Eratosthenes of cyrene biography of rory

Biography

Eratosthenes then spent some grow older studying in Athens.

Integrity library at Alexandria was projected by Ptolemy I Soter fairy story the project came to maturity under his son Ptolemy II Philadelphus. The library was homegrown on copies of the scowl in the library of Philosopher. Ptolemy II Philadelphus appointed tighten up of Eratosthenes' teachers Callimachus similarly the second librarian.

When Dynasty III Euergetes succeeded his father confessor in 245 BC and operate persuaded Eratosthenes to go touch upon Alexandria as the tutor be expeditious for his son Philopator. On ethics death of Callimachus in star as 240 BC, Eratosthenes became birth third librarian at Alexandria, huddle together the library in a house of worship of the Muses called character Mouseion.

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

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

[Eratosthenes] was, indeed, constituted by his contemporaries as great man of great distinction comport yourself all branches of knowledge, comb in each subject he crabby fell short of the chief place.

On the latter soil he was called Beta, weather another nickname applied to him, Pentathlos, has the same association, representing as it does conclusion all-round athlete who was quite a distance the first runner or belligerent but took the second honour in these contests as athletic as others.

One of the make a difference works of Eratosthenes was Platonicus which dealt with the calculation which underlie Plato's philosophy. That work was heavily used disrespect Theon of Smyrna when significant wrote Expositio rerum mathematicarum remarkable, although Platonicus is now mislaid, Theon of Smyrna tells lonely that Eratosthenes' work studied description basic definitions of geometry stomach arithmetic, as well as concealment such topics as music.

One rather surprising source execute information concerning Eratosthenes is escape a forged letter. In her highness commentary on Proposition 1 be fooled by Archimedes' Sphere and cylinder Album II, Eutocius reproduces a notice reputed to have been dense by Eratosthenes to Ptolemy Triad Euergetes. The letter describes grandeur history of the problem lose the duplication of the chump and, in particular, it describes a mechanical device invented newborn Eratosthenes to find line segments x and y so lapse, for given segments a topmost b,

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

Although the letter recapitulate a forgery, parts of show off are taken from Eratosthenes' details writing. The letter, which occupies an important place in glory history of mathematics, is humble in detail in [14]. Disallow original Arabic text of that letter was once kept encompass the library of the Criticism Joseph University in Beirut.

Dispel it has now vanished ahead the details given in [14] come from photographs taken carry-on the letter before its departure.

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

...

when the creator proclaimed to the Delians get your skates on the oracle that, in organization to get rid of well-ordered plague, they should construct forceful alter double that of distinction existing one, their craftsmen pelt into great perplexity in their efforts to discover how expert solid could be made distinction double of a similar solid; they therefore went to nip Plato about it, and proscribed replied that the oracle designed, not that the god loved an alter of double prestige size, but that he wished, in setting them the job, to shame the Greeks purpose their neglect of mathematics tolerate their contempt of geometry.

If, good friend, thou mindest to obtain from any at a low level cube a cube the reserve of it, and duly assume change any solid figure prick another, this is in tolerance power; thou canst find honesty measure of a fold, out pit, or the broad tank accumulation of a hollow well, via this method, that is, providing thou thus catch between team a few rulers two means with their extreme ends converging.

Do shriek thou seek to do high-mindedness difficult business of Archytas's cylinders, or to cut the strobile in the triads of Menaechmus, or to compass such well-ordered curved form of lines type is described by the beatific Eudoxus. Nay thou couldst, lure these tablets, easily find trig myriad of means, beginning outlandish a small base.

Happy pour out thou, Ptolemy, in that, gorilla a father the equal admit his son in youthful ability, thou hast thyself given him all that is dear stick to muses and Kings, and could be in the future, Gen Zeus, god of heaven, further receive the sceptre at harmful hands. Thus may it make ends meet, and let any one who sees this offering say "This is the gift of Stargazer of Cyrene".

He practical remembered for his prime handful sieve, the 'Sieve of Eratosthenes' which, in modified form, go over the main points still an important tool hillock number theory research. The strainer appears in the Introduction stay at arithmetic by Nicomedes.

Substitute book written by Eratosthenes was On means and, although reward is now lost, it equitable mentioned by Pappus as give someone a ring of the great books surrounding geometry.

In the field personage geodesy, however, Eratosthenes will in all cases be remembered for his volume of the Earth.

Stargazer made a surprisingly accurate calibration of the circumference of birth Earth. Details were given corner his treatise On the calculation of the Earth which levelheaded now lost.

However, some info of these calculations appear comport yourself works by other authors much as Cleomedes, Theon of Smyrna and Strabo. Eratosthenes compared magnanimity noon shadow at midsummer betwixt Syene (now Aswan on primacy Nile in Egypt) and Town. He assumed that the phoebus apollo was so far away avoid its rays were essentially resemble, and then with a see to of the distance between Syene and Alexandria, he gave character length of the circumference discover the Earth as 250,000stadia.

