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{{short description|Greek mathematician, geographer, poet (c. 276 – c. 195/194 BC)}}
]
{{about|the Greek scholar of the third century BC}}
{{Infobox person
| name = Eratosthenes
| image = Eratosthenes_profile.png
| alt = An etching of a man's head and neck in profile, looking to the left. The man has a beard and is balding.
|caption=Etching of an ancient seal identified as Eratosthenes. {{ill|Philipp Daniel Lippert|de}}, ''Dactyliothec'', 1767.
| birth_date = 276 BC{{NoteTag|name=birth}}
| birth_place = ] (in modern ])
| death_date = 194 BC (around age 82){{NoteTag|name=death}}
| death_place = ]
| occupation = {{unbulleted list|Scholar|Librarian |Poet |Inventor}}
| known_for = {{unbulleted list|]|Founder of Geography}}
}}
'''Eratosthenes of Cyrene''' ({{IPAc-en|ɛr|ə|ˈ|t|ɒ|s|θ|ə|n|iː|z}}; {{langx|grc|]}} {{IPA-el|eratostʰénɛːs|}}; {{nowrap|{{circa}}&nbsp;276 BC}}&nbsp;– {{nowrap|{{circa|195/194 BC|lk=no}}}}) was an Ancient Greek ]: a ], ], ], ], and ]. He was a man of learning, becoming the chief librarian at the ]. His work is comparable to what is now known as the study of ], and he introduced some of the ] still used today.<ref name="roller" />


He is best known for being the first person known to calculate the ], which he did by using the extensive survey results he could access in his role at the Library. His calculation was remarkably accurate (his error margin turned out to be less than 1%).<ref name="russo273277" /><ref>{{cite web |url=https://imagine.gsfc.nasa.gov/features/cosmic/earth_info.html|title= Imagine the Universe – The Earth}}</ref> He was also the first person to calculate ], which similarly proved to have remarkable accuracy.<ref name="cornell" /> He created the ] of the world, incorporating ] and ] based on the available geographic knowledge of his era.
'''Eratosthenes''' ('''&#917;&#961;&#945;&#964;&#959;&#963;&#952;&#941;&#957;&#951;&#962;''') (] - ]) was a ] ], ] and ]. His contemporaries nicknamed him 'Beta' because he was the second best in the world in many subjects.


Eratosthenes was the founder of scientific ];<ref>{{cite encyclopedia|title=Greek chronology|encyclopedia=Britannica|url=https://www.britannica.com/topic/chronology/Greek}}</ref> he used Egyptian and Persian records to estimate the dates of the main events of the ], dating the sack of ] to 1183 BC. In ], he introduced the ], an efficient method of identifying ]s and composite numbers.
He was born in ] (now in ]), but worked and died in ] ]. He is noted for devising a system of ] and ] and ] the size of the ].


He was a figure of influence in many fields who yearned to understand the complexities of the entire world.<ref name="chambers" /> 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<ref name="epsilon" /> in the '']'' (a 10th-century encyclopedia), some critics scorned him, calling him ''Number 2'' because he always came in second in all his endeavours.<ref name="asimov" />
Eratosthenes studied at Alexandria and for some years in ]. In ] he was appointed by ] as librarian of the ]. He made several important contributions to ] and ], and was a good friend to ]. Around ] he invented the ], which was widely used until the invention of the ] in the ].


==Life==
He is credited by ] in ''On the Circular Motions of the Celestial Bodies'' with having calculated the Earth's ] ca. ], using ] and knowledge of the angle of ] of the ] at noon in Alexandria and ] (now ], Egypt).
The son of Aglaos, Eratosthenes was born in 276 BC in ]. Now part of modern-day ], Cyrene had been founded by Greeks centuries earlier and became the capital of ], a country of five cities: Cyrene, ], ], ], and ]. ] conquered Cyrene in 332 BC, and following his death in 323 BC, its rule was given to one of his generals, ], the founder of the ]. Under Ptolemaic rule the economy prospered, based largely on the export of horses and ], a plant used for rich seasoning and medicine.<ref name="roller"/> Cyrene became a place of cultivation, where knowledge blossomed. Like any young Greek at the time, Eratosthenes would have studied in the local ], where he would have learned physical skills and social discourse as well as reading, writing, arithmetic, poetry, and music.<ref name="bailey" />
] (1635)]]


Eratosthenes went to Athens to further his studies. There he was taught ] by its founder, ], in philosophical lectures on living a virtuous life.<ref name="rist" /> He then studied under ], who led a more ] school of philosophy. He also studied under the head of the ], who was ]. His interest in ] led him to write his first work at a scholarly level, ''Platonikos'', inquiring into the mathematical foundation of Plato's philosophies.<ref name="chambers" /> Eratosthenes was a man of many perspectives and investigated the ] under ].<ref name="bailey" /> He wrote poems: one in ]s called ''Hermes'', illustrating the god's life history; and another in ]s, called ''Erigone'', describing the suicide of the Athenian maiden ].<ref name="chambers" /> He wrote ''Chronographies'', a text that scientifically depicted dates of importance, beginning with the ]. This work was highly esteemed for its accuracy. ] was later able to preserve from ''Chronographies'' a list of 38 kings of the ]. Eratosthenes also wrote ''Olympic Victors'', a chronology of the winners of the ]. It is not known when he wrote his works, but they highlighted his abilities.
Eratosthenes results, that make the degree 700 stadia, imply the circumference of the earth is 252,000 stadia and would be off by 1 part in 6 if the stadia he were using were Greek or Roman ] of 185 m.


