Eratosthenes of Cyrene

Born: 276 BC in Cyrene, North Africa ( now Shahhat, Libya )

Died: 194 BC in Alexandria, Egypt

Eratosthenes was born in Cyrene which is now in Libya in North Africa. His instructors included the bookman Lysanias of Cyrene and the philosopher Ariston of Chios who had studied under Zeno, the laminitis of the Stoic school of doctrine. Eratosthenes besides studied under the poet and scholar Callimachus who had besides been born in Cyrene. Eratosthenes so spent some old ages analyzing in Athens.

The library at Alexandria was planned by Ptolemy I Soter and the undertaking came to fruition under his boy Ptolemy II Philadelphus. The library was based on transcripts of the plants in the library of Aristotle. Ptolemy II Philadelphus appointed one of Eratosthenes ‘ instructors Callimachus as the 2nd bibliothec. When Ptolemy III Euergetes succeeded his male parent in 245 BC and he persuaded Eratosthenes to travel to Alexandria as the coach of his boy Philopator. On the decease of Callimachus in approximately 240 BC, Eratosthenes became the 3rd librarian at Alexandria, in the library in a temple of the Muses called the Mouseion. The library is said to hold contained 100s of 1000s of papyrus and vellum coils.

Despite being a taking all-around bookman, Eratosthenes was considered to fall short of the highest rank. Heath writes: –

[ Eratosthenes ] was, so, recognised by his coevalss as a adult male of great differentiation in all subdivisions of cognition, though in each topic he merely fell short of the highest topographic point. On the latter land he was called Beta, and another moniker applied to him, Pentathlos, has the same deduction, stand foring as it does an all-around jock who was non the first smuggler or grappler but took the 2nd award in these competitions every bit good as others.

Surely this is a rough moniker to give to a adult male whose achievements in many different countries are remembered today non merely as historically of import but, unusually in many instances, still supplying a footing for modern scientific methods.

One of the of import plants of Eratosthenes was Platonicus which dealt with the mathematics which underlie Plato ‘s doctrine. This work was to a great extent used by Theon of Smyrna when he wrote Expositio rerum mathematicarum and, although Platonicus is now lost, Theon of Smyrna tells us that Eratosthenes ‘ work studied the basic definitions of geometry and arithmetic, every bit good as covering such subjects as music.

One instead surprising beginning of information refering Eratosthenes is from a bad missive. In his commentary on Proposition 1 of Archimedes ‘ Sphere and cylinder Book II, Eutocius reproduces a missive reputed to hold been written by Eratosthenes to Ptolemy III Euergetes. The missive describes the history of the job of the duplicate of the regular hexahedron and, in peculiar, it describes a mechanical device invented by Eratosthenes to happen line sections ten and Ys so that, for given sections a and B,

a: ten = tens: Y = Y: B.

By the celebrated consequence of Hippocrates it was known that work outing the job of happening two average proportionals between a figure and its two-base hit was tantamount to work outing the job of doubling the regular hexahedron. Although the missive is a counterfeit, parts of it are taken from Eratosthenes ‘ ain authorship. The missive, which occupies an of import topographic point in the history of mathematics, is discussed in item in. An original Arabic text of this missive was one time kept in the library of the St Joseph University in Beirut. However it has now vanished and the inside informations given in semen from exposure taken of the missive before its disappearing.

Other inside informations of what Eratosthenes wrote in Platonicus are given by Theon of Smyrna. In peculiar he described there the history of the job of doubling the regular hexahedron ( see Heath ) : –

… when the God proclaimed to the Delians through the prophet that, in order to acquire rid of a pestilence, they should build an alter two-base hit that of the bing one, their craftsmen fell into great perplexity in their attempts to detect how a solid could be made the two-base hit of a similar solid ; they therefore went to inquire Plato about it, and he replied that the prophet meant, non that the God wanted an alter of dual the size, but that he wished, in puting them the undertaking, to dishonor the Greeks for their disregard of mathematics and their disdain of geometry.

Eratosthenes erected a column at Alexandria with an quip inscribed on it associating to his ain mechanical solution to the job of duplicating the regular hexahedron: –

If, good friend, thou mindest to obtain from any little regular hexahedron a regular hexahedron the two-base hit of it, and punctually to alter any solid figure into another, this is in thy power ; thou canst find the step of a crease, a cavity, or the wide basin of a hollow good, by this method, that is, if thou therefore catch between two swayers two agencies with their utmost terminals meeting. Do non thou seek to make the hard concern of Archytas ‘s cylinders, or to cut the cone in the threes of Menaechmus, or to compass such a curving signifier of lines as is described by the devout Eudoxus. Nay 1000 couldst, on these tablets, easy happen a myriad of agencies, get downing from a little base. Happy art 1000, Ptolemy, in that, as a male parent the equal of his boy in vernal six

gour, 1000 hast thyself given him all that is beloved to Muses and Kings, and may be in the hereafter, O Zeus, God of Eden, besides receive the scepter at thy custodies. Therefore may it be, and allow any one who sees this offering say “ This is the gift of Eratosthenes of Cyrene ” .

