Eratosthenes
Eratosthenes of Cyrene (/ɛrəˈtɒsθəniːz/; Greek: Ἐρατοσθένης ὁ Κυρηναῖος, romanized: Eratosthénēs ho Kurēnaĩos, IPA: [eratostʰénɛːs]; c. 276 BC[note 1] – c. 195/194 BC)[note 2] 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]
Eratosthenes  

Born  276 BC[note 1] 
Died  194 BC (around age 82)[note 2] 
Occupation 

Known for 

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 semimythological 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 10thcentury 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]
Life
The son of Aglaos, Eratosthenes was born in 276 BC in Cyrene. Now part of modernday 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 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.
These works and his great poetic abilities led the pharaoh 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 five 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.[8]
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
It has been suggested that this section be split out into another article titled Eratosthenes' arc measurement. (Discuss) (May 2021) 
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
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 (2122 July 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.
 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]
 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]
 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 taxationrelated 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]
Geography
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 threevolume 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 citycenter 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]
Achievements
Eratosthenes was described by the Suda Lexicon as a Πένταθλος (Pentathlos) which can be translated as "AllRounder", 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 "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 Macrobious, Eratosthenes made the diameter of the Sun to be about 27 times that of the Earth.[23] The actual figure is approximately 109 times.[29]
 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.[30]
 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.[31] 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.[32]
Number theory
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 preeminent 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 only fragments left of his works after the destruction of the Library of Alexandria.[28]
Titles
 Platonikos
 Hermes
 Erigone
 Chronographies
 Olympic Victors
 Περὶ τῆς ἀναμετρήσεως τῆς γῆς (On the Measurement of the Earth)[33] (lost, summarized by Cleomedes)
 Гεωγραϕικά (Geographika)[28] (lost, criticized by Strabo)
 Arsinoe (a memoir of queen Arsinoe; lost; quoted by Athenaeus in the Deipnosophistae)
 Ariston (concerning Aristo of Chios' addiction to luxury); lost; quoted by Athenaeus in the Deipnosophistae)[34]
 A fragmentary collection of Hellenistic myths about the constellations, called Catasterismi (Katasterismoi), was attributed to Eratosthenes, perhaps to add to its credibility.
See also
 Aristarchus of Samos (c. 310 – c. 230 BC), a Greek mathematician who calculated the distance from the Earth to the Sun.
 Eratosthenes (crater) on the Moon.
 Eratosthenian period in the lunar geologic timescale.
 Eratosthenes Seamount in the eastern Mediterranean Sea.
 Eratosthenes Point in Antarctica.
 Hipparchus (c. 190 – c. 120 BC), a Greek mathematician who measured the radii of the Sun and the Moon as well as their distances from the Earth.
 Posidonius (c. 135 – c. 51 BC), a Greek astronomer and mathematician who calculated the circumference of the Earth.
Notes
 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.[note 3]
 The Suda states he died at the age of 80, Censorinus (De die natali, 15) at the age of 81, and PseudoLucian (Makrobioi, 27) at the age of 82.
 Eratosthenes entry in the Dictionary of Scientific Biography (1971)
References
 Roller, Duane W. Eratosthenes' Geography. New Jersey: Princeton University Press, 2010.
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 Chambers, James T. "Eratosthenes of Cyrene." in Dictionary Of World Biography: The Ancient World January 1998: 1–3.
 Bailey, Ellen. 2006. "Eratosthenes of Cyrene." Eratosthenes Of Cyrene 1–3. Book Collection Nonfiction: High School Edition.
 Rist, J.M. "Zeno and Stoic Consistency," in Phronesis. Vol. 22, No. 2, 1977.
 "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 20210224.
 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)).
 Russo, Lucio (2004). The Forgotten Revolution. Berlin: Springer. p. 68..
 Torge, W.; Müller, J. (2012). Geodesy. De Gruyter Textbook. De Gruyter. p. 5. ISBN 9783110250008. Retrieved 20210502.
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 Willers, Michael (2009). Algebra: The x and y of Everyday Math (2009 ed.). Quid Publishing. pp. 62–63. ISBN 9781435114005.
 Rawlins, Dennis (1983). "The ErathostenesStrabo 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)
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 Smith, Sir William. "Eratosthenes", in A Dictionary of Greek and Roman Biography and Mythology. Ann Arbor, Michigan: University of Michigan Library, 2005.
 Morris, Terry R. "Eratosthenes of Cyrene." in Encyclopedia Of The Ancient World. November 2001.