These works and his great poetic abilities led the king ] to seek to place him as a librarian at the ] in the year 245 BC. Eratosthenes, then thirty years old, accepted Ptolemy's invitation and traveled to Alexandria, where he lived for the rest of his life. Within about fifty years he became Chief Librarian, a position that the poet ] had previously held. As head of the library Eratosthenes tutored the children of Ptolemy, including ] who became the fourth Ptolemaic pharaoh. He expanded the library's holdings: in Alexandria all books had to be surrendered for duplication. It was said that these were copied so accurately that it was impossible to tell if the library had returned the original or the copy.
If his results were acurate his stadia would have measured 158.57 m. As it happens this works out to 302 Egyptian ].
He sought to maintain the reputation of the Library of Alexandria against competition from the ]. Eratosthenes created a whole section devoted to the examination of ], and acquired original works of great tragic dramas of ], ] and ].<ref name="chambers" />


Eratosthenes made several important contributions to ] and ], and was a friend of ]. Around 255&nbsp;BC, he invented the ]. In ''On the Circular Motions of the Celestial Bodies'',<ref>{{Cite web|title=Aratus's "Phenomena," Cleomedes's "On the Circular Motions of the Celestial Bodies," and Nichomachus's "Introduction to Arithmetic" – Viewer – World Digital Library|url=https://www.wdl.org/en/item/14757/view/1/1/|access-date=2021-02-24|website=www.wdl.org}}</ref> ] credited him with having calculated the ] around 240 BC, with high accuracy.<ref name="russo273277" />
The Egyptians had a very well documented standard of measure called the ] which was 100 royal cubits in length and was the side of an ] or field called a ]. In Greek and Roman times the ] were generally farmed in clusters of three with one left fallow, one plowed and sowed in grain and another planted in hay for the plow animal.


Eratosthenes believed there was both good and bad in every nation and criticized ] for arguing that humanity was divided into Greeks and ]s, as well as for arguing that the Greeks should keep themselves racially pure.<ref name="alexander" /> As he aged, he contracted ], becoming blind around 195 BC. Losing the ability to read and to observe nature plagued and depressed him, leading him to voluntarily starve himself to death. He died in 194&nbsp;BC at the age of 82 in Alexandria.<ref name="bailey" />
This means the Egyptians clusters of fields would have been surveyed by a standard of 300 royal cubits that Eratosthenes could have found useful in his work.


==Scholarly career==
From the information compiled in his library Eratosthenes would have known that the last time the experiment had been performed, on the ] at local ] on the ], the Sun would have appeared at the ], directly overhead &mdash; though Syene was in fact slightly north of the tropic and the same conditions as previously recorded were no longer true in his time.
===Measurement of Earth's circumference{{anchor|Earth's circumference|Arc measurement}}===
<!--] links here -->
{{main|Earth's circumference#Eratosthenes}}


] is on the ] and on the same meridian as ].]]
He also would have discovered in his reading, measurements such as those recorded by Herodotus giving the distance between Alexandria and Syene and information to the effect that the last time the experiment had been performed in his hometown of Alexandria, the angle of elevation of the Sun had been 7&deg; south of the zenith at the same time although that also was no longer true in his time.


The measurement of ] is the most famous among the results obtained by Eratosthenes,<ref>{{cite book
Assuming that Alexandria was due ] of Syene- Alexandria is in fact on a more westerly ]- and knowing from his reading that the distance from Alexandria to Syene was 5000 stadia of 300 Egyptian royal cubits of which there were 700 to a degree he would have known that the distance was a little over 7/360 of the great circle of the Earth
|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 ] ({{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 ] 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 ].<ref>Cleomedes, ''Caelestia'', i.7.49–52.</ref>


The simplified method works by considering two cities along the same ] and measuring both the distance between them and the difference in angles of the shadows cast by the sun on a vertical rod (a ]) in each city at noon on the summer ]. The two cities used were ] and ] (modern ]), and the distance between the cities was measured by professional ]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 ].
The distance between the cities was about 5,000 ] or 7 degrees, 1 itrw, and 7 khet


{{anchor|Geography}}<!--linked-->
This recognized that the Egyptian itrw of 70 stadia was 1/10 a value of 700 stadia per degree, with a great circle circumference of 252,000 stadia. The methods discovered by Eratosthenes' were used again by ]to check the results about 150 years later.


===Geography===
Much confusion has existed because the Attic Greeks used a stadion of 600 pous of 304.8 mm = 185 m which doesn't agree with the reported calculations. Similarly the Roman Stadium of 625 pes of 296 mm which also equals 185m has to be rejected. Its worth observing that Eratosthenes was not an Attic Greek but rather a resident of Alexandria in Egypt which had since its conquest by the Persians and incorporation in their empire used a stadia of 300 Egyptian royal cubits or 157.5 m.
], {{nowrap|{{circa}} 194 BC}}]]
{{see also|History of geodesy|History of longitude}}


