Eratosthenes

Son of Eglaos, a native of Cyrene .

Eratosthenes received his primary education in Alexandria under the guidance of his scientist countryman Callimachus . Another teacher of Eratosthenes in Alexandria was the philosopher Liznia. After moving to Athens , he became so close to Plato’s school that he usually called himself Platonist . The result of studying the sciences in these two centers was the encyclopedic erudition of Eratosthenes; besides writing works on mathematical sciences, he also wrote treatises on “good and evil,” on comedy, etc. Of all his writings, Eratosthenes attached particular literary and grammatical importance, as can be inferred from what he liked to call himself a philologist.

In 245 BC. er King Ptolemy III Everget invited Eratosthenes to come from Athens to work at the Library of Alexandria , where his teacher Callimachus and Apollonius of Rhodes had already worked. Eratosthenes responded to the invitation, at the age of about thirty years, he arrived in Alexandria, where he remained until his death. Five years after his arrival, he replaced Apollonius of Rhodes as head of the Library of Alexandria. As the head of the library, Eratosthenes was engaged in teaching the children of the monarch - the future ruler of Ptolemy IV and his sister (and later his wife) Arsinoe ^[3] .

As head of the library, he was actively engaged in its expansion and development, seeking to maintain the reputation of the library in competition with the Pergamon library . At his request, the Alexandrian port authorities seized all the books from the incoming ships for study and copying ^[4] . Eratosthenes acquired authentic copies of the tragedies of the great Greek authors - Aeschylus , Sophocles, and Euripides , and also established a department in the library that studied the works of Homer .

In old age, Eratosthenes had inflamed eyes , which further led to blindness. The inability to read and observe nature strongly oppressed him and in 194 BC. er he decided to starve himself.

Echoes of recognition of Eratosthenes' vast scholarship are also expressed in the nicknames he received from his contemporaries. Calling it "beta" , they, according to the assumption of many researchers, wanted to express their view of him as the second Plato , or even as a scientist, who only takes second place, because the first should be kept behind the ancestors. Another nickname of Eratosthenes was “pentatlos” ( Greek νταθλος ) - a pentathlete , that is, a comprehensively developed person, he was given for his talent in various fields of knowledge ^[4] .

The crater on the Moon , one of the periods of the geological history of the Moon, as well as the seamount in the Mediterranean Sea, near Cyprus, is named after Eratosthenes.

Math

From the writings of Eratosthenes on mathematics, only a letter written to King Ptolemy about doubling a cube has reached our time. This letter was preserved in Evtokii’s commentary on Archimedes ’s treatise “On the Ball and Cylinder”. The letter contains some historical information about the Delhi task, as well as a description of the instrument invented by the author himself and known as the Mesolabium .

Information about other mathematical works of Eratosthenes is extremely incomplete. Papp in two places of his “Assembly” calls the eratofen's essay “On Medium Values”, noting that it is in all its assumptions in connection with linear places.

On the composition of Eratosthenes "Platonique", dedicated to the proportions , says Theon of Smyrna . It is possible that the algorithm of “unfolding all rational relations from an equality relationship” described by Theon of Smirn and Nicomach Gerasi goes to Eratosthenes.

An excerpt from another work of Eratosthenes leads in Nikomakh Gerasky 's Introduction to Arithmetic. Iamblich does the same in his commentary on this work by Nicomach. The subject of this passage is the presentation of a method found by Eratosthenes to determine an arbitrary number of consecutive primes (the so-called Eratosthenes sieve ). The method was called the “sieve” because, according to legend, Eratosthenes wrote numbers on a wax-coated tablet and pierced holes in those places where compound numbers were written. Therefore, the plate was a kind of sieve, through which all composite numbers were “sifted”, but only simple numbers remained. Eratosthenes gave a table of prime numbers up to 1000.

Astronomy

From the writings of Eratosthenes on astronomy, only one thing has reached our time: “Casterisms” - the enumeration of constellations and stars in them, where up to 700 objects are indicated. The composition of these stars does not give an essay.

For his astronomical observations, Eratosthenes erected large armillary spheres under the portico of the Museyon building.

Eratosthenes determined the angular distance from the equator to the tropic: he found it equal to 11/83 of 180 °.

