Array ( [0] => {{short description|Greek mathematician, geographer, poet (c. 276 – c. 195/194 BC)}} [1] => {{about|the Greek scholar of the third century BC}} [2] => {{Infobox person [3] => | name = Eratosthenes [4] => | image = Eratosthenes_profile.png [5] => | alt = An etching of a man's head and neck in profile, looking to the left. The man has a beard and is balding. [6] => |caption=Etching of an ancient seal identified as Eratosthenes. {{ill|Philipp Daniel Lippert|de}}, ''Dactyliothec'', 1767. [7] => | birth_date = 276 BC{{NoteTag|name=birth}} [8] => | birth_place = [[Cyrene, Libya|Cyrene]] (in modern [[Libya]]) [9] => | death_date = 194 BC (around age 82){{NoteTag|name=death}} [10] => | death_place = [[Alexandria]] [11] => | occupation = {{unbulleted list|Scholar|Librarian |Poet |Inventor}} [12] => | known_for = {{unbulleted list|[[Sieve of Eratosthenes]]|Founder of Geography}} [13] => }} [14] => '''Eratosthenes of Cyrene''' ({{IPAc-en|ɛr|ə|ˈ|t|ɒ|s|θ|ə|n|iː|z}}; {{lang-grc-gre|[[wikt:Ἐρατοσθένης|Ἐρατοσθένης]]}} {{IPA-el|eratostʰénɛːs|}}; {{nowrap|{{circa}} 276 BC}} – {{nowrap|{{circa|195/194 BC|lk=no}}}}) was a Greek [[polymath]]: a [[Greek mathematics|mathematician]], [[geographer]], [[poet]], [[astronomer]], and [[music theory|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. [15] => [16] => 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.{{cite web |url=https://imagine.gsfc.nasa.gov/features/cosmic/earth_info.html|title= Imagine the Universe – The Earth}} He was also the first to calculate [[Earth's axial tilt]], which has also proved to have remarkable accuracy. 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 available geographic knowledge of his era. [17] => [18] => Eratosthenes was the founder of scientific [[chronology]];{{cite encyclopedia|title=Greek chronology|encyclopedia=Britannica|url=https://www.britannica.com/topic/chronology/Greek}} 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 number]]s and composite numbers. [19] => [20] => 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 [[Twelve Olympians|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. [21] => [22] => ==Life== [23] => 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 centuries earlier and became the capital of [[Pentapolis (North Africa)]], a country of five cities: Cyrene, [[Tocra|Arsinoe]], [[Berenice]], [[Ptolemais, Cyrenaica|Ptolemias]], and [[Apollonia, Cyrenaica|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 (antiquity)|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 (ancient Greece)|gymnasium]], where he would have learned physical skills and social discourse as well as reading, writing, arithmetic, poetry, and music. [24] => [[File:Eratosthenes Teaching in Alexandria (Bernardo Strozzi, Montreal).jpg|thumb|''Eratosthenes teaching in Alexandria'' by [[Bernardo Strozzi]] (1635)]] [25] => [26] => 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 [[Cynicism (philosophy)|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 very 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 [[Poetry|art of poetry]] under [[Callimachus]]. He wrote poems: one in [[hexameter]]s called ''Hermes'', illustrating the god's life history; and another in [[elegiac]]s, 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. [27] => [28] => 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. [29] => 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]]. [30] => [31] => 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'',{{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}} [[Cleomedes]] credited him with having calculated the [[Earth's circumference]] around 240 BC, with high accuracy. [32] => [33] => Eratosthenes believed there was both good and bad in every nation and criticized [[Aristotle]] for arguing that humanity was divided into Greeks and [[barbarian]]s, 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. [34] => [35] => ==Scholarly career== [36] => ===Measurement of Earth's circumference{{anchor|Earth's circumference|Arc measurement}}=== [37] => [38] => {{main|Earth's circumference#Eratosthenes}} [39] => [40] => [[File:Eratosthenes_measure_of_Earth_circumference.svg|thumb|upright=1.4|Measure of Earth's circumference according to Cleomedes' simplified version, based on the approximation that [[Syene]] is on the [[Tropic of Cancer]] and on the same meridian as [[Alexandria]]]] [41] => [42] => The measurement of [[Earth's circumference]] is the most famous among the results obtained by