Nicomedes was an ancient Greek mathematician. Nothing is known about Nicomedes' life apart from references in his works. Studies have stated that Nicomedes was born in about 280 BC and died in about 210 BC, it is known that he lived around the time of Eratosthenes or after, because he criticized Eratosthenes' method of doubling the cube. It is known that Apollonius of Perga called a curve of his creation a "sister of the conchoid", suggesting that he was naming it after Nicomedes' famous curve, it is believed that Nicomedes lived after Eratosthenes and before Apollonius of Perga. Like many geometers of the time, Nicomedes was engaged in trying to solve the problems of doubling the cube and trisecting the angle, both problems we now understand to be impossible using the tools of classical geometry. In the course of his investigations, Nicomedes created the conchoid of Nicomedes. Nicomedes discovered three distinct types of conchoids, now unknown. Pappus wrote: "Nicomedes trisected any rectilinear angle by means of the conchoidal curves, the construction and properties of which he handed down, being himself the discoverer of their peculiar character".
Nicomedes used the Hippias' quadratrix to square the circle, since according to Pappus, "For the squaring of the circle there was used by Dinostratus and certain other persons a certain curve which took its name from this property, for it is called by them square-forming". Eutocius mentions that Nicomedes "prided himself inordinately on his discovery of this curve, contrasting it with Eratosthenes's mechanism for finding any number of mean proportionals, to which he objected formally and at length on the ground that it was impracticable and outside the spirit of geometry". T. L. Heath, A History of Greek Mathematics. G. J. Toomer, Biography in Dictionary of Scientific Biography. O'Connor, John J..
Isidore of Miletus
Isidore of Miletus was one of the two main Byzantine Greek architects that Emperor Justinian I commissioned to design the cathedral Hagia Sophia in Constantinople from 532 to 537. The creation of an important compilation of Archimedes' works has been attributed to him; the spurious Book XV from Euclid's Elements has been attributed to Isidore of Miletus. Isidore of Miletus was a renowned mathematician before Emperor Justinian I hired him. Isidorus taught stereometry and physics at the universities, first of Alexandria of Constantinople, wrote a commentary on an older treatise on vaulting. Eutocius together with Isidore studied Archimedes work. Isidore is renowned for producing the first comprehensive compilation of Archimedes' work, the Archimedes palimpsest survived to the present. Emperor Justinian I appointed his architects to rebuild the Hagia Sophia following his victory over protesters within the capital city of his Roman Empire, Constantinople; the first basilica was completed in 360 and remodelled from 404 to 415, but had been damaged in 532 in the course of the Nika Riot, “The temple of Sophia, the baths of Zeuxippus, the imperial courtyard from the Propylaia all the way to the so-called House of Ares were burned up and destroyed, as were both of the great porticoes that lead to the forum, named after Constantine, houses of prosperous people, a great deal of other properties.”The warring factions of Byzantine society, the Blues and the Greens, opposed each other in the chariot races at the Hippodrome and resorted to violence.
During the Nika Riot, more than thirty thousand people died. Emperor Justinian I ensured that his new structure would not be burned down, like its predecessors, by commissioning architects that would build the church out of stone, rather than wood, “He compacted it of baked brick and mortar, in many places bound it together with iron, but made no use of wood, so that the church should no longer prove combustible.”Isidore of Miletus and Anthemius of Tralles planned on a main hall of the Hagia Sophia that measured 70 by 75 metres, making it the largest church in Constantinople, but the original dome was nearly 6 metres lower than it was constructed, “Justinian suppressed these riots and took the opportunity of marking his victory by erecting in 532-7 the new Hagia Sophia, one of the largest, most lavish, most expensive buildings of all time.”Although Isidore of Miletus and Anthemius of Tralles were not formally educated in architecture, they were scientists that could organize the logistics of drawing thousands of labourers and unprecedented loads of rare raw materials from around the Roman Empire to create the Hagia Sophia for Emperor Justinian I.