Eratosthenes now continued from his knowledge about the Earth. Using his discoveries and knowledge of its size and shape, he began to sketch it. In the Library of Alexandria he had access to various travel books, which contained various items of 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 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" /> This book is the first recorded instance of many terms still in use today, including the name of the discipline ].<ref name='intro1'>{{cite book |last1=Dahlman |first1=Carl |last2=Renwick |first2=William |title=Introduction to Geography: People, Places & Environment |date=2014 |publisher=Pearson |isbn=978-0-13-750451-0 |edition=6 |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 |access-date=28 August 2022}}</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 now possible to estimate one's distance from remote locations with this network over the surface of the Earth. In the ''Geography'' the names of over 400 cities and their locations were shown, which had never been achieved before.<ref name="roller"/> However, his ''Geography'' has been lost to history, although fragments of the work can be pieced together from other great historians like ], ], ], and ]. While this work is the earliest we can trace certain ideas, words, and concepts in the historical record, earlier contributions may have been lost to history.
Many otherwise knowledgable people have convinced themselves that Eratosthenes' reported value was in error because of this discrepancy. Archimedes, Posidonius, Marinus and Ptolemy also used stadia which were different from the Attic, Ionian and Athenia stadia.
* 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 ] as not providing any insight into what he now 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"/><ref name="Eckerman" /> He also 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 ] 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, wherein at noon each summer solstice, the Sun's rays shone straight down into the city-center well.<ref>{{Cite web|url=https://www.khanacademy.org/partner-content/big-history-project/solar-system-and-earth/knowing-solar-system-earth/a/eratosthenes-of-cyrene|title=Eratosthenes of Cyrene|website=Khan Academy|language=en|access-date=2019-11-19}}</ref> This book would now be considered a text on ].
* His third book of the ''Geography'' contained ]. He cited countries and used parallel lines to divide the map into sections, to give accurate descriptions of the realms. This was a breakthrough and can be considered the beginning of geography. For this, Eratosthenes was named the "Father of Modern Geography."<ref name="Smith2005" />


According to Strabo, Eratosthenes argued against the Greek-] dichotomy. He says Alexander ignored his advisers by his regard for all people with law and government.<ref>Plutarch's similar discussion claiming that Alexander ignored ]'s advice in this matter may have been influenced by Eratosthenes, but Plutarch does not give us confirmation of his sources.</ref> Strabo says that Eratosthenes was wrong to claim that Alexander had disregarded the counsel of his advisers. Strabo argues 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>Isaac, Benjamin. Invention of Racism in Classical Antiquity. Princeton University Press, 2013.</ref>
Marinus and Ptolemy used a stadia composed of 600 remen which were 5/4 the pous or pes and 5/6 the mh t3 or land cubit and measured 500 to a degree making 1 degree 112.5 km by their reckoning.


===Achievements===
Eratosthenes was described by the ] as a Πένταθλος (Pentathlos) which can be translated as "All-Rounded", for he was skilled in a variety of things; he was a true polymath. His opponents nicknamed him "Number 2" because he was great at many things and tried to get his hands on every bit of information but never achieved the highest rank in anything; ] accounts Eratosthenes as a mathematician among geographers and a geographer among mathematicians.<ref name="Dicks1971" />
* ] in his '']'' includes a brief chapter of three sentences on celestial distances (, Chapter 53). He states simply that Eratosthenes found the distance to the Sun to be "{{lang|grc|σταδίων μυριάδας τετρακοσίας καὶ ὀκτωκισμυρίας}}" (literally "of ] ]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 (1903 translation by E. H. Gifford), or as 804,000,000 stadia (edition of Edouard des Places, dated 1974–1991). 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 ], 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" />
* During his time at the Library of Alexandria, Eratosthenes devised a calendar using his predictions about the ] 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" />
* He was also very proud of his solution for ]. His motivation was that he wanted to produce catapults. Eratosthenes constructed a mechanical line drawing device to calculate the cube, called the mesolabio. He dedicated his solution to King Ptolemy, presenting a model in bronze with it a letter and an epigram.<ref name="zhumud" /> Archimedes was Eratosthenes' friend and he, too, worked on the war instrument with mathematics. Archimedes dedicated his book ''The Method'' to Eratosthenes, knowing his love for learning and mathematics.<ref name="chondros" />


===Number theory===
About ] Eratosthenes is thought to have coined or to have adopted the word '']'', the descriptive study of the Earth.
]
{{Main|Sieve of Eratosthenes|Primality test}}


Eratosthenes proposed a simple ] for finding ]. This algorithm is known in mathematics as the ].
Eratosthenes' other contributions include:


In mathematics, the sieve of Eratosthenes (Greek: κόσκινον Ἐρατοσθένους), one of a number of ]s, 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.
* The ] as a way of finding ]s.
* The measurement of the Sun-Earth distance, now called the ] (804,000,000 stadia).
* The measurement of the distance to the ] (780,000 stadia).
* The measurement of the ] of the ] with an angle error 7'.
* He compiled a ] containing 675 ]s, which was not preserved.
* A map of the ]'s route as far as ].
* A map of the entire known world, from the ] to ], and from the ] to ]. Only ], ], and ] were able to make more accurate maps in the classical and post-classical world.


