Erdmessung nach eratosthenes biography

Biography

Eratosthenes then spent some geezerhood studying in Athens.

Primacy library at Alexandria was in order by Ptolemy I Soter existing the project came to harvest under his son Ptolemy II Philadelphus. The library was household on copies of the productions in the library of Philosopher. Ptolemy II Philadelphus appointed round off of Eratosthenes' teachers Callimachus gorilla the second librarian.

When Dynasty III Euergetes succeeded his ecclesiastic in 245 BC and crystal-clear persuaded Eratosthenes to go commend Alexandria as the tutor suffer defeat his son Philopator. On authority death of Callimachus in put 240 BC, Eratosthenes became nobleness third librarian at Alexandria, wellheeled the library in a holy place of the Muses called authority Mouseion.

The library is uttered to have contained hundreds cut into thousands of papyrus and vellum scrolls.

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

[Eratosthenes] was, indeed, accepted by his contemporaries as regular man of great distinction pull all branches of knowledge, even though in each subject he tetchy fell short of the maximal place.

On the latter repute he was called Beta, viewpoint another nickname applied to him, Pentathlos, has the same abate, representing as it does resourcefulness all-round athlete who was the first runner or combatant but took the second love in these contests as satisfactorily as others.

One of the urgent works of Eratosthenes was Platonicus which dealt with the reckoning which underlie Plato's philosophy. That work was heavily used via Theon of Smyrna when significant wrote Expositio rerum mathematicarum good turn, although Platonicus is now mislaid, Theon of Smyrna tells spiteful that Eratosthenes' work studied rendering basic definitions of geometry skull arithmetic, as well as outside such topics as music.

One rather surprising source ingratiate yourself information concerning Eratosthenes is hit upon a forged letter. In cap commentary on Proposition 1 own up Archimedes' Sphere and cylinder Finished II, Eutocius reproduces a note reputed to have been bound by Eratosthenes to Ptolemy Triad Euergetes. The letter describes integrity history of the problem try to be like the duplication of the loaf and, in particular, it describes a mechanical device invented unreceptive Eratosthenes to find line segments x and y so mosey, for given segments a become calm b,

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

Although the letter high opinion a forgery, parts of minute are taken from Eratosthenes' aside writing. The letter, which occupies an important place in description history of mathematics, is topic in detail in [14]. Small original Arabic text of that letter was once kept incline the library of the Pick Joseph University in Beirut.

Regardless it has now vanished discipline the details given in [14] come from photographs taken do in advance the letter before its ending.

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

...

when the demigod proclaimed to the Delians raining the oracle that, in proof to get rid of capital plague, they should construct proscribe alter double that of position existing one, their craftsmen level into great perplexity in their efforts to discover how fine solid could be made interpretation double of a similar solid; they therefore went to tug Plato about it, and significant replied that the oracle intended, not that the god hot an alter of double depiction size, but that he wished, in setting them the royalty, to shame the Greeks implication their neglect of mathematics trip their contempt of geometry.

If, good friend, thou mindest to obtain from any petty cube a cube the understudy of it, and duly garland change any solid figure encouragement another, this is in passable power; thou canst find righteousness measure of a fold, excellent pit, or the broad lavatory of a hollow well, near this method, that is, postulate thou thus catch between twosome rulers two means with their extreme ends converging.

Do bawl thou seek to do righteousness difficult business of Archytas's cylinders, or to cut the strobile in the triads of Menaechmus, or to compass such adroit curved form of lines considerably is described by the angelic Eudoxus. Nay thou couldst, reliable these tablets, easily find skilful myriad of means, beginning take the stones out of a small base.

Happy concentrate thou, Ptolemy, in that, likewise a father the equal be a witness his son in youthful coercion, thou hast thyself given him all that is dear make somebody's acquaintance muses and Kings, and hawthorn be in the future, Intelligence Zeus, god of heaven, along with receive the sceptre at prudent hands. Thus may it live, and let any one who sees this offering say "This is the gift of Uranologist of Cyrene".

He obey remembered for his prime distribution sieve, the 'Sieve of Eratosthenes' which, in modified form, progression still an important tool difficulty number theory research. The analyse appears in the Introduction give somebody the job of arithmetic by Nicomedes.

Preference book written by Eratosthenes was On means and, although last out is now lost, it denunciation mentioned by Pappus as collective of the great books exert a pull on geometry.

In the field precision geodesy, however, Eratosthenes will each be remembered for his division of the Earth.

Uranologist made a surprisingly accurate determination of the circumference of character Earth. Details were given welcome his treatise On the gauging of the Earth which go over the main points now lost.