Eratosthenes besides worked on premier Numberss. He is remembered for his premier figure screen, the ‘Sieve of Eratosthenes ‘ which, in modified signifier, is still an of import tool in figure theory research. The sieve appears in the Introduction to arithmetic by Nicomedes.

Another book written by Eratosthenes was On agencies and, although it is now lost, it is mentioned by Pappus as one of the great books of geometry. In the field of geodesy, nevertheless, Eratosthenes will ever be remembered for his measurings of the Earth.

Eratosthenes made a surprisingly accurate measuring of the perimeter of the Earth. Detailss were given in his treatise On the measuring of the Earth which is now lost. However, some inside informations of these computations appear in plants by other writers such as Cleomedes, Theon of Smyrna and Strabo. Eratosthenes compared the midday shadow at summer solstice between Syene ( now Aswan on the Nile in Egypt ) and Alexandria. He assumed that the Sun was so far off that its beams were basically parallel, and so with a cognition of the distance between Syene and Alexandria, he gave the length of the perimeter of the Earth as 250,000 bowl.

Of class how accurate this value is depends on the length of the bowl and bookmans have argued over this for a long clip. The article discusses the assorted values bookmans have given for the bowl. It is surely true that Eratosthenes obtained a good consequence, even a singular consequence if one takes 157.2 meters for the bowl as some have deduced from values given by Pliny. It is less good if 166.7 meters was the value used by Eratosthenes as Gulbekian suggests in.

Several of the documents referenced, for illustration, and, discourse the truth of Eratosthenes ‘ consequence. The paper is peculiarly interesting. In it Rawlins argues convincingly that the lone measuring which Eratosthenes made himself in his computations was the zenith distance on the summer solstice at Alexandria, and that he obtained the value of 712 ‘ . Rawlins argues that this is in mistake by 16 ‘ while other informations which Eratosthenes used, from unknown beginnings, was well more accurate.

Eratosthenes besides measured the distance to the Sun as 804,000,000 bowl and the distance to the Moon as 780,000 bowl. He computed these distances utilizing informations obtained during lunar occultations. Ptolemy tells us that Eratosthenes measured the joust of the Earth ‘s axis with great truth obtaining the value of 11
/83
of 180, viz. 23 51 ‘ 15 ” .

The value 11
/83
has fascinated historiographers of mathematics, for illustration the documents and are written merely to analyze the beginning of this value. Possibly the most commonly held position is that the value 11
/83
is due to Ptolemy and non to Eratosthenes. Heath argues that Eratosthenes used 24 and that 11
/83
of 180 was a polish due to Ptolemy. Taisbak agrees with imputing 11
/83
to Ptolemy although he believes that Eratosthenes used the value 2
/15
of 180. However Rawlins believes that a continued fraction method was used to cipher the value 11
/83
while Fowler proposes that the anthyphairesis ( or Euclidean algorithm ) method was used ( see besides ) .

Eratosthenes made many other major parts to the advancement of scientific discipline. He worked out a calendar that included leap old ages, and he laid the foundations of a systematic chronography of the universe when he tried to give the day of the months of literary and political events from the clip of the besieging of Troy. He is besides said to hold compiled a star catalogue incorporating 675 stars.

Eratosthenes made major parts to geography. He sketched, rather accurately, the path of the Nile to Khartoum, demoing the two Ethiopian feeders. He besides suggested that lakes were the beginning of the river. A survey of the Nile had been made by many bookmans before Eratosthenes and they had attempted to explicate the instead unusual behavior of the river, but most like Thales were rather incorrect in their accounts. Eratosthenes was the first to give what is basically the correct reply when he suggested that heavy rains sometimes fell in parts near the beginning of the river and that these would explicate the implosion therapy lower down the river. Another part that Eratosthenes made to geography was his description of the part “ Eudaimon Arabia ” , now the Yemen, as inhabited by four different races. The state of affairs was slightly more complicated than that proposed by Eratosthenes, but today the names for the races proposed by Eratosthenes, viz. Minaeans, Sabaeans, Qatabanians, and Hadramites, are still used.

Eratosthenes Hagiographas include the verse form Hermes, inspired by uranology, every bit good as literary plants on the theater and on moralss which was a favorite subject of the Greeks. Eratosthenes is said to hold became blind in old age and it has been claimed that he committed self-destruction by famishment.

J J O’Connor and E F Robertson