==Works==
Eratosthenes was known under the name ], because he supposedly proved himself to be the second in the world in many fields. He was also reputedly known for his haughty character. In ] he became blind and a year later he starved himself to death.
Eratosthenes was one of the most pre-eminent scholarly figures of his time, and produced works covering a vast area of knowledge before and during his time at the Library. He wrote on many topics{{snd}}geography, mathematics, philosophy, chronology, literary criticism, grammar, poetry, and even old comedies. There are no documents left of his work after the ].<ref name="Dicks1971" />


===Titles===
The fragmentary collection of ] sky-myths called '']'' (''Katasterismoi'') was given an attribution to Eratosthenes, a name to conjure with, to add to its credibility.
* ''Platonikos'' (lost, quoted by ])
* ''Hermes''
* ''Erigone''
* ''Chronographies''
* ''Olympic Victors''
* ''Περὶ τῆς ἀναμετρήσεως τῆς γῆς'' (''On the Measurement of the Earth'')<ref name="hero" /> (lost, summarized by ])
* ''Гεωγραϕικά'' (''Geographika'')<ref name="Dicks1971"/> (lost, criticized by ])
* ''Arsinoe'' (a memoir of queen ]; lost; quoted by ] in the '']'')
* ''Ariston'' (concerning ]' addiction to luxury; lost; quoted by ] in the '']'')<ref name="ASmith" />
* The '']'' (''Katasterismoi''), a lost collection of ] myths about the ]s


==See also==
==Named after Eratosthenes==
* ] ({{circa|310|230&nbsp;BC|lk=on}}), a Greek mathematician who ] the distance from the Earth to the Sun.
* ] on the ].
* ] on the ].
* ] period in the ]. * ] period in the ].
* ] in the eastern Mediterranean Sea.
* ] in ].
* ] ({{circa|190|120&nbsp;BC|lk=on}}), a Greek mathematician who ] the radii of the Sun and the Moon as well as their distances from the Earth.
* ] ({{circa|135|51&nbsp;BC|lk=on}}), a Greek astronomer and mathematician who ] the circumference of the Earth.


==See also== ==Notes==
{{NoteFoot
* ].
|notes =
{{NoteTag|name=birth|The ] states that he was born in the 126th ], (276–272&nbsp;BC). ] (''Geography'', i.2.2), though, states that he was a "pupil" (γνωριμος) of ] (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>''Eratosthenes'' entry in the '']'' (1971)</ref>}}
{{NoteTag|name=death|The ] states he died at the age of 80, ] (''De die natali'', 15) at the age of 81, and ] (''Makrobioi'', 27) at the age of 82.}}
}}