Eratosthenes,{{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 |pages=68 |oclc=52945835}} who estimated that the meridian has a length of 252,000 [[Stadion (unit)|stadia]] ({{convert|39060|to|40320|km|mi}}), with an error on the real value between −2.4% and +0.8% (assuming a value for the stadion between {{convert|155|and|160|m|ft}}). Eratosthenes described his [[arc measurement]] technique,{{cite book | last1=Torge | first1=W. | last2=Müller | first2=J. | title=Geodesy | publisher=De Gruyter | series=De Gruyter Textbook | year=2012 | isbn=978-3110250008 | url=https://books.google.com/books?id=RcfmBQAAQBAJ&pg=PA6 | access-date=2021-05-02 | page=5}} in a book entitled ''{{visible anchor|On the measure of the Earth}}'', which has not been preserved. However, a simplified version of the method has been preserved, as described by [[Cleomedes]].Cleomedes, ''Caelestia'', i.7.49–52. [43] => [44] => The simplified method works by considering two cities along the same [[meridian (geography)|meridian]] and measuring both the distance between them and the difference in angles of the shadows cast by the sun on a vertical rod (a [[gnomon]]) in each city at noon on the summer [[solstice]]. The two cities used were [[Alexandria]] and [[Syene]] (modern [[Aswan]]), and the distance between the cities was measured by professional [[bematist]]s.Martianus Capella, ''De nuptiis Philologiae et Mercurii'', VI.598. A geometric calculation reveals that the circumference of the Earth is the distance between the two cities divided by the difference in shadow angles expressed as a fraction of [[turn (angle)|one turn]]. [45] => [46] => {{anchor|Geography}} [47] => [48] => ===Geography=== [49] => [[File:Mappa di Eratostene.jpg|thumb|right|alt=Eratosthenes' map of the world (194 BC)|19th-century reconstruction of [[Eratosthenes' Map of the World|Eratosthenes' map of the (for the Greeks) known world]], {{nowrap|{{circa}} 194 BC}}]] [50] => {{see also|History of geodesy|history of longitude}} [51] => 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'' ({{lang-grc-gre|Geographika|script=Latn}}), 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]].{{cite book |last1=Dahlman |first1=Carl |last2=Renwick |first2=William |title=Introduction to Geography: People, Places & Environment |date=2014 |publisher=Pearson |isbn=9780137504510 |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}} 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 the Elder|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. [52] => * 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. [53] => * 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.{{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}} This book would now be considered a text on [[mathematical geography]]. [54] => * 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." [55] => [56] => 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.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. 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".Isaac, Benjamin. Invention of Racism in Classical Antiquity. Princeton University Press, 2013. [57] => [58] => ===Achievements=== [59] => Eratosthenes was described by the [[Suda Lexicon]] as 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; [[Strabo]] accounts Eratosthenes as a mathematician among geographers and a geographer among mathematicians. [60] => * [[Eusebius of Caesarea]] in his ''[[Preparatio Evangelica]]'' includes a brief chapter of three sentences on celestial distances ([http://www.tertullian.org/fathers/eusebius_pe_15_book15.htm Book XV], Chapter 53). 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 (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. [61] => * 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. [62] => * 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. [63] => * 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. [64] => [65] => ===Number theory=== [66] => [[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).]] [67] => {{Main|Sieve of Eratosthenes|primality test}} [68] => [69] => Eratosthenes proposed a simple [[algorithm]] for finding [[prime numbers]]. This algorithm is known in mathematics as the [[Sieve of Eratosthenes]]. [70] => [71] => In mathematics, the sieve of Eratosthenes (Greek: κόσκινον Ἐρατοσθένους), one of a number of [[prime number sieve]]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. [72] => [73] => ==Works== [74] => 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 [[destruction of the Library of Alexandria]]. [75] => [76] => ===Titles=== [77] => * ''Platonikos'' (lost, quoted by [[Theon of Smyrna]]) [78] => * ''Hermes'' [79] => * ''Erigone'' [80] => * ''Chronographies'' [81] => * ''Olympic Victors'' [82] => * ''Περὶ τῆς ἀναμετρήσεως τῆς γῆς'' (''On the Measurement of the Earth'') (lost, summarized by [[Cleomedes]]) [83] => * ''Гεωγραϕικά'' (''Geographika'') (lost, criticized by [[Strabo]]) [84] => * ''Arsinoe'' (a memoir of queen [[Arsinoe III of Egypt|Arsinoe]]; lost; quoted by [[Athenaeus]] in the ''[[Deipnosophistae]]'') [85] => * ''Ariston'' (concerning [[Aristo of Chios]]' addiction to luxury; lost; quoted by [[Athenaeus]] in the ''[[Deipnosophistae]]'') [86] => * The ''[[Catasterismi]]'' (''Katasterismoi''), a lost collection of [[Hellenistic]] myths about the [[constellation]]s [87] => [88] => ==See also== [89] => * [[Aristarchus of Samos]] ({{circa|310|230 BC|lk=on}}), a Greek mathematician who [[On the Sizes and Distances (Aristarchus)|calculated]] the distance from the Earth to the Sun. [90] => * [[Eratosthenes (crater)]] on the [[Moon]]. [91] => * [[Eratosthenian]] period in the [[lunar geologic timescale]]. [92] => * [[Eratosthenes Seamount]] in the eastern Mediterranean Sea. [93] => * [[Eratosthenes Point]] in [[Antarctica]]. [94] => * [[Hipparchus]] ({{circa|190|120 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. [95] => * [[Posidonius]] ({{circa|135|51 BC|lk=on}}), a Greek astronomer and mathematician who [[Posidonius#Calculation of Earth's circumference|calculated]] the circumference of the Earth. [96] => [97] => ==Notes== [98] => {{NoteFoot [99] => |notes = [100] => {{NoteTag|name=birth|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 ({{nowrap|{{circa}} 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.''Eratosthenes'' entry in the ''[[Dictionary of Scientific Biography]]'' (1971)}} [101] => {{NoteTag|name=death|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.}} [102] => }} [103] => [104] => ==References== [105] => {{Reflist [106] => |refs = [107] => [http://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. [108] => [https://www.cs.uky.edu/~raphael/sol/sol-entries/epsilon/2898 "Entry {{lang|grc|ε}} 2898"] [109] => 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|0330243233}}. This was also asserted by Carl Sagan 31 minutes into his Cosmos episode ''The Shores of the Cosmic Ocean'' [110] => Bailey, Ellen. 2006. "Eratosthenes of Cyrene." Eratosthenes Of Cyrene 1–3. Book Collection Nonfiction: High School Edition. [111] => Rist, J.M. "Zeno and Stoic Consistency," in Phronesis. Vol. 22, No. 2, 1977. [112] => Chambers, James T. "Eratosthenes of Cyrene." in ''Dictionary of World Biography: The Ancient World January'' 1998: 1–3. [113] => 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|0521531373}})). [114] => Smith, Sir William. "Eratosthenes", in ''A Dictionary of Greek and Roman Biography and Mythology''. Ann Arbor, Michigan: University of Michigan Library, 2005. [115] => Morris, Terry R. "Eratosthenes of Cyrene." in ''Encyclopedia Of The Ancient World''. November 2001. [116] => 2011. "Eratosthenes." Hutchinson's Biography Database 1. [117] => Eckerman, Chris. Review of (D.W.) Roller 'Eratosthenes' Geography. Fragments Collected and Translated, with Commentary and Additional Material. The Classical Review. 2011. [118] => {{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|url-status=dead|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}} [119] => {{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 |pages=273–277 |oclc=52945835}} [120] => Greek Scholar's Work Shows Usefulness of Measurement." ''Manawatu Standard'', June 19, 2012. 07, Newspaper Source Plus [121] => Zhumud, Leonid. Plato as "Architect of Science". in ''Phonesis''. Vol. 43 (3) 1998. 211–244. [122] => Chondros, Thomas G. Archimedes Life Works and Machines. in ''Mechanism and Machine Theory''. Vol. 45(11) 2010. 