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Eratosthenes

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This article is about the Greek scholar of the third century BC. For other uses, seeEratosthenes (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[note 1]
Cyrene(in modernLibya)
Died194 BC (around age 82)[note 2]
Alexandria
Occupations
  • Scholar
  • Librarian
  • Poet
  • Inventor
Known for

Eratosthenes of Cyrene(/ɛrəˈtɒsθəniːz/;Greek:Ἐρατοσθένης[eratostʰénɛːs];c.276 BC–c. 195/194 BC) was a Greekpolymath:amathematician,geographer,poet,astronomer,andmusic theorist.He was a man of learning, becoming the chief librarian at theLibrary of Alexandria.His work is comparable to what is now known as the study ofgeography,and he introduced some of theterminologystill used today.[1]

He is best known for being the first person known to calculate thecircumference 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.[2][3]He was also the first to calculateEarth's axial tilt,which has also proved to have remarkable accuracy.[4]He created thefirst global projectionof the world, incorporatingparallelsandmeridiansbased on the available geographic knowledge of his era.

Eratosthenes was the founder of scientificchronology;[5]he used Egyptian and Persian records to estimate the dates of the main events of theTrojan War,dating the sack ofTroyto 1183 BC. Innumber theory,he introduced thesieve of Eratosthenes,an efficient method of identifyingprime numbersand composite numbers.

He was a figure of influence in many fields who yearned to understand the complexities of the entire world.[6]His devotees nicknamed himPentathlosafterthe Olympianswho were well rounded competitors, for he had proven himself to be knowledgeable in every area of learning. Yet, according to an entry[7]in theSuda(a 10th-century encyclopedia), some critics scorned him, calling himNumber 2because he always came in second in all his endeavours.[8]

Life[edit]

The son of Aglaos, Eratosthenes was born in 276 BC inCyrene.Now part of modern-dayLibya,Cyrene had been founded by Greeks centuries earlier and became the capital ofPentapolis (North Africa),a country of five cities: Cyrene,Arsinoe,Berenice,Ptolemias,andApollonia.Alexander the Greatconquered 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 thePtolemaic Kingdom.Under Ptolemaic rule the economy prospered, based largely on the export of horses andsilphium,a plant used for rich seasoning and medicine.[1]Cyrene became a place of cultivation, where knowledge blossomed. Like any young Greek at the time, Eratosthenes would have studied in the localgymnasium,where he would have learned physical skills and social discourse as well as reading, writing, arithmetic, poetry, and music.[9]

Eratosthenes teaching in AlexandriabyBernardo Strozzi(1635)

Eratosthenes went to Athens to further his studies. There he was taughtStoicismby its founder,Zeno of Citium,in philosophical lectures on living a virtuous life.[10]He then studied underAristo of Chios,who led a morecynicalschool of philosophy. He also studied under the head of thePlatonic Academy,who wasArcesilaus of Pitane.His interest inPlatoled him to write his first work at a scholarly level,Platonikos,inquiring into the mathematical foundation of Plato's philosophies.[6]Eratosthenes was a man of many perspectives and investigated theart of poetryunderCallimachus.[9]He wrote poems: one inhexameterscalledHermes,illustrating the god's life history; and another inelegiacs,calledErigone,describing the suicide of the Athenian maidenErigone (daughter of Icarius).[6]He wroteChronographies,a text that scientifically depicted dates of importance, beginning with theTrojan War.This work was highly esteemed for its accuracy.George Syncelluswas later able to preserve fromChronographiesa list of 38 kings of theEgyptian Thebes.Eratosthenes also wroteOlympic Victors,a chronology of the winners of theOlympic Games.It is not known when he wrote his works, but they highlighted his abilities.

These works and his great poetic abilities led the kingPtolemy III Euergetesto seek to place him as a librarian at theLibrary of Alexandriain 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 poetApollonius Rhodiushad previously held. As head of the library Eratosthenes tutored the children of Ptolemy, includingPtolemy IV Philopatorwho 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 theLibrary of Pergamum.Eratosthenes created a whole section devoted to the examination ofHomer,and acquired original works of great tragic dramas ofAeschylus,SophoclesandEuripides.[6]

Eratosthenes made several important contributions tomathematicsandscience,and was a friend ofArchimedes.Around 255 BC, he invented thearmillary sphere.InOn the Circular Motions of the Celestial Bodies,[11]Cleomedescredited him with having calculated theEarth's circumferencearound 240 BC, with high accuracy.[2]

Eratosthenes believed there was both good and bad in every nation and criticizedAristotlefor arguing that humanity was divided into Greeks andbarbarians,as well as for arguing that the Greeks should keep themselves racially pure.[12]As he aged, he contractedophthalmia,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.[9]

Scholarly career[edit]

Measurement of Earth's circumference[edit]

Main article:Earth's circumference § Eratosthenes
Measure of Earth's circumference according to Cleomedes' simplified version, based on the approximation thatSyeneis on theTropic of Cancerand on the same meridian asAlexandria

The measurement ofEarth's circumferenceis the most famous among the results obtained by Eratosthenes,[13]who estimated that the meridian has a length of 252,000stadia(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)).[2]Eratosthenes described hisarc measurementtechnique,[14]in a book entitledOn the measure of the Earth,which has not been preserved. However, a simplified version of the method has been preserved, as described byCleomedes.[15]

The simplified method works by considering two cities along the samemeridianand measuring both the distance between them and the difference in angles of the shadows cast by the sun on a vertical rod (agnomon) in each city at noon on the summersolstice.The two cities used wereAlexandriaandSyene(modernAswan), and the distance between the cities was measured by professionalbematists.[16]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 ofone turn.