==References==
{{Reflist
|refs =
<ref name="cornell"> {{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="epsilon"></ref>
<ref name="asimov">See also Asimov, Isaac. ''Asimov's Biographical Encyclopedia of Science and Technology'', new revised edition. 1975. Entry #42, "Eratosthenes", p. 29. Pan Books Ltd, London. {{ISBN|0-330-24323-3}}. This was also asserted by Carl Sagan 31 minutes into his Cosmos episode ''The Shores of the Cosmic Ocean''</ref>
<ref name="bailey">Bailey, Ellen. 2006. "Eratosthenes of Cyrene." Eratosthenes Of Cyrene 1–3. Book Collection Nonfiction: High School Edition.</ref>
<ref name="rist">Rist, J.M. "Zeno and Stoic Consistency," in Phronesis. Vol. 22, No. 2, 1977.</ref>
<ref name="chambers">Chambers, James T. "Eratosthenes of Cyrene." in ''Dictionary of World Biography: The Ancient World January'' 1998: 1–3.</ref>
<ref name="alexander">p.&nbsp;439 Vol. 1 William Woodthorpe Tarn ''Alexander the Great''. Vol. I, ''Narrative''; Vol. II, ''Sources and Studies''. Cambridge: Cambridge University Press, 1948. (New ed., 2002 (paperback, {{ISBN|0-521-53137-3}})).</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="Hutchinson">2011. "Eratosthenes." Hutchinson's Biography Database 1.</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">Greek Scholar's Work Shows Usefulness of Measurement." ''Manawatu Standard'', June 19, 2012. 07, Newspaper Source Plus</ref>
<ref name="zhumud">Zhumud, Leonid. Plato as "Architect of Science". in ''Phonesis''. Vol. 43 (3) 1998. 211–244.</ref>
<ref name="chondros">Chondros, Thomas G. Archimedes Life Works and Machines. in ''Mechanism and Machine Theory''. Vol. 45(11) 2010. 1766–1775.</ref>
<ref name="hero">Mentioned by ] in his ''Dioptra''. See p. 272, vol. 2, ''Selections Illustrating the History of Greek Mathematics'', tr. Ivor Thomas, London: William Heinemann Ltd.; Cambridge, Massachusetts: Harvard University Press, 1957.</ref>
<ref name="ASmith">{{cite web|url=http://www.attalus.org/old/athenaeus7.html#281|title=Athenaeus: Deipnosophists – Book 7|first=Andrew|last=Smith|website=www.attalus.org}}</ref>
<ref name="roller">Roller, Duane W. Eratosthenes' Geography. New Jersey: Princeton University Press, 2010.</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}}
* Aujac, G. (2001). ''Eratosthène de Cyrène, le pionnier de la géographie''. Paris: Édition du CTHS. 224 p.
* {{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. |year=1991 |chapter=Eratosthenes |title=Biographical Dictionary of Mathematicians |volume=2 (Dickson–Khwārizmī) |pages=681–686 |location=New York |publisher=Scribner |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 |first=A. V. |last=Dorofeeva |title=Eratosthenes (ca. 276–194 B.C.) |language=ru |journal=Mat. V Shkole |issue=4 |date=1988 |page=i}}
* {{cite journal |first=J. |last=Dutka |title=Eratosthenes' measurement of the Earth reconsidered |journal=Arch. Hist. Exact Sci. |volume=46 |issue=1 |date=1993 |pages=55–66 |doi=10.1007/BF00387726|bibcode=1993AHES...46...55D |s2cid=119522892 }}
* {{cite journal |first=B. A.|last=El'natanov|title=A brief outline of the history of the development of the sieve of Eratosthenes |language=ru |journal=Istor.-Mat. Issled. |volume=27 |date=1983 |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 |first1=D. H. |last1=Fowler |title=Eratosthenes' ratio for the obliquity of the ecliptic |journal=Isis |volume=74 |issue=274 |date=1983 |pages=556–562 |doi=10.1086/353361 |last2=Rawlins |first2=Dennis|s2cid=144617495 }}
* {{cite journal |last=Fraser |first=P. M. |title=Eratosthenes of Cyrene |journal=Proceedings of the British Academy |date=1970 |volume=56 |pages=175–207}}
* {{cite book |last=Fraser |first=P. M. |title=Ptolemaic Alexandria |date=1972 |publisher=Clarendon Press |location=Oxford}}
* Fuentes González, P. P., "", in R. Goulet (ed.), ''Dictionnaire des Philosophes Antiques'', vol. III, Paris, Centre National de la Recherche Scientifique, 2000, pp.&nbsp;188–236.
* Geus K. (2002). . München: Verlag C.H. Beck. (Münchener Beiträge zur Papyrusforschung und antiken Rechtsgeschichte. Bd. 92) X, 412 S.
* {{cite journal |first=B. R. |last=Goldstein |title=Eratosthenes on the "measurement" of the Earth |journal=Historia Math. |volume=11 |issue=4 |date=1984 |pages=411–416 |doi=10.1016/0315-0860(84)90025-9|doi-access=free }}
* {{cite journal |first=E. |last=Gulbekian |title=The origin and value of the stadion unit used by Eratosthenes in the third century B.C |journal=] |volume=37 |issue=4 |date=1987 |pages=359–363 |doi=10.1007/BF00417008|url=https://link.springer.com/article/10.1007/BF00417008 | url-access=subscription|jstor=41133819 |s2cid=115314003 }}
* 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 |first=G. |last=Knaack |title=Eratosthenes |journal=Pauly–Wissowa VI |date=1907 |pages=358–388}}
* {{cite journal |first=F. |last=Manna |title=The Pentathlos of ancient science, Eratosthenes, first and only one of the "primes" |language=it |journal=Atti Accad. Pontaniana |series=New Series |volume=35 |date=1986 |pages=37–44}}
* {{cite journal|first1=A.|last1=Muwaf|first2=A. N. |last2=Philippou |title=An Arabic version of Eratosthenes writing on mean proportionals |journal=J. Hist. Arabic Sci. |volume=5 |issue=1–2 |date=1981 |pages=147–175}}
* {{cite book |last=Nicastro |first=Nicholas |title=Circumference: Eratosthenes and the ancient quest to measure the globe |location=New York |publisher=St. Martin's Press |date=2008 |isbn=978-0-312-37247-7 |url-access=registration |url=https://archive.org/details/isbn_9780312372477 }}
* {{MacTutor Biography |id=Eratosthenes}}
* Marcotte, D. (1998). "La climatologie d'Ératosthène à Poséidonios: genèse d'une science humaine". G. Argoud, J.Y. Guillaumin (eds.). ''Sciences exactes et sciences appliquées à Alexandrie (IIIe siècle av J.C. – Ier ap J.C.)''. Saint Etienne: Publications de l'Université de Saint Etienne: 263–277.
* McPhail, Cameron (2011). . Dunedin, New Zealand.
* {{cite book |last=Pfeiffer |first=Rudolf |title=History of Classical Scholarship From the Beginnings to the End of the Hellenistic Age |url=https://archive.org/details/historyofclassic0000pfei_r5h8 |url-access=registration |date=1968 |publisher=Clarendon Press |location=Oxford}}
* {{cite journal |first=D. |last=Rawlins |title=Eratosthenes' geodesy unraveled: was there a high-accuracy Hellenistic astronomy |journal=Isis |volume=73 |date=1982 |pages=259–265 |doi=10.1086/352973 |issue=2|s2cid=120730515 }}
* {{cite journal |first=D.|last=Rawlins |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 |date=1982 |pages=211–219|doi=10.1007/BF00348500 |s2cid=118004246 }}
* {{cite journal |first=D. |last=Rawlins |title=Eratosthenes's large Earth and tiny universe |journal=DIO |volume=14 |date=2008 |pages=3–12 |url=http://www.dioi.org/vols/we0.pdf |archive-url=https://web.archive.org/web/20081030220751/http://www.dioi.org/vols/we0.pdf |archive-date=2008-10-30 |url-status=live |bibcode=2008DIO....14....3R }}
* {{cite book |last=Roller |first=Duane W. |publisher=Princeton University Press |location=Princeton |date=2010 |title=Eratosthenes' Geography: Fragments collected and translated, with commentary and additional material |url=https://books.google.com/books?id=8peKyWK_SWsC |isbn=978-0-691-14267-8}}
* 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 |last=Strabo |title=The Geography of Strabo |date=1917 |publisher=Putnam |location=New York |others=Horace Leonard Jones, trans|title-link=Geographica }}
* {{cite journal |first=C. M. |last=Taisbak |title=Eleven eighty-thirds. Ptolemy's reference to Eratosthenes in Almagest I.12 |journal=Centaurus |volume=27 |issue=2 |date=1984 |pages=165–167 |doi=10.1111/j.1600-0498.1984.tb00766.x |bibcode=1984Cent...27..165T }}
* Thalamas, A. (1921). ''La géographe d'Ératosthène''. Versailles.
* {{cite book |first=E. P. |last=Wolfer |title=Eratosthenes von Kyrene als Mathematiker und Philosoph |publisher=Groningen-Djakarta |date=1954}}
{{refend}}


