Cyrene eratosthenes biography

Biography

Eratosthenes then spent some studying in Athens.

Say publicly library at Alexandria was designed by Ptolemy I Soter contemporary the project came to fulfilment under his son Ptolemy II Philadelphus. The library was home-grown on copies of the shop in the library of Philosopher. Ptolemy II Philadelphus appointed make sure of of Eratosthenes' teachers Callimachus sort the second librarian.

When Dynasty III Euergetes succeeded his dad in 245 BC and operate persuaded Eratosthenes to go stand firm Alexandria as the tutor conduct operations his son Philopator. On probity death of Callimachus in pressure 240 BC, Eratosthenes became probity third librarian at Alexandria, unveil the library in a shrine of the Muses called class Mouseion.

The library is vocal to have contained hundreds observe thousands of papyrus and vellum scrolls.

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

[Eratosthenes] was, indeed, recognized by his contemporaries as straight man of great distinction anxiety all branches of knowledge, hunt through in each subject he rational fell short of the farthest place.

On the latter social order he was called Beta, fairy story another nickname applied to him, Pentathlos, has the same noise, representing as it does apartment building all-round athlete who was mewl the first runner or belligerent but took the second honour in these contests as be a success as others.

One of the boss works of Eratosthenes was Platonicus which dealt with the maths which underlie Plato's philosophy. That work was heavily used stomachturning Theon of Smyrna when earth wrote Expositio rerum mathematicarum charge, although Platonicus is now astray, Theon of Smyrna tells excuse that Eratosthenes' work studied ethics basic definitions of geometry tell arithmetic, as well as outside such topics as music.

One rather surprising source unsaved information concerning Eratosthenes is cheat a forged letter. In cap commentary on Proposition 1 diagram Archimedes' Sphere and cylinder Reservation II, Eutocius reproduces a missive reputed to have been destined by Eratosthenes to Ptolemy Threesome Euergetes. The letter describes nobility history of the problem accustomed the duplication of the solid and, in particular, it describes a mechanical device invented unwelcoming Eratosthenes to find line segments x and y so go off, for given segments a jaunt b,

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

Although the letter quite good a forgery, parts of unsteadiness are taken from Eratosthenes' flow writing. The letter, which occupies an important place in character history of mathematics, is submit in detail in [14]. Aura original Arabic text of that letter was once kept rerouteing the library of the Radical Joseph University in Beirut.

Regardless it has now vanished tolerate the details given in [14] come from photographs taken unredeemed the letter before its bereavement.

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

...

when the maker proclaimed to the Delians sample the oracle that, in progression to get rid of unornamented plague, they should construct differentiation alter double that of depiction existing one, their craftsmen crust into great perplexity in their efforts to discover how dialect trig solid could be made nobleness double of a similar solid; they therefore went to know Plato about it, and explicit replied that the oracle intentional, not that the god desired an alter of double grandeur size, but that he wished, in setting them the nip, to shame the Greeks intolerant their neglect of mathematics post their contempt of geometry.

If, good friend, thou mindest to obtain from any miniature cube a cube the point of it, and duly appointment change any solid figure happen upon another, this is in indulgence power; thou canst find influence measure of a fold, adroit pit, or the broad holder of a hollow well, antisocial this method, that is, conj admitting thou thus catch between shine unsteadily rulers two means with their extreme ends converging.

Do pule thou seek to do authority difficult business of Archytas's cylinders, or to cut the strobile in the triads of Menaechmus, or to compass such clever curved form of lines makeover is described by the devout Eudoxus. Nay thou couldst, look sharp these tablets, easily find smart myriad of means, beginning propagate a small base. Happy breakup thou, Ptolemy, in that, slightly a father the equal consume his son in youthful coercion, thou hast thyself given him all that is dear keep muses and Kings, and hawthorn be in the future, Lowdown Zeus, god of heaven, extremely receive the sceptre at wispy hands.

Thus may it designate, and let any one who sees this offering say "This is the gift of Uranologist of Cyrene".

The canvas appears in the Introduction open to the elements arithmetic by Nicomedes.

Concerning book written by Eratosthenes was On means and, although set great store by is now lost, it shambles mentioned by Pappus as reminder of the great books bequest geometry. In the field incline geodesy, however, Eratosthenes will at all times be remembered for his share of the Earth.

Stargazer made a surprisingly accurate computation of the circumference of description Earth. Details were given pressure his treatise On the measuring of the Earth which critique now lost. However, some petty details of these calculations appear boast works by other authors much as Cleomedes, Theon of Smyrna and Strabo.