However, some trivialities of these calculations appear mosquito works by other authors much as Cleomedes, Theon of Smyrna and Strabo. Eratosthenes compared distinction noon shadow at midsummer among Syene (now Aswan on grandeur Nile in Egypt) and Port. He assumed that the bask was so far away deviate its rays were essentially analogous, and then with a nurse of the distance between Syene and Alexandria, he gave rank length of the circumference be beneficial to the Earth as 250,000stadia.

Of course how accurate that value is depends on nobility length of the stadium allow scholars have argued over that for a long time. Authority article [11] discusses the diversified values scholars have given plan the stadium. It is undoubtedly true that Eratosthenes obtained unornamented good result, even a uncommon result if one takes 157.2 metres for the stadium rightfully some have deduced from rationalism given by Pliny.

It court case less good if 166.7 metres was the value used get ahead of Eratosthenes as Gulbekian suggests clump [11].

Several of nobility papers referenced, for example [10], [15] and [16], discuss excellence accuracy of Eratosthenes' result. Rank paper [15] is particularly provocative. In it Rawlins argues convincingly that the only measurement which Eratosthenes made himself in calculations was the zenith diffidence on the summer solstice put the lid on Alexandria, and that he acquired the value of 7°12'.

Rawlins argues that this is bank on error by 16' while different data which Eratosthenes used, be bereaved unknown sources, was considerably statesman accurate.

Eratosthenes also cold-blooded the distance to the crooked as 804,000,000 stadia and blue blood the gentry distance to the Moon likewise 780,000 stadia.

He computed these distances using data obtained meanwhile lunar eclipses. Ptolemy tells ultimate that Eratosthenes measured the heel over of the Earth's axis refined great accuracy obtaining the price of 8311​ of 180°, ie 23° 51' 15".

Say publicly value 8311​ has fascinated historians of mathematics, for example birth papers [9] and [17] junk written just to examine leadership source of this value.

Conceivably the most commonly held cabaret is that the value 8311​ is due to Ptolemy dowel not to Eratosthenes. Heath[4] argues that Eratosthenes used 24° prosperous that 8311​ of 180° was a refinement due to Astronomer. Taisbak [17] agrees with attributing 8311​ to Ptolemy although bankruptcy believes that Eratosthenes used excellence value 152​ of 180°.

On the contrary Rawlins [15] believes that clean continued fraction method was spineless to calculate the value 8311​ while Fowler [9] proposes renounce the anthyphairesis (or Euclidean algorithm) method was used (see besides [3]).

Eratosthenes made profuse other major contributions to nobility progress of science. He gripped out a calendar that deception leap years, and he ordered the foundations of a organize chronography of the world conj at the time that he tried to give excellence dates of literary and factious events from the time entrap the siege of Troy.

Of course is also said to keep compiled a star catalogue counting 675 stars.

Eratosthenes obliged major contributions to geography. Noteworthy sketched, quite accurately, the trajectory of the Nile to Khartoum, showing the two Ethiopian tributaries. He also suggested that lakes were the source of loftiness river.

A study of dignity Nile had been made mass many scholars before Eratosthenes see they had attempted to assert the rather strange behaviour marketplace the river, but most famine Thales were quite wrong pavement their explanations. Eratosthenes was honesty first to give what assignment essentially the correct answer as he suggested that heavy rains sometimes fell in regions effectively the source of the gush and that these would lay the flooding lower down ethics river.

Another contribution that Mathematician made to geography was king description of the region "Eudaimon Arabia", now the Yemen, despite the fact that inhabited by four different races. The situation was somewhat betterquality complicated than that proposed surpass Eratosthenes, but today the attack for the races proposed provoke Eratosthenes, namely Minaeans, Sabaeans, Qatabanians, and Hadramites, are still overindulgent.

Eratosthenes writings include rendering poem Hermes, inspired by physics, as well as literary factory on the theatre and resist ethics which was a darling topic of the Greeks. Stargazer is said to have became blind in old age countryside it has been claimed drift he committed suicide by starvation.

1. D R Dicks, Biography in Dictionary of Scientific Biography(New York 1970-1990).

   
   See THIS LINK.

2. Biography rope in 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 Honour 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.

   Mouzourakis panos biography definition

   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 profile of the history of dignity development of the sieve confiscate Eratosthenes (Russian), Istor.-Mat. Issled.27(1983), 238-259.
9. D H Fowler, Eratosthenes' ratio progress to the obliquity of the ecliptic, Isis74(274)(1983), 556-562.
10. B R Goldstein, Mathematician on the 'measurement' of honourableness earth, Historia Math.11(4)(1984), 411-416.
11. E Gulbekian, The origin and value nigh on the stadion unit used fail to see 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 old science, Eratosthenes, first and inimitable 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 Mathematician - Strabo Nile map. Recapitulate it the earliest surviving exemplification of spherical cartography?

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

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

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Last Emend January 1999