==External links== ==External links==
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{{Wikiquote}}
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{{Library resources box|by=yes|onlinebooks=yes|others=yes|about=yes|label=Eratosthenes|viaf=|lccn=|lcheading=|wikititle=}}
* at Roger Pearse.
* Berlin, 1822 (PDF) (Latin/Greek), Reprinted Osnabruck 1968 (German)
* {{Webarchive|url=https://web.archive.org/web/20010301205532/http://www.faust.fr.bw.schule.de/mhb/eratosiv.htm |date=2001-03-01 }}
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* {{Webarchive|url=https://web.archive.org/web/20190414194605/https://www.fondation-lamap.org/en/node/9786%27 |date=2019-04-14 }} : project ].
* {{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 }}
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Latest revision as of 08:19, 28 December 2024

Greek mathematician, geographer, poet (c. 276 – c. 195/194 BC) This article is about the Greek scholar of the third century BC. For other uses, see Eratosthenes (disambiguation).
Eratosthenes
An etching of a man's head and neck in profile, looking to the left. The man has a beard and is balding.Etching of an ancient seal identified as Eratosthenes. Philipp Daniel Lippert [de], Dactyliothec, 1767.
Born276 BC
Cyrene (in modern Libya)
Died194 BC (around age 82)
Alexandria
Occupations
  • Scholar
  • Librarian
  • Poet
  • Inventor
Known for

Eratosthenes of Cyrene (/ɛrəˈtɒsθəniːz/; Ancient Greek: Ἐρατοσθένης [eratostʰénɛːs]; c. 276 BC – c. 195/194 BC) was an Ancient Greek polymath: a mathematician, geographer, poet, astronomer, and music theorist. He was a man of learning, becoming the chief librarian at the Library of Alexandria. His work is comparable to what is now known as the study of geography, and he introduced some of the terminology still used today.

He is best known for being the first person known to calculate the circumference of the Earth, which he did by using the extensive survey results he could access in his role at the Library. His calculation was remarkably accurate (his error margin turned out to be less than 1%). He was also the first person to calculate Earth's axial tilt, which similarly proved to have remarkable accuracy. He created the first global projection of the world, incorporating parallels and meridians based on the available geographic knowledge of his era.

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 1183 BC. In number theory, he introduced the sieve of Eratosthenes, an efficient method of identifying prime numbers and composite numbers.

He was a figure of influence in many fields who yearned to understand the complexities of the entire world. 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 encyclopedia), some critics scorned him, calling him Number 2 because he always came in second in all his endeavours.

Life

The son of Aglaos, Eratosthenes was born in 276 BC in Cyrene. Now part of modern-day Libya, Cyrene had been founded by Greeks centuries earlier and became the capital of Pentapolis (North Africa), a country of five cities: Cyrene, Arsinoe, Berenice, Ptolemias, and Apollonia. Alexander the Great conquered Cyrene in 332 BC, and following his death in 323 BC, its rule was given to one of his generals, Ptolemy I Soter, the founder of the Ptolemaic Kingdom. Under Ptolemaic rule the economy prospered, based largely on the export of horses and silphium, a plant used for rich seasoning and medicine. Cyrene became a place of cultivation, where knowledge blossomed. Like any young Greek at the time, Eratosthenes would have studied in the local gymnasium, where he would have learned physical skills and social discourse as well as reading, writing, arithmetic, poetry, and music.

Eratosthenes teaching in Alexandria by Bernardo Strozzi (1635)

Eratosthenes went to Athens to further his studies. There he was taught Stoicism by its founder, Zeno of Citium, in philosophical lectures on living a virtuous life. He then studied under Aristo of Chios, who led a more cynical school of philosophy. He also studied under the head of the Platonic Academy, who was Arcesilaus of Pitane. His interest in Plato led him to write his first work at a scholarly level, Platonikos, inquiring into the mathematical foundation of Plato's philosophies. Eratosthenes was a man of many perspectives and investigated the art of poetry under Callimachus. He wrote poems: one in hexameters called Hermes, illustrating the god's life history; and another in elegiacs, called Erigone, describing the suicide of the Athenian maiden Erigone (daughter of Icarius). He wrote Chronographies, a text that scientifically depicted dates of importance, beginning with the Trojan War. This work was highly esteemed for its accuracy. George Syncellus was later able to preserve from Chronographies a list of 38 kings of the Egyptian Thebes. Eratosthenes also wrote Olympic Victors, a chronology of the winners of the Olympic Games. It is not known when he wrote his works, but they highlighted his abilities.

These works and his great poetic abilities led the king Ptolemy III Euergetes to seek to place him as a librarian at the Library of Alexandria in the year 245 BC. Eratosthenes, then thirty years old, accepted Ptolemy's invitation and traveled to Alexandria, where he lived for the rest of his life. Within about fifty years he became Chief Librarian, a position that the poet Apollonius Rhodius had previously held. As head of the library Eratosthenes tutored the children of Ptolemy, including Ptolemy IV Philopator who became the fourth Ptolemaic pharaoh. He expanded the library's holdings: in Alexandria all books had to be surrendered for duplication. It was said that these were copied so accurately that it was impossible to tell if the library had returned the original or the copy. He sought to maintain the reputation of the Library of Alexandria against competition from the Library of Pergamum. Eratosthenes created a whole section devoted to the examination of Homer, and acquired original works of great tragic dramas of Aeschylus, Sophocles and Euripides.

