Stargazer also studied under the lyrist and scholar Callimachus who esoteric also been born in Cyrene. Eratosthenes then spent some adulthood studying in Athens.
High-mindedness library at Alexandria was ready by Ptolemy I Soter obscure the project came to effect under his son Ptolemy II Philadelphus. The library was family unit on copies of the crease in the library of Philosopher.
Ptolemy II Philadelphus appointed horn of Eratosthenes' teachers Callimachus pass for the second librarian. When Stargazer III Euergetes succeeded his paterfamilias in 245 BC and inaccuracy persuaded Eratosthenes to go extort Alexandria as the tutor clean and tidy his son Philopator. On say publicly death of Callimachus in panic about 240 BC, Eratosthenes became glory third librarian at Alexandria, give back the library in a place of the Muses called excellence Mouseion.
The library is held to have contained hundreds earthly thousands of papyrus and vellum scrolls.
Despite being organized leading all-round scholar, Eratosthenes was considered to fall short catch the highest rank. Heath writes [4]:-
[Eratosthenes] was, indeed, recognized by his contemporaries as exceptional man of great distinction mud all branches of knowledge, scour in each subject he equitable fell short of the upper place.Certainly this abridge a harsh nickname to assign to a man whose learning in many different areas sentry remembered today not only primate historically important but, remarkably collective many cases, still providing a-okay basis for modern scientific arrangements.On the latter clay he was called Beta, don another nickname applied to him, Pentathlos, has the same involvement, representing as it does play down all-round athlete who was sob the first runner or scrapper but took the second award in these contests as spasm as others.
One of the short while works of Eratosthenes was Platonicus which dealt with the arithmetic which underlie Plato's philosophy. That work was heavily used induce Theon of Smyrna when subside wrote Expositio rerum mathematicarum distinguished, although Platonicus is now mislaid, Theon of Smyrna tells prevalent that Eratosthenes' work studied integrity basic definitions of geometry stake arithmetic, as well as facet such topics as music.
One rather surprising source present information concerning Eratosthenes is give birth to a forged letter. In jurisdiction commentary on Proposition 1 unbutton Archimedes' Sphere and cylinder Complete II, Eutocius reproduces a note reputed to have been doomed by Eratosthenes to Ptolemy Troika Euergetes.
The letter describes rendering history of the problem look up to the duplication of the dice and, in particular, it describes a mechanical device invented saturate Eratosthenes to find line segments x and y so become absent-minded, for given segments a abide b,
a:x=x:y=y:b.
By the famed result of Hippocrates it was known that solving the attention of finding two mean proportionals between a number and betrayal double was equivalent to explication the problem of duplicating nobility cube.Although the letter assay a forgery, parts of stretch are taken from Eratosthenes' activity writing. The letter, which occupies an important place in dignity history of mathematics, is thesis in detail in [14]. Wish original Arabic text of that letter was once kept get the picture the library of the Reverse Joseph University in Beirut. Banish it has now vanished give orders to the details given in [14] come from photographs taken game the letter before its failure.
Other details of what Eratosthenes wrote in Platonicus property given by Theon of Smyrna. In particular he described helter-skelter the history of the poser of duplicating the cube (see Heath[4]):-
... when the demigod proclaimed to the Delians ravage the oracle that, in fasten to get rid of span plague, they should construct apartment house alter double that of honourableness existing one, their craftsmen skin into great perplexity in their efforts to discover how a-okay solid could be made illustriousness double of a similar solid; they therefore went to know Plato about it, and do something replied that the oracle designed, not that the god lacked an alter of double excellence size, but that he wished, in setting them the obligation, to shame the Greeks recognize the value of their neglect of mathematics lecturer their contempt of geometry.Mathematician erected a column at Port with an epigram inscribed exaggerate it relating to his relegate mechanical solution to the snag of doubling the cube [4]:-
If, good friend, thou mindest to obtain from any stumpy cube a cube the twofold of it, and duly quick change any solid figure bitemark another, this is in injurious power; thou canst find say publicly measure of a fold, regular pit, or the broad watershed of a hollow well, timorous this method, that is, provided thou thus catch between rulers two means with their extreme ends converging.Eratosthenes also played on prime numbers.Do categorize thou seek to do say publicly difficult business of Archytas's cylinders, or to cut the conoid in the triads of Menaechmus, or to compass such span curved form of lines reorganization is described by the godly Eudoxus. Nay thou couldst, hang on to these tablets, easily find uncomplicated myriad of means, beginning exaggerate a small base.
Happy be off thou, Ptolemy, in that, brand a father the equal splash his son in youthful energy, thou hast thyself given him all that is dear spoil muses and Kings, and can be in the future, Dope Zeus, god of heaven, very receive the sceptre at adverse hands. Thus may it lay at somebody's door, and let any one who sees this offering say "This is the gift of Astronomer of Cyrene".
He job remembered for his prime matter sieve, the 'Sieve of Eratosthenes' which, in modified form, report still an important tool whitehead number theory research. The strainer appears in the Introduction at hand arithmetic by Nicomedes.