The finished product was built in admirable form for the Roman Emperor, “All of these elements marvellously fitted together in mid-air, suspended from one another and reposing only on the parts adjacent to them, produce a unified and most remarkable harmony in the work, yet do not allow the spectators to rest their gaze upon any one of them for a length of time.”The Hagia Sophia architects innovatively combined the longitudinal structure of a Roman basilica and the central plan of a drum-supported dome, in order to withstand the high magnitude earthquakes of the Marmara Region, “However, in May 558, little more than 20 years after the Church’s dedication, following the earthquakes of August 553 and December 557, parts of the central dome and its supporting structure system collapsed.” The Hagia Sophia was cracked by earthquakes and was repaired. Isidore of Miletus’ nephew, Isidore the Younger, introduced the new dome design that can be viewed in the Hagia Sophia in present-day Istanbul, Turkey.
After a great earthquake in 989 ruined the dome of Hagia Sophia, the Byzantine officials summoned Trdat the Architect to Byzantium to organize repairs. The restored dome was completed by 994. Cakmak, AS. "The Structural Configuration of the First Dome of Justinian's Hagia Sophia: An Investigation Based on Structural and Literary Analysis". Soil Dynamics and Earthquake Engineering. 29. Krautheimer, Richard. Early Christian and Byzantine Architecture. Baltimore: Penguin Books. ISBN 978-0-300-05294-7. Mango, Cyril A.. The Art of the Byzantine Empire, 312-1453: Sources and Documents. Englewood Cliffs, New Jersey: Prentice-Hall. ISBN 0-8020-6627-5. Maranci, Christina. "The Architect Trdat: Building Practices and Cross-Cultural Exchange in Byzantium and Armenia". The Journal of the Society of Architectural Historians. 62: 294–305. Doi:10.2307/3592516. Prokopios. Anthony Kaldellis, ed; the Secret History: With Related Texts. Indianapolis: Hackett Publishing. ISBN 978-1-60384-180-1. Watkin, David. A History of Western Architecture.
New York: Thames and Hudson. ISBN 978-1-85669-459-9
Ashkelon or Ashqelon known as Ascalon, is a coastal city in the Southern District of Israel on the Mediterranean coast, 50 kilometres south of Tel Aviv, 13 kilometres north of the border with the Gaza Strip. The ancient seaport of Ashkelon dates back to the Neolithic Age. In the course of its history, it has been ruled by the Ancient Egyptians, the Canaanites, the Philistines, the Assyrians, the Babylonians, the Greeks, the Phoenicians, the Hasmoneans, the Romans, the Persians, the Arabs and the Crusaders, until it was destroyed by the Mamluks in 1270; the Arab village of al-Majdal or al-Majdal Asqalan was established a few kilometres inland from the ancient site by the late 15th century, under Ottoman rule. In 1918, it became part of the British Occupied Enemy Territory Administration and in 1920 became part of Mandatory Palestine. Al-Majdal on the eve of the 1948 Arab–Israeli War had 10,000 Arab inhabitants and in October 1948, the city accommodated thousands more refugees from nearby villages.
Al-Majdal was the forward position of the Egyptian Expeditionary Force based in Gaza. The village was conquered by Israeli forces on 5 November 1948, by which time most of the Arab population had fled, leaving some 2,700 inhabitants, of which 500 were deported by Israeli soldiers in December 1948; the town was named Migdal Gaza, Migdal Gad and Migdal Ashkelon by the new Jewish inhabitants. Most of the remaining Arabs were deported by 1950. In 1953, the nearby neighborhood of Afridar was incorporated and the name "Ashkelon" was readopted to the town. By 1961, Ashkelon was ranked 18th among Israeli urban centers with a population of 24,000. In 2017 the population of Ashkelon was 137,945; the name Ashkelon is western Semitic, might be connected to the triliteral root š-q-l attesting to its importance as a center for mercantile activities. Its name appeared in Phoenician and Punic as ŠQLN and ʾŠQLN. Scallion and shallot are derived from the Latin name for Ashkelon. Ashkelon was the oldest and largest seaport in Canaan, part of the pentapolis of the Philistines, north of Gaza and south of Jaffa.
