosophes Antiques |volume=III |publisher=Centre National de la Recherche Scientifique |year=2000 |location=Paris |pages=188–236 |hdl=10481/27536 |access-date=2026-01-07}}
* {{cite journal |last=Goldstein |first=B. R. |date=1984 |title=Eratosthenes on the "measurement" of the Earth |journal=Historia Math. |volume=11 |issue=4 |pages=411–416 |doi=10.1016/0315-0860(84)90025-9 |doi-access=free}}
* {{cite journal |last=Gulbekian |first=E. |date=1987 |title=The origin and value of the stadion unit used by Eratosthenes in the third century B.C |url=https://link.springer.com/article/10.1007/BF00417008 |journal=[[Archive for History of Exact Sciences]] |volume=37 |issue=4 |pages=359–363 |doi=10.1007/BF00417008 |jstor=41133819 |s2cid=115314003 |url-access=subscription}}
* Honigmann, E. (1929). ''Die sieben Klimata und die πολεις επισημοι''. Eine Untersuchung zur Geschichte der Geographie und Astrologie in Altertum und Mittelalter. Heidelberg: Carl Winter's Universitätsbuchhandlung. 247 S.
* {{cite journal |last=Knaack |first=G. |date=1907 |title=Eratosthenes |journal=Pauly–Wissowa VI |pages=358–388}}
* {{cite journal |last=Manna |first=F. |date=1986 |title=The Pentathlos of ancient science, Eratosthenes, first and only one of the "primes" |journal=Atti Accad. Pontaniana |series=New Series |language=it |volume=35 |pages=37–44}}
* {{cite journal |last1=Muwaf |first1=A. |last2=Philippou |first2=A. N. |date=1981 |title=An Arabic version of Eratosthenes writing on mean proportionals |journal=J. Hist. Arabic Sci. |volume=5 |issue=1–2 |pages=147–175}}
* {{cite book |last=Nicastro |first=Nicholas |url=https://archive.org/details/isbn_9780312372477 |title=Circumference: Eratosthenes and the ancient quest to measure the globe |date=2008 |publisher=St. Martin's Press |isbn=978-0-312-37247-7 |location=New York |url-access=registration}}
* {{MacTutor Biography|id=Eratosthenes}}
* {{cite book |last=Marcotte |first=D. |editor-last1=Argoud |editor-first1=G. |editor-last2=Guillaumin |editor-first2=J.Y. |chapter=La climatologie d'Ératosthène à Poséidonios: genèse d'une science humaine |title=Sciences exactes et sciences appliquées à Alexandrie (IIIe siècle av J.C. – Ier ap J.C.) |publisher=Publications de l'Université de Saint Etienne |year=1998 |location=Saint Etienne, France| language= fr |pages=263–277}}
* {{cite thesis |url=http://ourarchive.otago.ac.nz/bitstream/handle/10523/1713/McPhailCameron2011MA.pdf?sequence=1 |last=McPhail |first=Cameron |title=Reconstructing Eratosthenes' Map of the World: a Study in Source Analysis''. A Thesis Submitted for the Degree of Master of Arts at the University of Otago'' |location=Dunedin, New Zealand |year=2011 |access-date=2026-01-07}}
* {{cite book |last=Pfeiffer |first=Rudolf |url=https://archive.org/details/historyofclassic0000pfei_r5h8 |title=History of Classical Scholarship From the Beginnings to the End of the Hellenistic Age |date=1968 |publisher=Clarendon Press |location=Oxford |url-access=registration}}
* {{cite journal |last=Rawlins |first=D. |date=1982 |title=Eratosthenes' geodesy unraveled: was there a high-accuracy Hellenistic astronomy |journal=Isis |volume=73 |issue=2 |pages=259–265 |doi=10.1086/352973 |s2cid=120730515}}
* {{cite journal |last=Rawlins |first=D. |date=1982 |title=The Eratosthenes – Strabo Nile map. Is it the earliest surviving instance of spherical cartography? Did it supply the 5000 stades arc for Eratosthenes' experiment? |journal=Arch. Hist. Exact Sci. |volume=26 |issue=3 |pages=211–219 |doi=10.1007/BF00348500 |s2cid=118004246}}
* {{cite journal |last=Rawlins |first=D. |date=2008 |title=Eratosthenes's large Earth and tiny universe |url=http://www.dioi.org/vols/we0.pdf |url-status=live |journal=DIO |volume=14 |pages=3–12 |bibcode=2008DIO....14....3R |archive-url=https://web.archive.org/web/20081030220751/http://www.dioi.org/vols/we0.pdf |archive-date=2008-10-30}}
* {{cite book |last=Roller |first=Duane W. |url=https://books.google.com/books?id=8peKyWK_SWsC |title=Eratosthenes' Geography: Fragments collected and translated, with commentary and additional material |date=2010 |publisher=Princeton University Press |isbn=978-0-691-14267-8 |location=Princeton}}
* Rosokoki, A. (1995), ''Die Erigone des Eratosthenes. Eine kommentierte Ausgabe der Fragmente'', Heidelberg: C. Winter-Verlag
* Shcheglov, D.A. (2004/2006). "Ptolemy's System of Seven Climata and Eratosthenes' Geography". ''Geographia Antiqua'' '''13''': 21–37.
