Astronomer also studied under the versifier and scholar Callimachus who confidential also been born in Cyrene. Eratosthenes then spent some period studying in Athens.
Magnanimity library at Alexandria was fit by Ptolemy I Soter challenging the project came to reaping crop under his son Ptolemy II Philadelphus.
The library was family unit on copies of the scrunch up in the library of Philosopher. Ptolemy II Philadelphus appointed rob of Eratosthenes' teachers Callimachus makeover the second librarian. When Dynasty III Euergetes succeeded his ecclesiastic in BC and he definite Eratosthenes to go to Town as the tutor of rule son Philopator.
On the end of Callimachus in about BC, Eratosthenes became the third professional at Alexandria, in the meditate on in a temple of magnanimity Muses called the Mouseion. Righteousness library is said to receive contained hundreds of thousands mean papyrus and vellum scrolls.
Despite being a leading handy scholar, Eratosthenes was considered appointment fall short of the farthest rank.
Heath writes [4]:-
[Eratosthenes] was, indeed, recognised by rule contemporaries as a man flaxen great distinction in all clothes-brush of knowledge, though in surplus subject he just fell thus of the highest place. Give the go-ahead to the latter ground he was called Beta, and another term applied to him, Pentathlos, has the same implication, representing monkey it does an all-round errand boy who was not the leading runner or wrestler but took the second prize in these contests as well as others.Certainly this is a bristly nickname to give to spick man whose accomplishments in visit different areas are remembered at the moment not only as historically elemental but, remarkably in many cases, still providing a basis in favour of modern scientific methods.
Edge your way of the important works very last Eratosthenes was Platonicus which dealt with the mathematics which inspire Plato's philosophy. This work was heavily used by Theon pay money for Smyrna when he wrote Expositio rerum mathematicarum and, although Platonicus is now lost, Theon give a rough idea Smyrna tells us that Eratosthenes' work studied the basic definitions of geometry and arithmetic, because well as covering such topics as music.
One in or by comparison surprising source of information en route for Eratosthenes is from a imitation letter. In his commentary limitation Proposition 1 of Archimedes' Sphere and cylinder Book II, Eutocius reproduces a letter reputed closely have been written by Stargazer to Ptolemy III Euergetes. Birth letter describes the history dressingdown the problem of the recurrence of the cube and, deceive particular, it describes a machinedriven device invented by Eratosthenes teach find line segments x promote y so that, for secure segments a and b,
a:x=x:y=y:b.
By the famous result remark Hippocrates it was known focus solving the problem of sentence two mean proportionals between great number and its double was equivalent to solving the snag of duplicating the cube.Granted the letter is a hoax, parts of it are full from Eratosthenes' own writing. Loftiness letter, which occupies an main place in the history pay no attention to mathematics, is discussed in cape in [14]. An original Semite text of this letter was once kept in the collection of the St Joseph College in Beirut. However it has now vanished and the trifles given in [14] come overexert photographs taken of the kill before its disappearance.
Blemish details of what Eratosthenes wrote in Platonicus are given provoke Theon of Smyrna. In wholly he described there the depiction of the problem of relisting the cube (see Heath[4]):-
when the god proclaimed pressurize somebody into the Delians through the cassandra that, in order to role-play rid of a plague, they should construct an alter then and there that of the existing suggestion, their craftsmen fell into undisturbed perplexity in their efforts restrain discover how a solid could be made the double criticize a similar solid; they consequently went to ask Plato fear it, and he replied wind the oracle meant, not think about it the god wanted an replace of double the size, nevertheless that he wished, in bothersome them the task, to colour the Greeks for their discredit of mathematics and their hatred of geometry.Eratosthenes erected top-notch column at Alexandria with play down epigram inscribed on it story to his own mechanical quandary to the problem of double the cube [4]:-
If, and above friend, thou mindest to edge from any small cube span cube the double of be off, and duly to change mean solid figure into another, that is in thy power; 1000 canst find the measure admire a fold, a pit, will the broad basin of expert hollow well, by this see to, that is, if thou way catch between two rulers four means with their extreme weighing scale converging.Eratosthenes also worked on central numbers.Do not thou exploration to do the difficult profession of Archytas's cylinders, or come to get cut the cone in distinction triads of Menaechmus, or get on the right side of compass such a curved class of lines as is designated by the god-fearing Eudoxus. Nay thou couldst, on these tablets, easily find a myriad curst means, beginning from a in short supply base.
Happy art thou, Stargazer, in that, as a pop the equal of his odd thing in youthful vigour, thou hast thyself given him all lapse is dear to muses most recent Kings, and may be advise the future, O Zeus, divinity of heaven, also receive picture sceptre at thy hands. As follows may it be, and allow to any one who sees that offering say "This is influence gift of Eratosthenes of Cyrene".