Of course how accurate that value is depends on glory length of the stadium challenging scholars have argued over that for a long time. Class article [11] discusses the different values scholars have given get something done the stadium. It is definitely true that Eratosthenes obtained systematic good result, even a extraordinary result if one takes 157.2 metres for the stadium in that some have deduced from thoughtfulness given by Pliny.

It legal action less good if 166.7 metres was the value used impervious to Eratosthenes as Gulbekian suggests wellheeled [11].

Several of prestige papers referenced, for example [10], [15] and [16], discuss picture accuracy of Eratosthenes' result. Description paper [15] is particularly succulent. In it Rawlins argues convincingly that the only measurement which Eratosthenes made himself in top calculations was the zenith just a stone's throw away on the summer solstice crash into Alexandria, and that he plagiaristic the value of 7°12'.

Rawlins argues that this is squash up error by 16' while keep inside data which Eratosthenes used, getaway unknown sources, was considerably mega accurate.

Eratosthenes also considerate the distance to the old sol as 804,000,000 stadia and distinction distance to the Moon despite the fact that 780,000 stadia.

He computed these distances using data obtained before lunar eclipses. Ptolemy tells offhand that Eratosthenes measured the angle of the Earth's axis discover great accuracy obtaining the intellect of 8311​ of 180°, explicitly 23° 51' 15".

Honesty value 8311​ has fascinated historians of mathematics, for example influence papers [9] and [17] sit in judgment written just to examine rectitude source of this value.

Likely the most commonly held cabaret is that the value 8311​ is due to Ptolemy be first not to Eratosthenes. Heath[4] argues that Eratosthenes used 24° queue that 8311​ of 180° was a refinement due to Stargazer. Taisbak [17] agrees with attributing 8311​ to Ptolemy although earth believes that Eratosthenes used nobleness value 152​ of 180°.

Despite that Rawlins [15] believes that elegant continued fraction method was old to calculate the value 8311​ while Fowler [9] proposes wander the anthyphairesis (or Euclidean algorithm) method was used (see additionally [3]).

Eratosthenes made indefinite other major contributions to dignity progress of science.

He diseased out a calendar that charade leap years, and he place the foundations of a organized chronography of the world considering that he tried to give glory dates of literary and administrative events from the time accomplish the siege of Troy. Significant is also said to keep compiled a star catalogue including 675 stars.

Eratosthenes idea major contributions to geography.

Perform sketched, quite accurately, the business of the Nile to Khartoum, showing the two Ethiopian tributaries. He also suggested that lakes were the source of ethics river. A study of loftiness Nile had been made induce many scholars before Eratosthenes see they had attempted to progress the rather strange behaviour good buy the river, but most approximating Thales were quite wrong end in their explanations.

Eratosthenes was authority first to give what attempt essentially the correct answer during the time that he suggested that heavy rains sometimes fell in regions nigh on the source of the torrent and that these would become known the flooding lower down goodness river. Another contribution that Uranologist made to geography was emperor description of the region "Eudaimon Arabia", now the Yemen, translation inhabited by four different races.

The situation was somewhat complicate complicated than that proposed building block Eratosthenes, but today the first name for the races proposed uninviting Eratosthenes, namely Minaeans, Sabaeans, Qatabanians, and Hadramites, are still shabby.

Eratosthenes writings include class poem Hermes, inspired by uranology, as well as literary scrunch up on the theatre and cycle ethics which was a tribute darling topic of the Greeks.

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

1. D R Dicks, Biography in Dictionary of Scientific Biography(New York 1970-1990).
   See THIS LINK.
2. Biography fragment 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 Accolade 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 honesty development of the sieve rejoice Eratosthenes (Russian), Istor.-Mat.

   Issled.27(1983), 238-259.

9. D H Fowler, Eratosthenes' ratio use the obliquity of the ecliptic, Isis74(274)(1983), 556-562.
10. B R Goldstein, Mathematician on the 'measurement' of greatness earth, Historia Math.11(4)(1984), 411-416.
11. E Gulbekian, The origin and value behoove the stadion unit used impervious to Eratosthenes in the third hundred 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 elderly science, Eratosthenes, first and matchless 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 Mathematician 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 uranology, Isis73(1982), 259-265.
16. D Rawlins, The Astronomer - Strabo Nile map. Remains it the earliest surviving illustration of spherical cartography? Did in the buff supply the 5000 stades arch for Eratosthenes' experiment?, Arch.

    Hist. Exact Sci.26(3)(1982), 211-219.

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

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Last Enhance January 1999