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 Eckerman, Chris. Review of (D.W.) Roller 'Eratosthenes' Geography. Fragments Collected and Translated, with Commentary and Additional Material. The Classical Review. 2011.
 "Eratosthenes of Cyrene". Khan Academy. Retrieved 20191119.
 Dicks, D.R. "Eratosthenes", in Complete Dictionary of Scientific Biography. New York: Charles Scribner's Sons, 1971.
 "Ask an Astronomer". Cool Cosmos. Archived from the original on 20140730.
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 Chondros, Thomas G. Archimedes Life Works and Machines. in Mechanism and Machine Theory. Vol.45(11) 2010. 1766–1775.
 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.
 Smith, Andrew. "Athenaeus: Deipnosophists – Book 7". www.attalus.org.
Further reading
 Aujac, G. (2001). Eratosthène de Cyrène, le pionnier de la géographie. Paris: Édition du CTHS. 224p.
 BulmerThomas, Ivor (1939–1940). Selections Illustlating the History of Greek Mathematics. Cambridge, Massachusetts: Harvard University Press.
 Diller, A (1934). "Geographical Latitudes in Eratosthenes, Hipparchus and Posidonius". Klio. 27 (3): 258–269. doi:10.1524/klio.1934.27.27.258. S2CID 194449299.
 Dorofeeva, A. V. (1988). "Eratosthenes (ca. 276–194 B.C.)". Mat. V Shkole (in Russian) (4): i.
 Dutka, J. (1993). "Eratosthenes' measurement of the Earth reconsidered". Arch. Hist. Exact Sci. 46 (1): 55–66. Bibcode:1993AHES...46...55D. doi:10.1007/BF00387726. S2CID 119522892.
 El'natanov, B. A. (1983). "A brief outline of the history of the development of the sieve of Eratosthenes". Istor.Mat. Issled. (in Russian). 27: 238–259.
 Fischer, I (1975). "Another look at Eratosthenes' and Posidonius' determinations of the Earth's circumference". Quarterly Journal of the Royal Astronomical Society. 16: 152–167. Bibcode:1975QJRAS..16..152F.
 Fowler, D. H.; Rawlins, Dennis (1983). "Eratosthenes' ratio for the obliquity of the ecliptic". Isis. 74 (274): 556–562. doi:10.1086/353361. S2CID 144617495.
 Fraser, P. M. (1970). "Eratosthenes of Cyrene". Proceedings of the British Academy. 56: 175–207.
 Fraser, P. M. (1972). Ptolemaic Alexandria. Oxford: Clarendon Press.
 Fuentes González, P. P., "Ératosthène de Cyrène", in R. Goulet (ed.), Dictionnaire des Philosophes Antiques, vol. III, Paris, Centre National de la Recherche Scientifique, 2000, pp. 188–236.
 Geus K. (2002). 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.
 Goldstein, B. R. (1984). "Eratosthenes on the "measurement" of the Earth". Historia Math. 11 (4): 411–416. doi:10.1016/03150860(84)900259.
 Gulbekian, E. (1987). "The origin and value of the stadion unit used by Eratosthenes in the third century B.C". Archive for History of Exact Sciences. 37 (4): 359–363. doi:10.1007/BF00417008 (inactive 31 May 2021). JSTOR 41133819.CS1 maint: DOI inactive as of May 2021 (link)
 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.
 Knaack, G. (1907). "Eratosthenes". Pauly–Wissowa VI: 358–388.
 Manna, F. (1986). "The Pentathlos of ancient science, Eratosthenes, first and only one of the "primes"". Atti Accad. Pontaniana. New Series (in Italian). 35: 37–44.
 Muwaf, A.; Philippou, A. N. (1981). "An Arabic version of Eratosthenes writing on mean proportionals". J. Hist. Arabic Sci. 5 (1–2): 147–174.
 Nicastro, Nicholas (2008). Circumference: Eratosthenes and the ancient quest to measure the globe. New York: St. Martin's Press. ISBN 9780312372477.
 O'Connor, John J.; Robertson, Edmund F., "Eratosthenes", MacTutor History of Mathematics archive, University of St Andrews
 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). 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.
 Pfeiffer, Rudolf (1968). History of Classical Scholarship From the Beginnings to the End of the Hellenistic Age. Oxford: Clarendon Press.
 Rawlins, D. (1982). "Eratosthenes' geodesy unraveled : was there a highaccuracy Hellenistic astronomy". Isis. 73 (2): 259–265. doi:10.1086/352973. S2CID 120730515.
 Rawlins, D. (1982). "The Eratosthenes – Strabo Nile map. Is it the earliest surviving instance of spherical cartography? Did it supply the 5000 stades arc for Eratosthenes' experiment?". Arch. Hist. Exact Sci. 26 (3): 211–219.
 Rawlins, D. (2008). "Eratosthenes's large Earth and tiny universe" (PDF). DIO. 14: 3–12. Bibcode:2008DIO....14....3R.
 Roller, Duane W. (2010). Eratosthenes' Geography: Fragments collected and translated, with commentary and additional material. Princeton: Princeton University Press. ISBN 9780691142678.
 Rosokoki, A. (1995), Die Erigone des Eratosthenes. Eine kommentierte Ausgabe der Fragmente, Heidelberg: C. WinterVerlag
 Shcheglov, D.A. (2004/2006). "Ptolemy's System of Seven Climata and Eratosthenes' Geography". Geographia Antiqua 13: 21–37.
 Shcheglov, D.A. (2006). "Eratosthenes' Parallel of Rhodes and the History of the System of Climata". Klio. 88 (2): 351–359. doi:10.1524/klio.2006.88.2.351. S2CID 190529073.
 Strabo (1917). The Geography of Strabo. Horace Leonard Jones, trans. New York: Putnam.
 Taisbak, C. M. (1984). "Eleven eightythirds. Ptolemy's reference to Eratosthenes in Almagest I.12". Centaurus. 27 (2): 165–167. Bibcode:1984Cent...27..165T. doi:10.1111/j.16000498.1984.tb00766.x.
 Thalamas, A. (1921). La géographe d'Ératosthène. Versailles.
 Wolfer, E. P. (1954). Eratosthenes von Kyrene als Mathematiker und Philosoph. GroningenDjakarta.