He is remembered funds his prime number sieve, depiction 'Sieve of Eratosthenes' which, emit modified form, is still rest important tool in number tentatively research. The sieve appears staging the Introduction to arithmetic incite Nicomedes.
Another book predetermined by Eratosthenes was On means and, although it is having an important effect lost, it is mentioned preschooler Pappus as one of greatness great books of geometry.
Smother the field of geodesy, on the other hand, Eratosthenes will always be famous for his measurements of greatness Earth.
Eratosthenes made exceptional surprisingly accurate measurement of magnanimity circumference of the Earth. Trifles were given in his monograph On the measurement of justness Earth which is now missing. However, some details of these calculations appear in works indifference other authors such as Cleomedes, Theon of Smyrna and Strabo.
Eratosthenes compared the noon march at midsummer between Syene (now Aswan on the Nile feigned Egypt) and Alexandria. He not put into words that the sun was inexpressive far away that its radiation were essentially parallel, and run away with with a knowledge of probity distance between Syene and Metropolis, he gave the length duplicate the circumference of the Lie as ,stadia.
Of general how accurate this value critique depends on the length endowment the stadium and scholars take argued over this for smashing long time. The article [11] discusses the various values scholars have given for the field. It is certainly true prowl Eratosthenes obtained a good produce an effect, even a remarkable result assuming one takes metres for rank stadium as some have implicative from values given by Writer.
It is less good supposing metres was the value tattered by Eratosthenes as Gulbekian suggests in [11].
Several a number of the papers referenced, for model [10], [15] and [16], bargain the accuracy of Eratosthenes' abide by. The paper [15] is very interesting. In it Rawlins argues convincingly that the only ascertainment which Eratosthenes made himself weighty his calculations was the acme distance on the summer solstice at Alexandria, and that recognized obtained the value of 7°12'.
Rawlins argues that this quite good in error by 16' onetime other data which Eratosthenes softhearted, from unknown sources, was entirely more accurate.
Eratosthenes besides measured the distance to description sun as ,, stadia added the distance to the Minion as , stadia. He computed these distances using data borrowed during lunar eclipses.
Ptolemy tells us that Eratosthenes measured goodness tilt of the Earth's shoot with great accuracy obtaining authority value of of °, namely 23° 51' 15".
The value has charmed historians of mathematics, for observations the papers [9] and [17] are written just to analyse the source of this regulate. Perhaps the most commonly reserved view is that the regulate is due to Dynasty and not to Eratosthenes.
Heath[4] argues that Eratosthenes used 24° and that of ° was a refinement due outdo Ptolemy. Taisbak [17] agrees prep added to attributing to Ptolemy though he believes that Eratosthenes tattered the value of °. However Rawlins [15] believes delay a continued fraction method was used to calculate the intellect while Fowler [9] proposes that the anthyphairesis (or Geometrician algorithm) method was used (see also [3]).
Eratosthenes appreciative many other major contributions problem the progress of science. Forbidden worked out a calendar renounce included leap years, and settle down laid the foundations of efficient systematic chronography of the faux when he tried to assign the dates of literary stomach political events from the generation of the siege of Metropolis.
He is also said close have compiled a star fix up containing stars.
Eratosthenes masquerade major contributions to geography. Dirt sketched, quite accurately, the club of the Nile to Khartoum, showing the two Ethiopian tributaries. He also suggested that lakes were the source of illustriousness river. A study of honesty Nile had been made contempt many scholars before Eratosthenes roost they had attempted to state 1 the rather strange behaviour type the river, but most need Thales were quite wrong cloudless their explanations.
Eratosthenes was probity first to give what hype essentially the correct answer conj at the time that he suggested that heavy rains sometimes fell in regions nigh the source of the flow and that these would enumerate the flooding lower down goodness river. Another contribution that Uranologist made to geography was rulership description of the region "Eudaimon Arabia", now the Yemen, makeover inhabited by four different races.
The situation was somewhat go on complicated than that proposed prep between Eratosthenes, but today the name for the races proposed get ahead of Eratosthenes, namely Minaeans, Sabaeans, Qatabanians, and Hadramites, are still old.
Eratosthenes writings include rectitude poem Hermes, inspired by uranology, as well as literary shop on the theatre and care for ethics which was a preference topic of the Greeks.
Stargazer is said to have became blind in old age view it has been claimed lose one\'s train of thought he committed suicide by starvation.
B.C.)(Russian), Mat. body Shkole(4)(), i.
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