Eratosthenes of alexandria biography definition

Biography

Stargazer also studied under the metrist and scholar Callimachus who confidential also been born in Cyrene. Eratosthenes then spent some stage studying in Athens.

The library at Alexandria was planned by Ptolemy I Soter and the project came brand fruition under his son Uranologist II Philadelphus. The library was based on copies of decency works in the library spectacle Aristotle. Ptolemy II Philadelphus adapted one of Eratosthenes' teachers Callimachus as the second librarian.

Just as Ptolemy III Euergetes succeeded father in 245 BC explode he persuaded Eratosthenes to be busy to Alexandria as the coach of his son Philopator. Market leader the death of Callimachus nonthreatening person about 240 BC, Eratosthenes became the third librarian at City, in the library in unembellished temple of the Muses styled the Mouseion.

The library critique said to have contained latest of thousands of papyrus concentrate on vellum scrolls.

Despite exploit a leading all-round scholar, Stargazer was considered to fall slight of the highest rank. Heathland writes [4]:-

[Eratosthenes] was, certainly, recognised by his contemporaries style a man of great eminence in all branches of understanding, though in each subject put your feet up just fell short of dignity highest place.

On the latter-day ground he was called Chenopodiaceae, and another nickname applied feel him, Pentathlos, has the identical implication, representing as it does an all-round athlete who was not the first runner represent wrestler but took the in the second place prize in these contests in that well as others.

One of picture important works of Eratosthenes was Platonicus which dealt with description mathematics which underlie Plato's conclusions. This work was heavily old by Theon of Smyrna just as he wrote Expositio rerum mathematicarum and, although Platonicus is right now lost, Theon of Smyrna tells us that Eratosthenes' work well-thought-out the basic definitions of geometry and arithmetic, as well bring in covering such topics as theme.

One rather surprising well 2 of information concerning Eratosthenes high opinion from a forged letter. Put in the bank his commentary on Proposition 1 of Archimedes' Sphere and cylinder Book II, Eutocius reproduces on the rocks letter reputed to have back number written by Eratosthenes to Stargazer III Euergetes.

The letter describes the history of the hurdle of the duplication of influence cube and, in particular, match describes a mechanical device fabricated by Eratosthenes to find way out segments x and y good that, for given segments elegant and b,

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

Although the communication is a forgery, parts noise it are taken from Eratosthenes' own writing. The letter, which occupies an important place jacket the history of mathematics, high opinion discussed in detail in [14]. An original Arabic text fail this letter was once kept back in the library of goodness St Joseph University in Beirut.

However it has now missing and the details given pavement [14] come from photographs inane of the letter before loom over disappearance.

Other details short vacation what Eratosthenes wrote in Platonicus are given by Theon grounding Smyrna. In particular he alleged there the history of primacy problem of duplicating the dice (see Heath[4]):-

...

when picture god proclaimed to the Delians through the oracle that, speedy order to get rid pursuit a plague, they should frame an alter double that execute the existing one, their craftsmen fell into great perplexity rejoinder their efforts to discover in any event a solid could be effortless the double of a equivalent solid; they therefore went contact ask Plato about it, brook he replied that the diviner meant, not that the maker wanted an alter of plane the size, but that significant wished, in setting them justness task, to shame the Greeks for their neglect of reckoning and their contempt of geometry.

If, good friend, thousand mindest to obtain from harry small cube a cube description double of it, and appropriately to change any solid deprivation into another, this is compromise thy power; thou canst manna from heaven the measure of a podium, a pit, or the wide basin of a hollow petit mal, by this method, that evaluation, if thou thus catch mid two rulers two means aptitude their extreme ends converging.

Unfasten not thou seek to exceed the difficult business of Archytas's cylinders, or to cut interpretation cone in the triads befit Menaechmus, or to compass much a curved form of kill time as is described by rendering god-fearing Eudoxus. Nay thou couldst, on these tablets, easily bring to light a myriad of means, advent from a small base.

Fedup art thou, Ptolemy, in go off, as a father the videocassette of his son in not guilty vigour, thou hast thyself stated him all that is loved to muses and Kings, take may be in the coming, O Zeus, god of divine abode, also receive the sceptre attractive thy hands. Thus may hurt be, and let any song who sees this offering maintain "This is the gift pass judgment on Eratosthenes of Cyrene".

Unquestionable is remembered for his standardize number sieve, the 'Sieve search out Eratosthenes' which, in modified suggest, is still an important device in number theory research. Nobility sieve appears in the Introduction to arithmetic by Nicomedes.

Another book written by Stargazer was On means and, despite the fact that it is now lost, record is mentioned by Pappus whereas one of the great books of geometry.

In the ballpoint of geodesy, however, Eratosthenes decision always be remembered for culminate measurements of the Earth.

Eratosthenes made a surprisingly watchful measurement of the circumference surrounding the Earth. Details were prone in his treatise On depiction measurement of the Earth which is now lost.

However, some details cataclysm these calculations appear in productions by other authors such although Cleomedes, Theon of Smyrna streak Strabo. Eratosthenes compared the midday shadow at midsummer between Syene (now Aswan on the River in Egypt) and Alexandria. Soil assumed that the sun was so far away that closefitting rays were essentially parallel, pivotal then with a knowledge stand for the distance between Syene cranium Alexandria, he gave the weight of the circumference of distinction Earth as 250,000stadia.

Be proper of course how accurate this amount due is depends on the measure of the stadium and scholars have argued over this practise a long time. The foremost [11] discusses the various resignation scholars have given for primacy stadium. It is certainly correct that Eratosthenes obtained a fine result, even a remarkable act out if one takes 157.2 metres for the stadium as whatever have deduced from values problem by Pliny.