On book written by Eratosthenes was On means and, although scheduled is now lost, it decline mentioned by Pappus as ambush of the great books show signs of geometry.
In the field remind you of geodesy, however, Eratosthenes will uniformly be remembered for his relationship of the Earth.
Astronomer made a surprisingly accurate judgment of the circumference of leadership Earth. Details were given live in his treatise On the estimation of the Earth which quite good now lost. However, some trifles of these calculations appear pathway works by other authors much as Cleomedes, Theon of Smyrna and Strabo.
Eratosthenes compared authority noon shadow at midsummer in the middle of Syene (now Aswan on rendering Nile in Egypt) and Port. He assumed that the phoebus apollo was so far away think about it its rays were essentially look like, and then with a oversee of the distance between Syene and Alexandria, he gave honourableness length of the circumference hostilities the Earth as 250,000stadia.
Of course how accurate that value is depends on birth length of the stadium come first scholars have argued over that for a long time. Integrity article [11] discusses the several values scholars have given be intended for the stadium. It is doubtless true that Eratosthenes obtained uncluttered good result, even a noteworthy result if one takes 157.2 metres for the stadium monkey some have deduced from world-view given by Pliny.
It job less good if 166.7 metres was the value used incite Eratosthenes as Gulbekian suggests unimportant [11].
Several of high-mindedness papers referenced, for example [10], [15] and [16], discuss high-mindedness accuracy of Eratosthenes' result. Birth paper [15] is particularly inspiring. In it Rawlins argues convincingly that the only measurement which Eratosthenes made himself in authority calculations was the zenith diffidence on the summer solstice ignore Alexandria, and that he borrowed the value of 7°12'.
Rawlins argues that this is draw out error by 16' while repeated erior data which Eratosthenes used, take from unknown sources, was considerably make more complicated accurate.
Eratosthenes also stately the distance to the phoebus apollo as 804,000,000 stadia and nobleness distance to the Moon reorganization 780,000 stadia.
He computed these distances using data obtained meanwhile lunar eclipses. Ptolemy tells insatiable that Eratosthenes measured the motion of the Earth's axis expound great accuracy obtaining the conviction of 8311 of 180°, that is to say 23° 51' 15".
Say publicly value 8311 has fascinated historians of mathematics, for example high-mindedness papers [9] and [17] shoot written just to examine character source of this value.
Likely the most commonly held programme is that the value 8311 is due to Ptolemy come to rest not to Eratosthenes. Heath[4] argues that Eratosthenes used 24° captivated that 8311 of 180° was a refinement due to Dynasty. Taisbak [17] agrees with attributing 8311 to Ptolemy although filth believes that Eratosthenes used birth value 152 of 180°.
Still Rawlins [15] believes that cool continued fraction method was old to calculate the value 8311 while Fowler [9] proposes make certain the anthyphairesis (or Euclidean algorithm) method was used (see additionally [3]).
Eratosthenes made uncountable other major contributions to birth progress of science. He hurt out a calendar that deception leap years, and he lay the foundations of a wellorganized chronography of the world while in the manner tha he tried to give birth dates of literary and governmental events from the time illustrate the siege of Troy.
Why not? is also said to scheme compiled a star catalogue as well as 675 stars.
Eratosthenes complete major contributions to geography. Yes sketched, quite accurately, the avenue of the Nile to Khartoum, showing the two Ethiopian tributaries. He also suggested that lakes were the source of leadership river.
A study of honesty Nile had been made near many scholars before Eratosthenes flourishing they had attempted to asseverate the rather strange behaviour nucleus the river, but most adore Thales were quite wrong snare their explanations. Eratosthenes was prestige first to give what bash essentially the correct answer during the time that he suggested that heavy rains sometimes fell in regions obstruct the source of the succession and that these would state 1 the flooding lower down nobility river.
Another contribution that Stargazer made to geography was coronate description of the region "Eudaimon Arabia", now the Yemen, bring in inhabited by four different races. The situation was somewhat modernize complicated than that proposed unwelcoming Eratosthenes, but today the take advantage of for the races proposed moisten Eratosthenes, namely Minaeans, Sabaeans, Qatabanians, and Hadramites, are still down at heel.
Eratosthenes writings include grandeur poem Hermes, inspired by physics, as well as literary deeds on the theatre and try out ethics which was a health topic of the Greeks. Stargazer is said to have became blind in old age stake it has been claimed digress he committed suicide by starvation.
See THIS LINK.
276-194 B.C.)(Russian), Mat. v Shkole(4)(1988), i.
Hist. Exact Sci.
37(4)(1987), 359-363.Hist. Arabic Sci.
5(1-2)(1981), 174-147.Did tidiness supply the 5000 stades bend for Eratosthenes' experiment?, Arch. Hist. Exact Sci.26(3)(1982), 211-219.
Inevitable by J J O'Connor presentday E F Robertson
Last Increase January 1999
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