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An etching of a man's head and neck in profile, looking to the left. The man has a beard and is balding.
Born276 BC[note 1]
Cyrene (in modern Libya)
Died194 BC (around age 82)[note 2]
  • Scholar
  • Librarian
  • Poet
  • Inventor
Known for

Eratosthenes of Cyrene (; Greek: [eratost?én?:s];  - ) was a 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.[1]

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.[2][3] He was also the first to calculate Earth's axial tilt, which also proved to have remarkable accuracy.[4] 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;[5] he endeavoured to revise the dates of the main events of the semi-mythological 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.

He was a figure of influence in many fields. According to an entry[6] in the Suda (a 10th-century encyclopedia), his critics scorned him, calling him Beta (the second letter of the Greek alphabet) because he always came in second in all his endeavours.[7] Nonetheless, 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. Eratosthenes yearned to understand the complexities of the entire world.[8]


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.[1] 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.[9]

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.[10] 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 very first work at a scholarly level, Platonikos, inquiring into the mathematical foundation of Plato's philosophies.[8] Eratosthenes was a man of many perspectives and investigated the art of poetry under Callimachus.[9] 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).[8] 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.


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,[11] Cleomedes credited him with having calculated the Earth's circumference around 240 BC, with a high precision.[2]

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.[12] 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 82 in Alexandria.[9]

Scholarly career

Measurement of Earth's circumference

The measurement of Earth's circumference is the most famous among the results obtained by Eratosthenes,[13] who estimated that the meridian has a length of 252,000 stadia, with an error on the real value between -2.4% and +0.8% (assuming a value for the stadion between 155 and 160 metres).[2] Eratosthenes described his arc measurement technique,[14] in a book entitled On the measure of the Earth, which has not been preserved.

Cleomedes' simplified version

Measure of Earth's circumference according to Cleomedes' simplified version, based on the wrong assumption that Syene is on the Tropic of Cancer and on the same meridian as Alexandria

Eratosthenes' method to calculate the Earth's circumference has been lost; what has been preserved is the simplified version described by Cleomedes to popularise the discovery.[15] Cleomedes invites his reader to consider two Egyptian cities, Alexandria and Syene, modern Aswan. At midday on summer solstice (21-22 June for the north hemisphere) in Syene, the sun was so precisely overhead and no shadows were cast: whereas in Alexandria on the same date, a measuring obelisk cast a shadow of 7.2 degrees.

  1. Cleomedes assumes that the distance between Syene and Alexandria was 5,000 stadia (a figure that was checked yearly by professional bematists, mensores regii);[16]
  2. he assumes the simplified (but false) hypothesis that Syene was precisely on the Tropic of Cancer, saying that at local solar noon on the summer solstice the Sun was directly overhead;[17]
  3. he assumes the simplified (but false) hypothesis that Syene and Alexandria are on the same meridian.

Under the previous assumptions, says Cleomedes, you can measure the Sun's angle of elevation at noon of the summer solstice in Alexandria, by using a vertical rod (a gnomon) of known length and measuring the length of its shadow on the ground;[18] it is then possible to calculate the angle of the Sun's rays,[19] which he claims to be 7° 12', 7.2°, or 1/50th the circumference of a circle.[20] Taking the Earth as spherical, the Earth's circumference would be fifty times the distance between Alexandria and Syene, that is 250,000 stadia. Since 1 Egyptian stadium is equal to 157.5 metres, the result is 39,375 km, which is 1.4% less than the real number, 40,076 km.

Eratosthenes' method

Eratosthenes' method was actually more complicated, as stated by the same Cleomedes, whose purpose was to present a simplified version of the one described in Eratosthenes' book. The method was based on several surveying trips conducted by professional bematists, whose job was to precisely measure the extent of the territory of Egypt for agricultural and taxation-related purposes.[2] Furthermore, the fact that Eratosthenes' measure corresponds precisely to 252,000 stadia might be intentional, since it is a number that can be divided by all natural numbers from 1 to 10: some historians believe that Eratosthenes changed from the 250,000 value written by Cleomedes to this new value to simplify calculations;[21] other historians of science, on the other side, believe that Eratosthenes introduced a new length unit based on the length of the meridian, as stated by Pliny, who writes about the stadion "according to Eratosthenes' ratio".[2][22]


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.[23] In his three-volume work Geography (Greek: Geographika), he described and mapped his entire known world, even dividing the Earth into five climate zones:[24] two freezing zones around the poles, two temperate zones, and a zone encompassing the equator and the tropics.[25] He had invented geography. He created terminology that is still used today. 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.[1] Unfortunately, his Geography has been lost to history, but fragments of the work can be pieced together from other great historians like Pliny, Polybius, Strabo, and Marcianus.