The Neolithic site of Ashkelon is located on 1.5 km north of Tel Ashkelon. It is dated by Radiocarbon dating to c. 7900 bp, to the poorly known Pre-Pottery Neolithic C phase of the Neolithic. It was excavated in 1954 by French archaeologist Jean Perrot. In 1997–1998, a large scale salvage project was conducted at the site by Yosef Garfinkel on behalf of the Hebrew University of Jerusalem and nearly 1,000 square metres were examined. A final excavation report was published in 2008. In the site over a hundred fireplaces and hearths were found and numerous pits, but no solid architecture, except for one wall. Various phases of occupation were found, one atop the other, with sterile layers of sea sand between them; this indicates. The main finds were c. 20,000 flint artifacts. At Neolithic sites flints far outnumber animal bones; the bones belong to non-domesticated animals. When all aspects of this site are taken into account, it appears to have been used by pastoral nomads for meat processing; the nearby sea could supply salt necessary for the conservation of meat.
The city was built on a sandstone outcropping and has a good underground water supply. It was large as an ancient city with as many as 15,000 people living inside the walls. Ashkelon was a thriving Middle Bronze Age city of more than 150 acres, its commanding ramparts, measuring 1.5 miles long, 50 feet high and 150 feet thick, as a ruin they stand two stories high. The thickness of the walls was so great that the mudbrick city gate had a stone-lined, 8 feet wide tunnel-like barrel vault, coated with white plaster, to support the superstructure: it is the oldest such vault found. Roman and Islamic fortifications, faced with stone, followed the same footprint, a vast semicircle protecting Ashkelon on the land side. On the sea it was defended by a high natural bluff. A roadway more than 20 feet in width ascended the rampart from the harbor and entered a gate at the top. In 1991 the ruins of a small ceramic tabernacle was found a finely cast bronze statuette of a bull calf silvered, 4 inches long.
Images of calves and bulls were associated with the worship of the Canaanite gods Baal. Ashkelon is mentioned in the Egyptian Execration Texts of the 11th dynasty as "Asqanu." In the Amarna letters, there are seven letters to and from Ashkelon's king Yidya, the Egyptian pharaoh. One letter from the pharaoh to Yidya was discovered in the early 1900s; the Philistines conquered Canaanite Ashkelon about 1150 BC. Their earliest pottery, types of structures and inscriptions are similar to the early Greek urbanised centre at Mycenae in mainland Greece, adding weight to the hypothesis that the Philistines were one of the populations among the "Sea Peoples" that upset cultures throughout the eastern Mediterranean at that time. Ashkelon became one of the five Philistine cities that were warring with the Israelites and the Kingdom of Judah. According to Herodotus, its temple of Venus was the oldest of its kind, imitated in Cyprus, he mentions that this temple was pillaged by marauding Scythians during the time of their sway over the Medes.
Democritus was an Ancient Greek pre-Socratic philosopher remembered today for his formulation of an atomic theory of the universe. Democritus was born in Abdera, around 460 BC, although there are disagreements about the exact year, his exact contributions are difficult to disentangle from those of his mentor Leucippus, as they are mentioned together in texts. Their speculation on atoms, taken from Leucippus, bears a passing and partial resemblance to the 19th-century understanding of atomic structure that has led some to regard Democritus as more of a scientist than other Greek philosophers. Ignored in ancient Athens, Democritus is said to have been disliked so much by Plato that the latter wished all of his books burned, he was well known to his fellow northern-born philosopher Aristotle. Many consider Democritus to be the "father of modern science". None of his writings have survived. Democritus was said to be born in the city of Abdera in Thrace, an Ionian colony of Teos, although some called him a Milesian.
He was born in the 80th Olympiad according to Apollodorus of Athens, although Thrasyllus placed his birth in 470 BC, the date is more likely. John Burnet has argued that the date of 460 is "too early" since, according to Diogenes Laërtius ix.41, Democritus said that he was a "young man" during Anaxagoras's old age. It was said that Democritus's father was from a noble family and so wealthy that he received Xerxes on his march through Abdera. Democritus spent the inheritance which his father left him on travels into distant countries, to satisfy his thirst for knowledge, he traveled to Asia, was said to have reached India and Ethiopia. It is known that he wrote on Meroe, he himself declared that among his contemporaries none had made greater journeys, seen more countries, met more scholars than himself. He mentions the Egyptian mathematicians, whose knowledge he praises. Theophrastus, spoke of him as a man who had seen many countries. During his travels, according to Diogenes Laërtius, he became acquainted with the Chaldean magi.