1766–1775. [123] => 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. [124] => {{cite web|url=http://www.attalus.org/old/athenaeus7.html#281|title=Athenaeus: Deipnosophists – Book 7|first=Andrew|last=Smith|website=www.attalus.org}} [125] => Roller, Duane W. Eratosthenes' Geography. New Jersey: Princeton University Press, 2010. [126] => Dicks, D.R. "Eratosthenes", in ''Complete Dictionary of Scientific Biography''. New York: Charles Scribner's Sons, 1971. [127] => }} [128] => [129] => [130] => ==Further reading== [131] => {{refbegin}} [132] => * Aujac, G. (2001). ''Eratosthène de Cyrène, le pionnier de la géographie''. Paris: Édition du CTHS. 224 p. [133] => * {{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}} [134] => * {{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 }} [135] => * {{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 }} [136] => * {{cite journal |first=A. V. |last=Dorofeeva |title=Eratosthenes (ca. 276–194 B.C.) |language=ru |journal=Mat. V Shkole |issue=4 |date=1988 |pages=i}} [137] => * {{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 }} [138] => * {{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}} [139] => * {{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}} [140] => * {{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 }} [141] => * {{cite journal |last=Fraser |first=P. M. |title=Eratosthenes of Cyrene |journal=Proceedings of the British Academy |date=1970 |volume=56 |pages=175–207}} [142] => * {{cite book |last=Fraser |first=P. M. |title=Ptolemaic Alexandria |date=1972 |publisher=Clarendon Press |location=Oxford}} [143] => * Fuentes González, P. P., "[http://hdl.handle.net/10481/27536 Ératosthène de Cyrène]", in R. Goulet (ed.), ''Dictionnaire des Philosophes Antiques'', vol. III, Paris, Centre National de la Recherche Scientifique, 2000, pp. 188–236. [144] => * Geus K. (2002). [https://www.academia.edu/attachments/12860252/download_file ''Eratosthenes von Kyrene. Studien zur hellenistischen Kultur- und Wissenschaftgeschichte'']. München: Verlag C.H. Beck. (Münchener Beiträge zur Papyrusforschung und antiken Rechtsgeschichte. Bd. 92) X, 412 S. [145] => * {{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 }} [146] => * {{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=[[Archive for History of Exact Sciences]] |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 }} [147] => * 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. [148] => * {{cite journal |first=G. |last=Knaack |title=Eratosthenes |journal=Pauly–Wissowa VI |date=1907 |pages=358–388}} [149] => * {{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}} [150] => * {{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}} [151] => * {{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=978-0312372477 |url-access=registration |url=https://archive.org/details/isbn_9780312372477 }} [152] => * {{MacTutor Biography |id=Eratosthenes}} [153] => * 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. [154] => * McPhail, Cameron (2011). [http://otago.ourarchive.ac.nz/bitstream/handle/10523/1713/McPhailCameron2011MA.pdf?sequence=1 ''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]. Dunedin, New Zealand. [155] => * {{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}} [156] => * {{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 }} [157] => * {{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 }} [158] => * {{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 }} [159] => * {{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=978-0691142678}} [160] => * Rosokoki, A. (1995), ''Die Erigone des Eratosthenes. Eine kommentierte Ausgabe der Fragmente'', Heidelberg: C. Winter-Verlag [161] => * Shcheglov, D.A. (2004/2006). "Ptolemy's System of Seven Climata and Eratosthenes' Geography". ''Geographia Antiqua'' '''13''': 21–37. [162] => * {{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 }} [163] => * {{cite book |last=Strabo |title=The Geography of Strabo |date=1917 |publisher=Putnam |location=New York |others=Horace Leonard Jones, trans|title-link=Geographica }} [164] => * {{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 }} [165] => * Thalamas, A. (1921). ''La géographe d'Ératosthène''. Versailles. [166] => * {{cite book |first=E. P. |last=Wolfer |title=Eratosthenes von Kyrene als Mathematiker und Philosoph |publisher=Groningen-Djakarta |date=1954}} [167] => {{refend}} [168] => [169] => ==External links== [170] => {{Commons category}} [171] => {{Wikiquote}} [172] => {{Wikisource author}} [173] => {{Library resources box|by=yes|onlinebooks=yes|others=yes|about=yes|label=Eratosthenes|viaf=|lccn=|lcheading=|wikititle=}} [174] => * [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. [175] => * [http://www.wilbourhall.org/index.html#eratosthenes Bernhardy, Gottfried: ''Eratosthenica'' ] Berlin, 1822 (PDF) (Latin/Greek), Reprinted Osnabruck 1968 (German) [176] => * [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 }} [177] => * [http://www.math.utah.edu/~pa/Eratosthenes.html About