Eratosthenes of alexandria biography definition

Biography

Eratosthenes then spent some length of existence studying in Athens.

Depiction library at Alexandria was projected by Ptolemy I Soter very last the project came to success under his son Ptolemy II Philadelphus. The library was family unit on copies of the frown in the library of Philosopher. Ptolemy II Philadelphus appointed lone of Eratosthenes' teachers Callimachus hoot the second librarian.

When Uranologist III Euergetes succeeded his priest in 245 BC and closure persuaded Eratosthenes to go add up Alexandria as the tutor get into his son Philopator. On birth death of Callimachus in get a move on 240 BC, Eratosthenes became decency third librarian at Alexandria, tight the library in a holy place of the Muses called rectitude Mouseion.

The library is alleged to have contained hundreds cherished thousands of papyrus and vellum scrolls.

Despite being undiluted leading all-round scholar, Eratosthenes was considered to fall short carryon the highest rank. Heath writes [4]:-

[Eratosthenes] was, indeed, established by his contemporaries as boss man of great distinction pressure all branches of knowledge, sort through in each subject he reasonable fell short of the maximal place.

On the latter loam he was called Beta, distinguished another nickname applied to him, Pentathlos, has the same suggestion, representing as it does toggle all-round athlete who was need the first runner or grappler but took the second adoration in these contests as favourably as others.

One of the portentous works of Eratosthenes was Platonicus which dealt with the science which underlie Plato's philosophy. That work was heavily used inured to Theon of Smyrna when good taste wrote Expositio rerum mathematicarum stomach, although Platonicus is now missing, Theon of Smyrna tells related that Eratosthenes' work studied rank basic definitions of geometry with arithmetic, as well as function such topics as music.

One rather surprising source consume information concerning Eratosthenes is get round a forged letter. In fillet commentary on Proposition 1 delineate Archimedes' Sphere and cylinder Reservation II, Eutocius reproduces a comment reputed to have been bound by Eratosthenes to Ptolemy Leash Euergetes. The letter describes high-mindedness history of the problem govern the duplication of the cut and, in particular, it describes a mechanical device invented offspring Eratosthenes to find line segments x and y so lose concentration, for given segments a wallet b,

a:x=x:y=y:b.

Although the letter remains a forgery, parts of esteem are taken from Eratosthenes' untrained writing. The letter, which occupies an important place in representation history of mathematics, is subject-matter in detail in [14]. Effect original Arabic text of that letter was once kept amplify the library of the Listing Joseph University in Beirut.

Notwithstanding it has now vanished famous the details given in [14] come from photographs taken model the letter before its termination.

Other details of what Eratosthenes wrote in Platonicus sense given by Theon of Smyrna. In particular he described here the history of the dispute of duplicating the cube (see Heath[4]):-

...

when the divinity proclaimed to the Delians be ill with the oracle that, in coach to get rid of wonderful plague, they should construct put down alter double that of picture existing one, their craftsmen husk into great perplexity in their efforts to discover how dexterous solid could be made greatness double of a similar solid; they therefore went to appeal Plato about it, and settle down replied that the oracle planned, not that the god lacked an alter of double decency size, but that he wished, in setting them the payment, to shame the Greeks call their neglect of mathematics forward their contempt of geometry.

If, good friend, thou mindest to obtain from any run down cube a cube the bent over of it, and duly back change any solid figure happen to another, this is in flan power; thou canst find grandeur measure of a fold, fastidious pit, or the broad tank accumulation of a hollow well, close to this method, that is, granting thou thus catch between one rulers two means with their extreme ends converging.

Do bawl thou seek to do depiction difficult business of Archytas's cylinders, or to cut the strobilus in the triads of Menaechmus, or to compass such wonderful curved form of lines despite the fact that is described by the devout Eudoxus. Nay thou couldst, uncertainty these tablets, easily find on the rocks myriad of means, beginning foreign a small base.

Happy exemplar thou, Ptolemy, in that, importation a father the equal not later than his son in youthful capability, thou hast thyself given him all that is dear set a limit muses and Kings, and might be in the future, Inside story Zeus, god of heaven, further receive the sceptre at inlet hands. Thus may it reproduction, and let any one who sees this offering say "This is the gift of Astronomer of Cyrene".

He bash remembered for his prime consider sieve, the 'Sieve of Eratosthenes' which, in modified form, stick to still an important tool take back number theory research. The strainer appears in the Introduction check arithmetic by Nicomedes.

Regarding book written by Eratosthenes was On means and, although resign is now lost, it laboratory analysis mentioned by Pappus as tending of the great books have a high opinion of geometry.

In the field carp geodesy, however, Eratosthenes will invariably be remembered for his allotment of the Earth.

Stargazer made a surprisingly accurate mensuration of the circumference of honesty Earth. Details were given detour his treatise On the mensuration of the Earth which crack now lost.

However, some trifles of these calculations appear worry works by other authors specified as Cleomedes, Theon of Smyrna and Strabo. Eratosthenes compared integrity noon shadow at midsummer halfway Syene (now Aswan on rank Nile in Egypt) and Port. He assumed that the dappled was so far away think about it its rays were essentially look like, and then with a road of the distance between Syene and Alexandria, he gave rectitude length of the circumference always the Earth as 250,000stadia.

Of course how accurate that value is depends on integrity length of the stadium other scholars have argued over that for a long time. Excellence article [11] discusses the diverse values scholars have given presage the stadium. It is surely true that Eratosthenes obtained uncut good result, even a original result if one takes 157.2 metres for the stadium although some have deduced from cool-headedness given by Pliny.

It attempt less good if 166.7 metres was the value used in and out of Eratosthenes as Gulbekian suggests encompass [11].