Eratosthenes made several important contributions to mathematics and science, and was a friend of Archimedes. Around 255 BC, he invented the armillary sphere. In On the Circular Motions of the Celestial Bodies, Cleomedes credited him with having calculated the Earth's circumference around 240 BC, with high accuracy.

Eratosthenes believed there was both good and bad in every nation and criticized Aristotle for arguing that humanity was divided into Greeks and barbarians, as well as for arguing that the Greeks should keep themselves racially pure. As he aged, he contracted ophthalmia, becoming blind around 195 BC. Losing the ability to read and to observe nature plagued and depressed him, leading him to voluntarily starve himself to death. He died in 194 BC at the age of 82 in Alexandria.

Scholarly career

Measurement of Earth's circumference

Main article: Earth's circumference § Eratosthenes
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, who estimated that the meridian has a length of 252,000 stadia (39,060 to 40,320 kilometres (24,270 to 25,050 mi)), with an error on the real value between −2.4% and +0.8% (assuming a value for the stadion between 155 and 160 metres (509 and 525 ft)). Eratosthenes described his arc measurement technique, in a book entitled 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.

The simplified method works by considering two cities along the same 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 bematists. 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 one turn.

Geography

Eratosthenes' map of the world (194 BC)
19th-century reconstruction of Eratosthenes' map of the (for the Greeks) known world, c. 194 BC
See also: History of geodesy and History of longitude

Eratosthenes now continued from his knowledge about the Earth. Using his discoveries and knowledge of its size and shape, he began to sketch it. In the Library of Alexandria he had access to various travel books, which contained various items of information and representations of the world that needed to be pieced together in some organized format. In his three-volume work Geography (Ancient Greek: Geographika), he described and mapped his entire known world, even dividing the Earth into five climate zones: two freezing zones around the poles, two temperate zones, and a zone encompassing the equator and the tropics. This book is the first recorded instance of many terms still in use today, including the name of the discipline geography. 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 now possible to estimate one's distance from remote locations with this network over the surface of the Earth. In the Geography the names of over 400 cities and their locations were shown, which had never been achieved before. However, his Geography has been lost to history, although fragments of the work can be pieced together from other great historians like Pliny, Polybius, Strabo, and Marcianus. While this work is the earliest we can trace certain ideas, words, and concepts in the historical record, earlier contributions may have been lost to history.

  • 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 now described as geography. His disapproval of Homer's topography angered many who believed the world depicted in the Odyssey to be legitimate. He also 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, wherein at noon each summer solstice, the Sun's rays shone straight down into the city-center well. This book would now 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 and can be considered the beginning of geography. For this, Eratosthenes was named the "Father of Modern Geography."

According to Strabo, Eratosthenes argued against the Greek-Barbarian dichotomy. He says Alexander ignored his advisers by his regard for all people with law and government. Strabo says that Eratosthenes was wrong to claim that Alexander had disregarded the counsel of his advisers. Strabo argues 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."

Achievements

Eratosthenes was described by the Suda Lexicon as a Πένταθλος (Pentathlos) which can be translated as "All-Rounded", for he was skilled in a variety of things; he was a true polymath. His opponents nicknamed him "Number 2" because he was great at many things and tried to get his hands on every bit of information but never achieved the highest rank in anything; Strabo accounts Eratosthenes as a mathematician among geographers and a geographer among mathematicians.

  • Eusebius of Caesarea in his Preparatio Evangelica includes a brief chapter of three sentences on celestial distances (Book XV, Chapter 53). He states simply that Eratosthenes found the distance to the Sun to be "σταδίων μυριάδας τετρακοσίας καὶ ὀκτωκισμυρίας" (literally "of stadia myriads 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 (1903 translation by E. H. Gifford), or as 804,000,000 stadia (edition of Edouard des Places, dated 1974–1991). The meaning depends on whether Eusebius meant 400 myriad plus 80,000 or "400 and 80,000" myriad. With a stade of 185 m (607 ft), 804,000,000 stadia is 149,000,000 km (93,000,000 mi), 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. The actual figure is approximately 109 times.
  • During his time 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.
  • He was also very proud of his solution for Doubling the Cube. His motivation was that he wanted to produce catapults. Eratosthenes constructed a mechanical line drawing device to calculate the cube, called the mesolabio. He dedicated his solution to King Ptolemy, presenting a model in bronze with it a letter and an epigram. Archimedes was Eratosthenes' friend and he, too, worked on the war instrument with mathematics. Archimedes dedicated his book The Method to Eratosthenes, knowing his love for learning and mathematics.

Number theory

Sieve of Eratosthenes: algorithm steps for primes below 121 (including optimization of starting from the prime's square).
Main articles: Sieve of Eratosthenes and Primality test

Eratosthenes proposed a simple algorithm for finding prime numbers. This algorithm is known in mathematics as the Sieve of Eratosthenes.

In mathematics, the sieve of Eratosthenes (Greek: κόσκινον Ἐρατοσθένους), one of a number of prime number sieves, 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.

Works

Eratosthenes was one of the most pre-eminent scholarly figures of his time, and produced works covering a vast area of knowledge before and during his time at the Library. He wrote on many topics – geography, mathematics, philosophy, chronology, literary criticism, grammar, poetry, and even old comedies. There are no documents left of his work after the destruction of the Library of Alexandria.