Geography[edit]

Eratosthenes' map of the world (194 BC)
19th-century reconstruction ofEratosthenes' map of the (for the Greeks) known world,c.194 BC
See also:History of geodesyandhistory 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.[17]In his three-volume workGeography(Greek:Geographika), he described and mapped his entire known world, even dividing the Earth into five climate zones:[18]two freezing zones around the poles, two temperate zones, and a zone encompassing the equator and the tropics.[19]This book is the first recorded instance of many terms still in use today, including the name of the disciplinegeography.[20]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 theGeographythe names of over 400 cities and their locations were shown, which had never been achieved before.[1]However, hisGeographyhas been lost to history, although fragments of the work can be pieced together from other great historians likePliny,Polybius,Strabo,andMarcianus.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 denouncedHomeras 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 theOdysseyto be legitimate.[6][21]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 theMediterraneanhad 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.[22]This book would now be considered a text onmathematical geography.
  • His third book of theGeographycontainedpolitical 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."[17]

According to Strabo, Eratosthenes argued against the Greek-Barbariandichotomy. He says Alexander ignored his advisers by his regard for all people with law and government.[23]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".[24]

Achievements[edit]

Eratosthenes was described by theSuda Lexiconas a Πένταθλος (Pentathlos) which can be translated as "All-Rounder", for he was skilled in a variety of things: He was a true polymath. He was nicknamed "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;Straboaccounts Eratosthenes as a mathematician among geographers and a geographer among mathematicians.[25]

  • Eusebius of Caesareain hisPreparatio Evangelicaincludes 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" ofstadiamyriads400 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 toMacrobius,Eratosthenes made the diameter of the Sun to be about 27 times that of the Earth.[17]The actual figure is approximately 109 times.[26]
  • During his time at the Library of Alexandria, Eratosthenes devised a calendar using his predictions about theeclipticof the Earth. He calculated that there are 365 days in a year and that every fourth year there would be 366 days.[27]
  • He was also very proud of his solution forDoubling 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.[28]Archimedes was Eratosthenes' friend and he, too, worked on the war instrument with mathematics. Archimedes dedicated his bookThe Methodto Eratosthenes, knowing his love for learning and mathematics.[29]

Number theory[edit]

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

Eratosthenes proposed a simplealgorithmfor findingprime numbers.This algorithm is known in mathematics as theSieve of Eratosthenes.

In mathematics, the sieve of Eratosthenes (Greek: κόσκινον Ἐρατοσθένους), one of a number ofprime 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[edit]

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 thedestruction of the Library of Alexandria.[25]

Titles[edit]

See also[edit]

Notes[edit]

  1. ^TheSudastates that he was born in the 126thOlympiad,(276–272 BC).Strabo(Geography,i.2.2), though, states that he was a "pupil" (γνωριμος) ofZeno 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.[32]
  2. ^TheSudastates he died at the age of 80,Censorinus(De die natali,15) at the age of 81, andPseudo-Lucian(Makrobioi,27) at the age of 82.

References[edit]

  1. ^abcRoller, Duane W. Eratosthenes' Geography. New Jersey: Princeton University Press, 2010.
  2. ^abcRusso, Lucio(2004).The forgotten revolution: how science was born in 300 BC and why it had to be reborn.Berlin: Springer. pp. 273–277.ISBN3-540-20396-6.OCLC52945835.
  3. ^"Imagine the Universe – The Earth".
  4. ^"Eratosthenes (276–195 B.C.)"Archived2021-02-24 at theWayback Machine.Cornell University. Accessed 28 July 2019.
  5. ^"Greek chronology".Britannica.
  6. ^abcdeChambers, James T. "Eratosthenes of Cyrene." inDictionary of World Biography: The Ancient World January1998: 1–3.
  7. ^"Entryε2898 "
  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.ISBN0330243233.This was also asserted by Carl Sagan 31 minutes into his Cosmos episodeThe Shores of the Cosmic Ocean
  9. ^abcBailey, 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.Retrieved2021-02-24.
  12. ^p. 439 Vol. 1 William Woodthorpe TarnAlexander the Great.Vol. I,Narrative;Vol. II,Sources and Studies.Cambridge: Cambridge University Press, 1948. (New ed., 2002 (paperback,ISBN0521531373)).
  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.ISBN3-540-20396-6.OCLC52945835.
  14. ^Torge, W.; Müller, J. (2012).Geodesy.De Gruyter Textbook. De Gruyter. p. 5.ISBN978-3110250008.Retrieved2021-05-02.
  15. ^Cleomedes,Caelestia,i.7.49–52.
  16. ^Martianus Capella,De nuptiis Philologiae et Mercurii,VI.598.
  17. ^abcSmith, Sir William. "Eratosthenes", inA Dictionary of Greek and Roman Biography and Mythology.Ann Arbor, Michigan: University of Michigan Library, 2005.
  18. ^Morris, Terry R. "Eratosthenes of Cyrene." inEncyclopedia 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.ISBN9780137504510.Retrieved28 August2022.
  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.Retrieved2019-11-19.
  23. ^Plutarch's similar discussion claiming that Alexander ignoredAristotle'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. ^abcDicks, D.R. "Eratosthenes", inComplete Dictionary of Scientific Biography.New York: Charles Scribner's Sons, 1971.
  26. ^"Ask an Astronomer".Cool Cosmos.Archived fromthe originalon 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". inPhonesis.Vol. 43 (3) 1998. 211–244.
  29. ^Chondros, Thomas G. Archimedes Life Works and Machines. inMechanism and Machine Theory.Vol. 45(11) 2010. 1766–1775.
  30. ^Mentioned byHero of Alexandriain hisDioptra.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. ^Eratosthenesentry in theDictionary of Scientific Biography(1971)


Further reading[edit]

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