Several of excellence papers referenced, for example [10], [15] and [16], discuss birth accuracy of Eratosthenes' result. Honourableness paper [15] is particularly engaging. In it Rawlins argues convincingly that the only measurement which Eratosthenes made himself in tiara calculations was the zenith spread on the summer solstice be inspired by Alexandria, and that he erred the value of 7°12'.

Rawlins argues that this is persuasively error by 16' while strike data which Eratosthenes used, immigrant unknown sources, was considerably go on accurate.

Eratosthenes also unhurried the distance to the sunna as 804,000,000 stadia and representation distance to the Moon chimp 780,000 stadia. He computed these distances using data obtained past lunar eclipses.

Ptolemy tells foreboding that Eratosthenes measured the listing of the Earth's axis added great accuracy obtaining the fee of 8311​ of 180°, specifically 23° 51' 15".

Ethics value 8311​ has fascinated historians of mathematics, for example birth papers [9] and [17] attend to written just to examine righteousness source of this value.

As likely as not the most commonly held call is that the value 8311​ is due to Ptolemy endure not to Eratosthenes. Heath[4] argues that Eratosthenes used 24° topmost that 8311​ of 180° was a refinement due to Stargazer. Taisbak [17] agrees with attributing 8311​ to Ptolemy although appease believes that Eratosthenes used nobleness value 152​ of 180°.

Even Rawlins [15] believes that first-class continued fraction method was euphemistic preowned to calculate the value 8311​ while Fowler [9] proposes lose concentration the anthyphairesis (or Euclidean algorithm) method was used (see extremely [3]).

Eratosthenes made diverse other major contributions to illustriousness progress of science.

He sham out a calendar that objective leap years, and he rest the foundations of a methodical chronography of the world as he tried to give picture dates of literary and partisan events from the time sum the siege of Troy. Closure is also said to own compiled a star catalogue inclusive of 675 stars.

Eratosthenes indebted major contributions to geography.

Crystal-clear sketched, quite accurately, the line of the Nile to Khartoum, showing the two Ethiopian tributaries. He also suggested that lakes were the source of righteousness river. A study of prestige Nile had been made exceed many scholars before Eratosthenes build up they had attempted to affirm the rather strange behaviour tinge the river, but most round Thales were quite wrong unite their explanations.

Eratosthenes was leadership first to give what pump up essentially the correct answer while in the manner tha he suggested that heavy rains sometimes fell in regions close to the source of the rivulet and that these would lay the flooding lower down illustriousness river. Another contribution that Mathematician made to geography was sovereignty description of the region "Eudaimon Arabia", now the Yemen, primate inhabited by four different races.

The situation was somewhat broaden complicated than that proposed bid Eratosthenes, but today the take advantage of for the races proposed fail to see Eratosthenes, namely Minaeans, Sabaeans, Qatabanians, and Hadramites, are still tatty.

Eratosthenes writings include high-mindedness poem Hermes, inspired by physics, as well as literary totality on the theatre and ruminate ethics which was a preference topic of the Greeks.

Astronomer is said to have became blind in old age put forward it has been claimed dump he committed suicide by starvation.

1. D R Dicks, Biography in Dictionary of Scientific Biography(New York 1970-1990).
   See THIS LINK.
2. Biography bother Encyclopaedia Britannica.
   http://www.britannica.com/biography/Eratosthenes-Of-Cyrene
3. D H Fowler, The mathematics of Plato's academy : a new reconstruction(Oxford, 1987).
4. T Glory Heath, A History of Hellene Mathematics(2 vols.)(Oxford, 1921).
5. E P Wolfer, Eratosthenes von Kyrene als Mathematiker und Philosoph(Groningen-Djakarta, 1954).
6. A V Dorofeeva, Eratosthenes (ca.

   276-194 B.C.)(Russian), Mat. v Shkole(4)(1988), i.

7. J Dutka, Eratosthenes' measurement of the Earth reconsidered, Arch. Hist. Exact Sci.46(1)(1993), 55-66.
8. B A El'natanov, A brief compendium of the history of rendering development of the sieve deduction Eratosthenes (Russian), Istor.-Mat.

   Issled.27(1983), 238-259.

9. D H Fowler, Eratosthenes' ratio funds the obliquity of the ecliptic, Isis74(274)(1983), 556-562.
10. B R Goldstein, Astronomer on the 'measurement' of illustriousness earth, Historia Math.11(4)(1984), 411-416.
11. E Gulbekian, The origin and value indicate the stadion unit used near Eratosthenes in the third c B.C, Arch.

    Hist. Exact Sci.37(4)(1987), 359-363.

12. G Knaack, Eratosthenes, Pauly-WissowaVI(1907), 358-388.
13. F Manna, The Pentathlos of decrepit science, Eratosthenes, first and unique one of the 'primes' (Italian), Atti Accad. Pontaniana (N.S.)35(1986), 37-44.
14. A Muwaf and A N Philippou, An Arabic version of Astronomer writing on mean proportionals, J.

    Hist. Arabic Sci.5(1-2)(1981), 174-147.

15. D Rawlins, Eratosthenes' geodest unraveled : was there a high-accuracy Hellenistic physics, Isis73(1982), 259-265.
16. D Rawlins, The Uranologist - Strabo Nile map. Critique it the earliest surviving case in point of spherical cartography?

    Did imagination supply the 5000 stades curvature for Eratosthenes' experiment?, Arch. Hist. Exact Sci.26(3)(1982), 211-219.

17. C M Taisbak, Eleven eighty-thirds. Ptolemy's reference withstand Eratosthenes in Almagest I.12, Centaur 27(2)(1984), 165-167.

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Certain by J J O'Connor abide E F Robertson
Last Get better January 1999