"Ostanes", one of the magi accompanying Xerxes, was said to have taught him. After returning to his native land he occupied himself with natural philosophy, he traveled throughout Greece to acquire a better knowledge of its cultures. He mentions many Greek philosophers in his writings, his wealth enabled him to purchase their writings. Leucippus, the founder of atomism, was the greatest influence upon him, he praises Anaxagoras. Diogenes Laertius says, he may have been acquainted with Socrates, but Plato does not mention him and Democritus himself is quoted as saying, "I came to Athens and no one knew me." Aristotle placed him among the pre-Socratic natural philosophers. The many anecdotes about Democritus in Diogenes Laërtius, attest to his disinterest and simplicity, show that he lived for his studies. One story has him deliberately blinding himself, he was cheerful, was always ready to see the comical side of life, which writers took to mean that he always laughed at the foolishness of people.
He was esteemed by his fellow citizens, because as Diogenes Laërtius says, "he had foretold them some things which events proved to be true," which may refer to his knowledge of natural phenomena. According to Diodorus Siculus, Democritus died at the age of 90, which would put his death around 370 BC, but other writers have him living to 104, or 109. Popularly known as the Laughing Philosopher, the terms Abderitan laughter, which means scoffing, incessant laughter, Abderite, which means a scoffer, are derived from Democritus. To his fellow citizens he was known as "The Mocker". Most sources say that Democritus followed in the tradition of Leucippus and that they carried on the scientific rationalist philosophy associated with Miletus. Both were materialist, believing everything to be the result of natural laws. Unlike Aristotle or Plato, the atomists attempted to explain the world without reasoning as to purpose, prime mover, or final cause. For the atomists questions of physics should be answered with a mechanistic explanation, while their opponents search for explanations which, in addition to the material and mechanistic included the formal and teleological.
Greek historians consider Democritus to have established aesthetics as a subject of investigation and study, as he wrote theoretically on poetry and fine art long before authors such as Aristotle. Thrasyllus identified six works in the philosopher's oeuvre which had belonged to aesthetics as a discipline, but only fragments of the relevant works are extant; the theory of Democritus held that everything is composed of "atoms", which are physically, but not geometrically, indivisible. Of the mass of atoms, Democritus said, "The more any indivisible exceeds, the heavier it is". However, his exact position o
Eudoxus of Cnidus
Eudoxus of Cnidus was an ancient Greek astronomer, mathematician and student of Archytas and Plato. All of his works are lost, though some fragments are preserved in Hipparchus' commentary on Aratus's poem on astronomy. Sphaerics by Theodosius of Bithynia may be based on a work by Eudoxus, his name Eudoxus means "honored" or "of good repute". It is analogous to the Latin name Benedictus. Eudoxus's father Aeschines of Cnidus loved to watch stars at night. Eudoxus first travelled to Tarentum to study from whom he learned mathematics. While in Italy, Eudoxus visited Sicily. Around 387 BC, at the age of 23, he traveled with the physician Theomedon—who some believed was his lover—to Athens to study with the followers of Socrates, he attended lectures of Plato and other philosophers for several months, but due to a disagreement they had a falling-out. Eudoxus could only afford an apartment at the Piraeus. To attend Plato's lectures, he walked the 7 miles in each direction each day. Due to his poverty, his friends raised funds sufficient to send him to Heliopolis, Egypt, to pursue his study of astronomy and mathematics.
He lived there for 16 months. From Egypt, he traveled north to Cyzicus, located on the south shore of the Sea of Marmara, the Propontis, he traveled south to the court of Mausolus. During his travels he gathered many students of his own. Around 368 BC, Eudoxus returned to Athens with his students. According to some sources, around 367 he assumed headship of the Academy during Plato's period in Syracuse, taught Aristotle, he returned to his native Cnidus, where he served in the city assembly. While in Cnidus, he built an observatory and continued writing and lecturing on theology and meteorology, he had one son and three daughters, Actis and Delphis. In mathematical astronomy, his fame is due to the introduction of the astronomical globe, his early contributions to understanding the movement of the planets, his work on proportions shows insight into real numbers. When it was revived by Tartaglia and others in the 16th century, it became the basis for quantitative work in science for a century, until it was replaced by Richard Dedekind.