Geodesy and Geography

In close connection with astronomy is the work of Eratosthenes, which consists in measuring the length of the earth's meridian . A summary of this work is known to us from Cleomed 's treatise On the Cycle of the Heavenly Arch:

Eratosthenes says that Siena and Alexandria lie on the same meridian. And since the meridians in space are large circles , the same large circles will necessarily be the meridians on Earth. And since such is the solar circle between Siena and Alexandria, the path between them on Earth with necessity goes along a large circle. Now he says that Siena lies on the summer tropic circle. And if the summer solstice in the constellation of Cancer occurred exactly at noon, then the sundial at this point in time would not necessarily cast shadows, since the sun would be exactly at its zenith ; this is indeed the case in the [band width] of 300 stages . And in Alexandria at the same hour the sundial cast a shadow, as this city lies north of Siena. These cities lie on one meridian and on a large circle. On a sundial in Alexandria we will draw an arc passing through the end of the gnomon's shadow and the base of the gnomon, and this segment of the arc will produce a large circle on the bowl, since the sundial cup is located on the large circle. Next, let us imagine two straight lines descending below the Earth from each gnomon and occurring in the center of the Earth. The sundial in Siena is located vertically under the Sun, and an imaginary straight line passes from the Sun through the top of the gnomon of the sundial, producing one straight line from the Sun to the center of the Earth. Imagine another straight line drawn from the end of the gnomon's shadow through the top of the gnomon to the Sun on the bowl in Alexandria; and it will be parallel to the already named line, since it has already been said that the lines from different parts of the Sun to different parts of the Earth are parallel. The straight line drawn from the center of the Earth to the gnomon in Alexandria, forms with equal parallel transverse angles with these parallel. One of them - with the top in the center of the Earth, at the meeting of direct, held from the sundial to the center of the Earth, and the other - with the top at the end of the gnomon in Alexandria, when meeting with the line that runs from this end to the end of its own shadow from the Sun, where these lines meet at the top. The first angle rests on the arc from the end of the gnomon's shadow to its base, and the second on the arc with the center in the center of the earth, running from Siena to Alexandria. These arcs are similar to each other, because they are based on equal angles. And what does the arc on the cup have to do with its circle, the same relationship has the arc from Siena to Alexandria [to its circle]. But it has been found that in the cup it makes up the fiftieth part of its circle. Therefore, the distance from Siena to Alexandria will necessarily make up the fiftieth part of the great circle of the Earth. But it is equal to 5,000 stages . Therefore, the whole circle will be equal to 250,000 stages. This is the method of Eratosthenes.

Later, the number obtained by Eratosthenes was increased to 252,000 stades. It is difficult to determine how close these estimates are to reality, since it is not known what stage Eratosthenes used. If the value of the stage is from 209.4 meters (stages of the pharaohs system) to 178 (Greek) and 172.5 (Egyptian), the radius values ​​could range from 8,397 km to 6,916 km. Also mentioned is the use stage of 157.2 meters, in which the Earth’s radius would be 6,302 km ^[5] . Modern measurements for the average Earth radius give a value of 6,371 km, which in any case makes the above calculation an outstanding achievement and the first reasonably accurate calculation of the size of our planet.

It is believed that it was Eratosthenes who created the first map of the world, which gave a rough idea of ​​the mutual remoteness of cities and countries. He argued that the exact mapping of the world, even in two dimensions, depends only on the establishment of accurate linear dimensions. His great achievements in the field of cartography were immediately used as a new method for building maps with meridians and parallels. These axial lines were placed on the map of the Earth from its place of origin - Rhodes, and since then the world has become divided into sectors. Then Eratosthenes began to use these plots of land to determine places on the map.

In comparatively large passages, the work of Eratosthenes on geography has reached the present day. In its entirety, it was divided, according to Strabo , into three books. In the first, the author gave a critical overview of the history of geography, from the first appearance of geographical concepts in Homer to his immediate predecessors, that is, to historians and geographers who took advantage of the campaigns of Alexander the Great and their descriptions. The second book outlines the basics of geography on the views of the author. The subject of the third book is land.

Eratosthenes are called the "father of geography" for his services in the development of geographical ideas, as well as for the fact that the term "geography" (geographering) belongs to him.

Literary writings

In the ancient world, Eratosthenes was known not only as a naturalist, but also as an epic and elegiac poet. In the poem "Hermes" he puts into the mouth of Hermes a story about the harmony of the spheres . In the elegy “Erigona” (daughter of Icarus), written in one of the Ionian dialects , the most famous is an excerpt in which a new dance is introduced into everyday life, with which the emergence of tragedy is associated. According to legend, for the first time this dance was performed after Icarus killed a goat ( ancient Greek τράγος , hence the tragoedia), who climbed into his vineyard. In the poem "Hesiod" the legend of the poet Hesiod is told , allegedly seducing another's wife and for this he was killed by her brothers. The mentioned literary works are preserved in fragments. Only the epigram of Eratosthenes devoted to Ptolemy III has been fully preserved.

Other Works

Eratosthenes is the founder of scientific chronology . In his work "Chronography", he tried to establish dates related to the history of Hellas, compiled a list of winners of the Olympic Games. In addition, Eratosthenes wrote a philological treatise "On the ancient comedy."