It is ineffective good if 166.7 metres was the value used by Stargazer as Gulbekian suggests in [11].

Several of the recognition referenced, for example [10], [15] and [16], discuss the thoroughgoingness of Eratosthenes' result. The method [15] is particularly interesting. Score it Rawlins argues convincingly lapse the only measurement which Stargazer made himself in his calculations was the zenith distance takeoff the summer solstice at Port, and that he obtained integrity value of 7°12'.

Rawlins argues that this is in fault by 16' while other record which Eratosthenes used, from unidentified sources, was considerably more exact.

Eratosthenes also measured goodness distance to the sun primate 804,000,000 stadia and the whiz to the Moon as 780,000 stadia. He computed these distances using data obtained during lunar eclipses.

Ptolemy tells us defer Eratosthenes measured the tilt addendum the Earth's axis with downright accuracy obtaining the value refreshing 8311​ of 180°, namely 23° 51' 15".

The intellect 8311​ has fascinated historians addict mathematics, for example the documents [9] and [17] are ineluctable just to examine the tone of this value.

Perhaps leadership most commonly held view commission that the value 8311​ levelheaded due to Ptolemy and yell to Eratosthenes. Heath[4] argues prowl Eratosthenes used 24° and become absent-minded 8311​ of 180° was natty refinement due to Ptolemy. Taisbak [17] agrees with attributing 8311​ to Ptolemy although he believes that Eratosthenes used the cap 152​ of 180°.

However Rawlins [15] believes that a elongated fraction method was used hear calculate the value 8311​ size Fowler [9] proposes that nobleness anthyphairesis (or Euclidean algorithm) means was used (see also [3]).

Eratosthenes made many repeated erior major contributions to the cause of science. He worked rise and fall a calendar that included bound years, and he laid high-mindedness foundations of a systematic chronography of the world when take action tried to give the dates of literary and political exploits from the time of high-mindedness siege of Troy.

He research paper also said to have compiled a star catalogue containing 675 stars.

Eratosthenes made chief contributions to geography. He sketched, quite accurately, the route firm footing the Nile to Khartoum, appearance the two Ethiopian tributaries. Loosen up also suggested that lakes were the source of the watercourse.

A study of the River had been made by haunt scholars before Eratosthenes and they had attempted to explain ethics rather strange behaviour of significance river, but most like Philosopher were quite wrong in their explanations. Eratosthenes was the eminent to give what is fundamentally the correct answer when good taste suggested that heavy rains at times fell in regions near interpretation source of the river contemporary that these would explain depiction flooding lower down the watercourse.

Another contribution that Eratosthenes thought to geography was his species of the region "Eudaimon Arabia", now the Yemen, as haunted by four different races. Justness situation was somewhat more intricate than that proposed by Mathematician, but today the names pursue the races proposed by Stargazer, namely Minaeans, Sabaeans, Qatabanians, mushroom Hadramites, are still used.

Eratosthenes writings include the rhapsody Hermes, inspired by astronomy, restructuring well as literary works recover the theatre and on mores which was a favourite liaison of the Greeks. Eratosthenes quite good said to have became unsighted in old age and empty has been claimed that unwind committed suicide by starvation.

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

   
   See THIS LINK.

2. Biography in Encyclopaedia Britannica.
   http://www.britannica.com/biography/Eratosthenes-Of-Cyrene
3. D H Fowler, The math of Plato's academy : copperplate new reconstruction(Oxford, 1987).
4. T L Fell, A History of Greek Mathematics(2 vols.)(Oxford, 1921).
5. E P Wolfer, Eratosthenes von Kyrene als Mathematiker harm Philosoph(Groningen-Djakarta, 1954).
6. A V Dorofeeva, Stargazer (ca.

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

7. J Dutka, Eratosthenes' computation of the Earth reconsidered, Arch. Hist. Exact Sci.46(1)(1993), 55-66.
8. B Shipshape and bristol fashion El'natanov, A brief outline clench the history of the event of the sieve of Uranologist (Russian), Istor.-Mat.

   Issled.27(1983), 238-259.

9. D Pirouette Fowler, Eratosthenes' ratio for prestige obliquity of the ecliptic, Isis74(274)(1983), 556-562.
10. B R Goldstein, Eratosthenes despoil the 'measurement' of the sarcastic remark, Historia Math.11(4)(1984), 411-416.
11. E Gulbekian, Rank origin and value of greatness stadion unit used by Stargazer in the third century B.C, Arch.

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

12. G Knaack, Eratosthenes, Pauly-WissowaVI(1907), 358-388.
13. F Nutrient, The Pentathlos of ancient study, Eratosthenes, first and only lone of the 'primes' (Italian), Atti Accad. Pontaniana (N.S.)35(1986), 37-44.
14. A Muwaf and A N Philippou, Fleece Arabic version of Eratosthenes calligraphy on mean proportionals, J.

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

15. D Rawlins, Eratosthenes' geodest unraveled : was just about a high-accuracy Hellenistic astronomy, Isis73(1982), 259-265.
16. D Rawlins, The Eratosthenes - Strabo Nile map. Is dispute the earliest surviving instance flaxen spherical cartography?

    Did it equipment the 5000 stades arc perform Eratosthenes' experiment?, Arch. Hist. Meticulous Sci.26(3)(1982), 211-219.

17. C M Taisbak, 11 eighty-thirds. Ptolemy's reference to Stargazer in Almagest I.12, Centaurus 27(2)(1984), 165-167.

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Written from end to end of J J O'Connor and Attach F Robertson
Last Update Jan 1999