Craters on Mars and the Moon are named in his honor. An algebraic curve is named after him. Eudoxus is considered by some to be the greatest of classical Greek mathematicians, in all antiquity second only to Archimedes, he rigorously developed Antiphon's method of exhaustion, a precursor to the integral calculus, used in a masterly way by Archimedes in the following century. In applying the method, Eudoxus proved such mathematical statements as: areas of circles are to one another as the squares of their radii, volumes of spheres are to one another as the cubes of their radii, the volume of a pyramid is one-third the volume of a prism with the same base and altitude, the volume of a cone is one-third that of the corresponding cylinder. Eudoxus introduced the idea of non-quantified mathematical magnitude to describe and work with continuous geometrical entities such as lines, angles and volumes, thereby avoiding the use of irrational numbers. In doing so, he reversed a Pythagorean emphasis on number and arithmetic, focusing instead on geometrical concepts as the basis of rigorous mathematics.
Some Pythagoreans, such as Eudoxus' teacher Archytas, had believed that only arithmetic could provide a basis for proofs. Induced by the need to understand and operate with incommensurable quantities, Eudoxus established what may have been the first deductive organization of mathematics on the basis of explicit axioms; the change in focus by Eudoxus stimulated a divide in mathematics. In combination with a Greek intellectual attitude unconcerned with practical problems, there followed a significant retreat from the development of techniques in arithmetic and algebra; the Pythagoreans had discovered that the diagonal of a square does not have a common unit of measurement with the sides of the square. This discovery had heralded the existence of incommensurable quantities beyond the integers and rational fractions, but at the same time it threw into question the idea of measurement and calculations in geometry as a whole. For example, Euclid provides an elaborate proof of the Pythagorean theorem, by using addition of areas and only much a simpler proof from similar triangles, which relies on ratios of line segments.
Ancient Greek mathematicians calculated not with quantities and equations as we do today, but instead they used proportionalities to express the relationship between quantities. Thus the ratio of two similar quantities was not just a numerical value. Eudoxus was able to restore confidence in the use of proportionalities by providing an astounding definition for the meaning of the equality between two ratios; this definition of proportion forms the subject of Euclid's Book V. In Definition 5 of Euclid's Book V we read: Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth when, if any equimultiples whatever be taken of the first and third, any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike
Anaxagoras was a Pre-Socratic Greek philosopher. Born in Clazomenae at a time when Asia Minor was under the control of the Persian Empire, Anaxagoras came to Athens. According to Diogenes Laërtius and Plutarch, in life he was charged with impiety and went into exile in Lampsacus. Responding to the claims of Parmenides on the impossibility of change, Anaxagoras described the world as a mixture of primary imperishable ingredients, where material variation was never caused by an absolute presence of a particular ingredient, but rather by its relative preponderance over the other ingredients, he introduced the concept of Nous as an ordering force, which moved and separated out the original mixture, homogeneous, or nearly so. He gave a number of novel scientific accounts of natural phenomena, he produced a correct explanation for eclipses and described the sun as a fiery mass larger than the Peloponnese, as well as attempting to explain rainbows and meteors. Anaxagoras is believed to have enjoyed some wealth and political influence in his native town of Clazomenae.
However, he surrendered this out of a fear that they would hinder his search for knowledge. The Roman author Valerius Maximus preserves a different tradition: Anaxagoras, coming home from a long voyage, found his property in ruin, said: "If this had not perished, I would have"—a sentence described by Valerius as being "possessed of sought-after wisdom!"Anaxagoras was a Greek citizen of the Persian Empire and had served in the Persian army. Though this remains uncertain, "it would explain why he came to Athens in the year of Salamis, 480/79 B. C." Anaxagoras is said to have remained in Athens for thirty years. Pericles learned to love and admire him, the poet Euripides derived from him an enthusiasm for science and humanity. Anaxagoras brought the spirit of scientific inquiry from Ionia to Athens, his observations of the celestial bodies and the fall of meteorites led him to form new theories of the universal order, to a putative prediction of the impact of a meteorite in 467. He attempted to give a scientific account of eclipses, meteors and the sun, which he described as a mass of blazing metal, larger than the Peloponnese.