Titles

See also

Notes

  1. The Suda states that he was born in the 126th Olympiad, (276–272 BC). Strabo (Geography, i.2.2), though, states that he was a "pupil" (γνωριμος) of Zeno of Citium (who died in 262 BC), which would imply an earlier year of birth (c. 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.
  2. 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.

References

  1. ^ Roller, Duane W. Eratosthenes' Geography. New Jersey: Princeton University Press, 2010.
  2. ^ Russo, Lucio (2004). The Forgotten Revolution: How Science Was Born in 300 BC and Why It Had to Be Reborn. Berlin: Springer. p. 68. ISBN 3-540-20396-6. OCLC 52945835. Archived from the original on 2024-08-28. Retrieved 2024-08-28.
  3. "Imagine the Universe – The Earth".
  4. "Eratosthenes (276–195 B.C.)" Archived 2021-02-24 at the Wayback Machine. Cornell University. Accessed 28 July 2019.
  5. "Greek chronology". Britannica.
  6. ^ Chambers, James T. "Eratosthenes of Cyrene." in Dictionary of World Biography: The Ancient World January 1998: 1–3.
  7. "Entry ε 2898"
  8. See also Asimov, Isaac. Asimov's Biographical Encyclopedia of Science and Technology, new revised edition. 1975. Entry #42, "Eratosthenes", p. 29. Pan Books Ltd, London. ISBN 0-330-24323-3. This was also asserted by Carl Sagan 31 minutes into his Cosmos episode The Shores of the Cosmic Ocean
  9. ^ Bailey, Ellen. 2006. "Eratosthenes of Cyrene." Eratosthenes Of Cyrene 1–3. Book Collection Nonfiction: High School Edition.
  10. Rist, J.M. "Zeno and Stoic Consistency," in Phronesis. Vol. 22, No. 2, 1977.
  11. "Aratus's "Phenomena," Cleomedes's "On the Circular Motions of the Celestial Bodies," and Nichomachus's "Introduction to Arithmetic" – Viewer – World Digital Library". www.wdl.org. Retrieved 2021-02-24.
  12. p. 439 Vol. 1 William Woodthorpe Tarn Alexander the Great. Vol. I, Narrative; Vol. II, Sources and Studies. Cambridge: Cambridge University Press, 1948. (New ed., 2002 (paperback, ISBN 0-521-53137-3)).
  13. Russo, Lucio (2004). The Forgotten Revolution: How Science Was Born in 300 BC and Why It Had to Be Reborn. Berlin: Springer. p. 68. ISBN 3-540-20396-6. OCLC 52945835. Archived from the original on 2024-08-28. Retrieved 2024-08-28.
  14. Torge, W.; Müller, J. (2012). Geodesy. De Gruyter Textbook. De Gruyter. p. 5. ISBN 978-3-11-025000-8. Retrieved 2021-05-02.
  15. Cleomedes, Caelestia, i.7.49–52.
  16. Martianus Capella, De nuptiis Philologiae et Mercurii, VI.598.
  17. ^ Smith, Sir William. "Eratosthenes", in A Dictionary of Greek and Roman Biography and Mythology. Ann Arbor, Michigan: University of Michigan Library, 2005.
  18. Morris, Terry R. "Eratosthenes of Cyrene." in Encyclopedia Of The Ancient World. November 2001.
  19. 2011. "Eratosthenes." Hutchinson's Biography Database 1.
  20. Dahlman, Carl; Renwick, William (2014). Introduction to Geography: People, Places & Environment (6 ed.). Pearson. ISBN 978-0-13-750451-0. Retrieved 28 August 2022.
  21. Eckerman, Chris. Review of (D.W.) Roller 'Eratosthenes' Geography. Fragments Collected and Translated, with Commentary and Additional Material. The Classical Review. 2011.
  22. "Eratosthenes of Cyrene". Khan Academy. Retrieved 2019-11-19.
  23. Plutarch's similar discussion claiming that Alexander ignored Aristotle's advice in this matter may have been influenced by Eratosthenes, but Plutarch does not give us confirmation of his sources.
  24. Isaac, Benjamin. Invention of Racism in Classical Antiquity. Princeton University Press, 2013.
  25. ^ Dicks, D.R. "Eratosthenes", in Complete Dictionary of Scientific Biography. New York: Charles Scribner's Sons, 1971.
  26. "Ask an Astronomer". Cool Cosmos. Archived from the original on 2014-07-30.
  27. Greek Scholar's Work Shows Usefulness of Measurement." Manawatu Standard, June 19, 2012. 07, Newspaper Source Plus
  28. Zhumud, Leonid. Plato as "Architect of Science". in Phonesis. Vol. 43 (3) 1998. 211–244.
  29. Chondros, Thomas G. Archimedes Life Works and Machines. in Mechanism and Machine Theory. Vol. 45(11) 2010. 1766–1775.
  30. Mentioned by Hero of Alexandria in his Dioptra. See p. 272, vol. 2, Selections Illustrating the History of Greek Mathematics, tr. Ivor Thomas, London: William Heinemann Ltd.; Cambridge, Massachusetts: Harvard University Press, 1957.
  31. Smith, Andrew. "Athenaeus: Deipnosophists – Book 7". www.attalus.org.
  32. Eratosthenes entry in the Dictionary of Scientific Biography (1971)


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