  • 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.[8][26] 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.[27] 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."[23]


Eratosthenes was described by the Suda Lexicon as a (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 Beta 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.[28]

  • 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 "? ?" (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.

Number theory

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




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. Unfortunately, there are no documents left of his work after the destruction of the Library of Alexandria.[28]


See also


  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" () of Zeno of Citium (who died in 262 BC), which would imply an earlier year of birth since he is unlikely to have studied under him at the young age of 14. However, can also mean "acquaintance", and the year of Zeno's death is by no means definite.[35]


  2. ^ a b c d e Russo, Lucio (2004). The Forgotten Revolution. Berlin: Springer. pp. 273-277.
  3. ^ "Imagine the Universe - The Earth".
  4. ^ "Eratosthenes (276-195 B.C.)". Cornell University. Accessed 28 July 2019.
  5. ^ "Greek chronology". Britannica.
  6. ^ "Entry ? 2898"
  7. ^ See also Asimov, Isaac. Asimov's Biographical Encyclopedia of Science and Technology, new revised edition. 1975. Entry #42, "Eratosthenes", Page 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
  8. ^ a b c d e Chambers, James T. "Eratosthenes of Cyrene." in Dictionary Of World Biography: The Ancient World January 1998: 1-3.
  9. ^ a b c Bailey, Ellen. 2006. "Eratosthenes of Cyrene." Eratosthenes Of Cyrene 1-3. Book Collection Nonfiction: High School Edition.
  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 .
  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. Berlin: Springer. p. 68..
  14. ^ Torge, W.; Müller, J. (2012). Geodesy. De Gruyter Textbook. De Gruyter. p. 5. ISBN 978-3-11-025000-8. Retrieved .
  15. ^ Cleomedes, Caelestia, i.7.49-52.
  16. ^ Martianus Capella, De nuptiis Philologiae et Mercurii, VI.598.
  17. ^ Balasubramaniam, R. (10 August 2017). Story of the Delhi Iron Pillar. Foundation Books. ISBN 9788175962781 – via Google Books.
  18. ^ "Astronomy 101 Specials: Eratosthenes and the Size of the Earth". www.eg.bucknell.edu. Retrieved .
  19. ^ "How did Eratosthenes measure the circumference of the earth?". 3 July 2012.
  20. ^ Willers, Michael (2009). Algebra: The x and y of Everyday Math (2009 ed.). Quid Publishing. pp. 62-63. ISBN 978-1-4351-1400-5.
  21. ^ Rawlins, Dennis (1983). "The Erathostenes-Strabo Nile Map. Is It the Earliest Surviving Instance of Spherical Cartography? Did It Supply the 5000 Stades Arc for Erathostenes' Experiment?". Archive for History of Exact Sciences. 26 (26): 211-219. doi:10.1007/BF00348500 (inactive 31 May 2021).CS1 maint: DOI inactive as of May 2021 (link)
  22. ^ Pliny, Naturalis Historia, XII $53.
  23. ^ a b c Smith, Sir William. "Eratosthenes", in A Dictionary of Greek and Roman Biography and Mythology. Ann Arbor, Michigan: University of Michigan Library, 2005.
  25. ^ 2011. "Eratosthenes." Hutchinson's Biography Database 1.
  27. ^ "Eratosthenes of Cyrene". Khan Academy. Retrieved .
  28. ^ a b c Dicks, D.R. "Eratosthenes", in Complete Dictionary of Scientific Biography. New York: Charles Scribner's Sons, 1971.
  29. ^ "Ask an Astronomer". Cool Cosmos. Archived from the original on 2014-07-30.
  31. ^ Zhumud, Leonid. Plato as "Architect of Science". in Phonesis. Vol. 43 (3) 1998. 211-244.
  32. ^ Chondros, Thomas G. Archimedes Life Works and Machines. in Mechanism and Machine Theory. Vol.45(11) 2010. 1766-1775.
  33. ^ 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.
  34. ^ Smith, Andrew. "Athenaeus: Deipnosophists - Book 7". www.attalus.org.
  35. ^ Eratosthenes entry in the Dictionary of Scientific Biography (1971)

Further reading

External links




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