Eratosthenes' methods, including a Java applet] [178] => * [http://galileoandeinstein.physics.virginia.edu/lectures/gkastr1.html How the Greeks estimated the distances to the Moon and Sun] [179] => * [http://astrosun2.astro.cornell.edu/academics/courses//astro201/eratosthenes.htm Measuring the Earth with Eratosthenes' method] [180] => * [http://aleph0.clarku.edu/~djoyce/mathhist/greece.html List of ancient Greek mathematicians and contemporaries of Eratosthenes] [181] => * [http://www.newadvent.org/cathen/01303a.htm New Advent Encyclopedia article on the Library of Alexandria] [182] => * [http://www.quitebasic.com/prj/math/eratosthenes/ Eratosthenes' sieve in classic BASIC all-web based interactive programming environment] [183] => * [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]]. [184] => * [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 }} [185] => * [https://web.archive.org/web/20151030065030/http://www.mozalearn.com/Extra-Videos-Eratosthenes-209501 Eratosthenes, video] [186] => * [https://www.astrologicon.org/eratosthenes/eratosthenes-katasterismoi1.html Eratosthenes, Katasterismoi (or Astrothesiae), original text] [187] => [188] => {{S-start}} [189] => {{S-bef|before=[[Apollonius of Rhodes]]}} [190] => {{S-ttl|title=Head of the [[Library of Alexandria]]}} [191] => {{S-aft|after=[[Aristophanes of Byzantium]]}} [192] => {{S-end}} [193] => [194] => {{Ancient Greek astronomy}} [195] => {{Ancient Greek mathematics}} [196] => {{Portal bar|Biography|Ancient Greece|Astronomy|Mathematics|Geography}} [197] => {{Authority control}} [198] => [199] => [[Category:270s BC births]] [200] => [[Category:190s BC deaths]] [201] => [[Category:276 BC births]] [202] => [[Category:3rd-century BC Egyptian people]] [203] => [[Category:3rd-century BC Greek people]] [204] => [[Category:3rd-century BC poets]] [205] => [[Category:3rd-century BC mathematicians]] [206] => [[Category:Ancient Greek astronomers]] [207] => [[Category:Ancient Greek geographers]] [208] => [[Category:Ancient Greek inventors]] [209] => [[Category:Ancient Greek music theorists]] [210] => [[Category:Ancient Greek geometers]] [211] => [[Category:Ancient Greek poets]] [212] => [[Category:Cyrenean Greeks]] [213] => [[Category:Deaths by starvation]] [214] => [[Category:Geodesists]] [215] => [[Category:Giftedness]] [216] => [[Category:Librarians of Alexandria]] [217] => [[Category:Number theorists]] [218] => [[Category:3rd-century BC geographers]] [219] => [[Category:3rd-century BC astronomers]] [220] => [[Category:Greek librarians]] [221] => [[Category:Ancient librarians]] [] => )
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Eratosthenes

Eratosthenes of Cyrene (c. 276 BCE – c.

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276 BCE – c. 194 BCE) was an ancient Greek scholar, mathematician, geographer, and librarian. He is best known for calculating the circumference of the Earth and his contributions to geography and cartography. Eratosthenes served as the chief librarian at the Library of Alexandria, where he fostered the exchange of knowledge and conducted extensive research. He is credited with measuring the Earth's circumference using a method known as the "Syene-Eratosthenes method. " By measuring the angle of the Sun's rays at two different locations, Alexandria and Syene, he was able to calculate the distance between the two and thus determine the Earth's size. Apart from his work in geography, Eratosthenes made significant contributions to various other fields. He developed a system of latitude and longitude and created maps based on his calculations. He also made advancements in the fields of mathematics, astronomy, and poetry. Eratosthenes discovered a method to find prime numbers and made significant progress in understanding the concept of prime numbers. Additionally, he calculated the tilt of the Earth's axis accurately and proposed theories on the cause of seasons. Eratosthenes' works and theories have had a lasting impact on ancient and modern scholarship. His calculations of the Earth's circumference were remarkably accurate, and his methods for mapmaking became influential in cartography. Moreover, his contributions to mathematics and astronomy laid the foundation for future advancements in these fields. Despite his significant achievements, many of Eratosthenes' writings have been lost over time. However, his reputation as one of the greatest scholars of the ancient world remains intact.

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