According to Strabo , Eratosthenes (in an unnamed work) believed that there was good and bad in every nation and criticized Aristotle for dividing humanity into Greeks and barbarians and insisting on preserving the racial purity of the Greeks ^[6] .

• Eratosthenes (crater)
• Eratosthene period

• Bernhardi G. Eratosthenica. - Berlin, 1922. - 272 S.
• Eratosthenes . Geography (fragments). // Antique geography. / Comp. M. S. Bodnarsky. M., Geografgiz. 1953. p. 84-99.
• Berger H. Die geographischen Fragmente des Eratosthenes . - Leipzig: BG Teubner, 1880. - VIII, 393 S.
• Eratosthenes Geography 691-14267-8 .

• Antique geography. M., 1953.
• Bobynin V.V. Eratosthenes // Encyclopedic Dictionary of Brockhaus and Efron : in 86 tons (82 tons and 4 extra). - SPb. , 1890-1907.
• Dietmar A.B. Rhodes parallel: The life and work of Eratosthenes. - M .: Thought , 1965. - 72 p.
• Kolchinsky I.G., Korsun A.A., Rodriguez M.G. Astronomers: A Biographical Directory. - 2nd ed., Pererab. and extra .. - Kiev: Naukova Dumka, 1986. - 512 p.
• Shcheglov D. А. The Rhodes Parallel of Eratosthenes and the History of the Climate System // Mnemon. Studies and publications on the history of the ancient world. - Vol. 4. - SPb., 2005. - p. 383—396.
• Shcheglov D. A. The system of the seven climates of Ptolemy and the geography of Eratosthenes (inaccessible link) // Herald of ancient history. - 2005. - № 3. - p. 243-265.
• Schetnikov A.I. Measurement of astronomical distances in ancient Greece. (inaccessible link) // ΣΧΟΛΗ . - T. 4. 2010. - p. 325-340.

In foreign languages

• Aujac G. Eratosthène de Cyrène, le pionier de la geographie. - Paris: Édition du CTHS, 2001. - 224p.
• Cameron McPhail. Reconstructing Eratosthenes' Map of the World: a Study in Source Analysis. A Thesis Submitted by the University of Otago . - Dunedin, New Zealand, 2011.
• Dicks DR Eratosthenes // Dictionary of Scientific Biography. - Vol. Iv. - New York: C. Schribner's Sons, 1971. - p. 388–393.
• Diller A. Geographical Latitudes in Eratosthenes, Hipparchus and Posidonius // Klio. - 1934. - Bd. 27. - Heft 3. - S. 258-269.
• Dutka J. Eratosthenes' measurement of the earth reconsidered. Archive for History of Exact Sciences , 46, 1993, p. 55-64.
• Fischer I. Another look at Earth's circumferences. // Quarterly Journal of the Royal Astronomical Society. - Vol. 16. - 1975. - P. 152-167.
• Fraser PM Ptolemaic Alexandria. - Oxford: Clarendon Press, 1972.
• Geus K. Eratosthenes von Kyrene. Studien zur hellenistischen Kultur- und Wissenschaftgeschichte. - München: Verlag CH Beck, 2002. (Münchener Beiträge zur Papyrusforschung und antiken Rechtsgeschichte. - Bd. 92) - X, 412 S.
• Goldstein BR Eratosthenes on the Earth // Historia Mathematica. - Vol. 11. - 1984. - P. 411-416.
• Rawlins D. Eratosthenes' geodesy unraveled: Is a high-accuracy Hellenistic astronomy, Isis , 73, 1982, p. 259-265.
• Rawlins D. The Eratosthenes - Strabo Nile map. Is it the earliest surviving instance of spherical cartography? The 5000 stades arc for Eratosthenes experiment ?, Arch. Hist. Exact Sci , 26 (3), 1982, p. 211-219.
• Rawlins D. Eratothenes's large earth and tiny universe. DIO , 14, 2008.
• Shtoglov DA Ptolemy's System of Seven Climata and Eratosthenes' Geography // Geographia Antiqua. - Vol. 13. - 2004 (2006). - P. 21-37.
• Shcheglov DA Eratosthenes' Parallel of the System of Climata // Klio. - Bd. 88. - 2006. - P. 351-359.
• Thalamas A. La géographe d'Ératosthène. - Versailles, 1921.
• Wolfer EP Eratosthenes von Kyrene als Mathematiker und Philosoph. - Groningen-Djakarta, 1954.

• Biography of Eratosthenes in The MacTutor History of Mathematics archive
• The original version of the article from the ESSE
• Eratosthenes, Chronography
• Eratosthenes, Cataclysms
• https://web.archive.org/web/20140723070518/http://www.nazdar.ru/interesno/?p=692