* {{cite journal |last1=Shcheglov |first1=D.A. |year=2006 |title=Eratosthenes' Parallel of Rhodes and the History of the System of Climata |url=https://www.academia.edu/191065 |journal=Klio |volume=88 |issue=2 |pages=351–359 |doi=10.1524/klio.2006.88.2.351 |s2cid=190529073}}
* {{cite book |author= Strabo |title=The Geography of Strabo |title-link=Geographica |date=1917 |publisher=Putnam |translator= Horace Leonard Jones |location=New York}}
* {{cite journal |last=Taisbak |first=C. M. |date=1984 |title=Eleven eighty-thirds. Ptolemy's reference to Eratosthenes in Almagest I.12 |journal=Centaurus |volume=27 |issue=2 |pages=165–167 |bibcode=1984Cent...27..165T |doi=10.1111/j.1600-0498.1984.tb00766.x}}
* Thalamas, A. (1921). ''La géographe d'Ératosthène''. Versailles.
* {{cite book |last=Wolfer |first=E. P. |title=Eratosthenes von Kyrene als Mathematiker und Philosoph |date=1954 |publisher=Groningen-Djakarta}}
{{refend}}

==External links==

{{Commons category}}{{Wikiquote}}{{wikisource|works=or}}{{Library resources box|by=yes|onlinebooks=yes|others=yes|about=yes|label=Eratosthenes}}
* [http://www.roger-pearse.com/weblog/2017/04/15/cleomedes-how-big-is-the-earth/ English translation of the primary source for Eratosthenes and the size of the Earth] at Roger Pearse.
* [http://www.wilbourhall.org/index.html#eratosthenes Bernhardy, Gottfried: ''Eratosthenica''] Berlin, 1822 (PDF) (Latin/Greek), Reprinted Osnabrück 1968 (German)
* [http://www.faust.fr.bw.schule.de/mhb/eratosiv.htm Eratosthenes' sieve in JavaScript] {{Webarchive|url=https://web.archive.org/web/20010301205532/http://www.faust.fr.bw.schule.de/mhb/eratosiv.htm|date=2001-03-01}}
* [https://www.math.utah.edu/~pa/Eratosthenes.html About Eratosthenes' methods, including a Java applet] {{Webarchive|url=https://web.archive.org/web/20070216080431/https://www.math.utah.edu/~pa/Eratosthenes.html|date=2007-02-16}}
* [http://galileoandeinstein.physics.virginia.edu/lectures/gkastr1.html How the Greeks estimated the distances to the Moon and Sun]
* [https://astrosun2.astro.cornell.edu/academics/courses//astro201/eratosthenes.htm Measuring the Earth with Eratosthenes' method] {{Webarchive|url=https://web.archive.org/web/20120113040950/https://astrosun2.astro.cornell.edu/academics/courses//astro201/eratosthenes.htm|date=2012-01-13}}
* [http://aleph0.clarku.edu/~djoyce/mathhist/greece.html List of ancient Greek mathematicians and contemporaries of Eratosthenes]
* [https://www.newadvent.org/cathen/01303a.htm New Advent Encyclopedia article on the Library of Alexandria]
* [http://www.quitebasic.com/prj/math/eratosthenes/ Eratosthenes' sieve in classic BASIC all-web based interactive programming environment]
* [https://www.fondation-lamap.org/en/node/9786' International pedagogical project] {{Webarchive|url=https://web.archive.org/web/20190414194605/https://www.fondation-lamap.org/en/node/9786%27|date=2019-04-14}} : project [[:fr:La main à la pâte]].
* [http://www.phy.ntnu.edu.tw/ntnujava/htmltag.php?code=users.sgeducation.lookang.Eratostheneswee_pkg.EratosthenesweeApplet.class&name=Eratostheneswee&muid=14019 Open source Physics Computer Model about Eratosthenes estimation of radius and circumference of Earth] {{Webarchive|url=https://web.archive.org/web/20200105154547/http://www.phy.ntnu.edu.tw/ntnujava/htmltag.php?code=users.sgeducation.lookang.Eratostheneswee_pkg.EratosthenesweeApplet.class&name=Eratostheneswee&muid=14019|date=2020-01-05}}
* [https://www.astrologicon.org/eratosthenes/eratosthenes-katasterismoi1.html Eratosthenes, Katasterismoi (or Astrothesiae), original text]
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