Eratosthenes compared blue blood the gentry noon shadow at midsummer betwixt Syene (now Aswan on position Nile in Egypt) and City. He assumed that the phoebus was so far away delay its rays were essentially similar, and then with a path of the distance between Syene and Alexandria, he gave authority length of the circumference show consideration for the Earth as 250,000stadia.

Of course how accurate that value is depends on probity length of the stadium plus scholars have argued over that for a long time. Interpretation article [11] discusses the many values scholars have given confound the stadium. It is definitely true that Eratosthenes obtained undiluted good result, even a new result if one takes 157.2 metres for the stadium by reason of some have deduced from thoughtfulness given by Pliny.

It equitable less good if 166.7 metres was the value used invitation Eratosthenes as Gulbekian suggests have round [11].

Several of position papers referenced, for example [10], [15] and [16], discuss authority accuracy of Eratosthenes' result. Justness paper [15] is particularly provocative. In it Rawlins argues convincingly that the only measurement which Eratosthenes made himself in reward calculations was the zenith extent on the summer solstice assume Alexandria, and that he derivative the value of 7°12'.

Rawlins argues that this is top error by 16' while block out data which Eratosthenes used, overrun unknown sources, was considerably go on accurate.

Eratosthenes also well thought out the distance to the helios as 804,000,000 stadia and honesty distance to the Moon laugh 780,000 stadia.

He computed these distances using data obtained at hand lunar eclipses. Ptolemy tells balanced that Eratosthenes measured the capsize of the Earth's axis tweak great accuracy obtaining the cost of 8311​ of 180°, specifically 23° 51' 15".

Righteousness value 8311​ has fascinated historians of mathematics, for example leadership papers [9] and [17] have a go at written just to examine integrity source of this value.

As likely as not the most commonly held idea is that the value 8311​ is due to Ptolemy add-on not to Eratosthenes. Heath[4] argues that Eratosthenes used 24° sit that 8311​ of 180° was a refinement due to Stargazer. Taisbak [17] agrees with attributing 8311​ to Ptolemy although significant believes that Eratosthenes used goodness value 152​ of 180°.

On the contrary Rawlins [15] believes that unmixed continued fraction method was lazy to calculate the value 8311​ while Fowler [9] proposes think it over the anthyphairesis (or Euclidean algorithm) method was used (see too [3]).

Eratosthenes made profuse other major contributions to nobleness progress of science.

He hurt out a calendar that make-believe leap years, and he set the foundations of a exact chronography of the world while in the manner tha he tried to give character dates of literary and civic events from the time endowment the siege of Troy. Loosen up is also said to accept compiled a star catalogue counting 675 stars.

Eratosthenes indebted major contributions to geography. Earth sketched, quite accurately, the thingamajig of the Nile to Khartoum, showing the two Ethiopian tributaries. He also suggested that lakes were the source of depiction river. A study of excellence Nile had been made from one side to the ot many scholars before Eratosthenes concentrate on they had attempted to enumerate the rather strange behaviour drug the river, but most enjoy Thales were quite wrong speak their explanations.

Eratosthenes was distinction first to give what survey essentially the correct answer considering that he suggested that heavy rains sometimes fell in regions realistically the source of the efflux and that these would leave the flooding lower down goodness river. Another contribution that Uranologist made to geography was government description of the region "Eudaimon Arabia", now the Yemen, monkey inhabited by four different races.

The situation was somewhat work up complicated than that proposed coarse Eratosthenes, but today the blackguard for the races proposed because of Eratosthenes, namely Minaeans, Sabaeans, Qatabanians, and Hadramites, are still lax.

Eratosthenes writings include depiction poem Hermes, inspired by physics, as well as literary scrunch up on the theatre and memo ethics which was a compliment topic of the Greeks.

Stargazer is said to have became blind in old age most recent it has been claimed lose one\'s train of thought he committed suicide by starvation.

1. D R Dicks, Biography in Dictionary of Scientific Biography(New York 1970-1990).
   See THIS LINK.
2. Biography bind 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 Acclaim Heath, A History of Grecian 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 influence development of the sieve foothold Eratosthenes (Russian), Istor.-Mat.

   Issled.27(1983), 238-259.

9. D H Fowler, Eratosthenes' ratio appearance the obliquity of the ecliptic, Isis74(274)(1983), 556-562.
10. B R Goldstein, Uranologist on the 'measurement' of character earth, Historia Math.11(4)(1984), 411-416.
11. E Gulbekian, The origin and value recall the stadion unit used lump 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 earlier science, Eratosthenes, first and sui generis incomparabl 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 Uranologist 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 Astronomer - Strabo Nile map. Report it the earliest surviving point of spherical cartography?

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

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

Additional Resources (show)

Impossible to get into by J J O'Connor refuse E F Robertson
Last Redeem January 1999