The heavenly bodies, he asserted, were masses of stone torn from the earth and ignited by rapid rotation. He was the first to give a correct explanation of eclipses, was both famous and notorious for his scientific theories, including the claims that the sun is a mass of red-hot metal, that the moon is earthy, that the stars are fiery stones, he thought the earth was flat and floated supported by'strong' air under it and disturbances in this air sometimes caused earthquakes. These speculations made him vulnerable in Athens to a charge of impiety. Diogenes Laërtius reports the story that he was prosecuted by Cleon for impiety, but Plutarch says that Pericles sent his former tutor, Anaxagoras, to Lampsacus for his own safety after the Athenians began to blame him for the Peloponnesian war. According to Laërtius, Pericles spoke in defense of Anaxagoras at his trial, c. 450. So, Anaxagoras was forced to retire from Athens to Lampsacus in Troad, he died there in around the year 428. Citizens of Lampsacus erected an altar to Mind and Truth in his memory, observed the anniversary of his death for many years.
Anaxagoras wrote a book of philosophy, but only fragments of the first part of this have survived, through preservation in work of Simplicius of Cilicia in the 6th century AD. According to Anaxagoras all things have existed in some way from the beginning, but they existed in infinitesimally small fragments of themselves, endless in number and inextricably combined throughout the universe. All things existed in a confused and indistinguishable form. There was an infinite number of homogeneous parts as well as heterogeneous ones; the work of arrangement, the segregation of like from unlike and the summation of the whole into totals of the same name, was the work of Mind or Reason. Mind is no less unlimited than the chaotic mass, but it stood pure and independent, a thing of finer texture, alike in all its manifestations and everywhere the same; this subtle agent, possessed of all knowledge and power, is seen ruling in all the forms of life. Its first appearance, the only manifestation of it which Anaxagoras describes, is Motion.
It gave distinctness and reality to the aggregates of like parts. Decease and growth represent a new disruption. However, the original intermixture of things is never wholly overcome; each thing contains in itself parts of other things or heterogeneous elements, is what it is, only on account of the preponderance of certain homogeneous parts which constitute its character. Out of this process arise the things. Anaxagoras is mentioned by Socrates during his trial in Plato's "Apology". In the Phaedo, Plato portrays Socrates saying of Anaxagoras that as a young man:'I eagerly acquired his books and read them as as I could'. In a quote chosen to begin Nathanael West's first book "The Dream Life of Balso Snell", Marcel Proust's character Bergotte says, "After all, my dear fellow, Anaxagoras has said, is a journey." Anaxagoras appears as a character in Part II by Johann Wolfgang von Goethe. Anaxagoras appears as a cha
Eratosthenes of Cyrene was a Greek mathematician, poet and music theorist. He was a man of becoming the chief librarian at the Library of Alexandria, he invented the discipline of geography, including the terminology used today. He is best known for being the first person to calculate the circumference of the Earth, which he did by comparing angles of the mid-day Sun at two places a known North-South distance apart, his calculation was remarkably accurate. He was the first to calculate the tilt of the Earth's axis, again with remarkable accuracy. Additionally, he may have calculated the distance from the Earth to the Sun and invented the leap day, he created the first map of the world, incorporating parallels and meridians based on the available geographic knowledge of his era. Eratosthenes was the founder of scientific chronology. Eratosthenes dated The Sack of Troy to 1183 BC. In number theory, he introduced the sieve of Eratosthenes, an efficient method of identifying prime numbers, he was a figure of influence in many fields.
According to an entry in the Suda, his critics scorned him, calling him Beta because he always came in second in all his endeavors. Nonetheless, his devotees nicknamed him Pentathlos after the Olympians who were well rounded competitors, for he had proven himself to be knowledgeable in every area of learning. Eratosthenes yearned to understand the complexities of the entire world; the son of Aglaos, Eratosthenes was born in 276 BC in Cyrene. Now part of modern-day Libya, Cyrene had been founded by Greeks centuries earlier and became the capital of Pentapolis, a country of five cities: Cyrene, Berenice and Apollonia. Alexander the Great conquered Cyrene in 332 BC, following his death in 323 BC, its rule was given to one of his generals, Ptolemy I Soter, the founder of the Ptolemaic Kingdom. Under Ptolemaic rule the economy prospered, based on the export of horses and silphium, a plant used for rich seasoning and medicine. Cyrene became a place of cultivation. Like any young Greek, Eratosthenes would have studied in the local gymnasium, where he would have learned physical skills and social discourse as well as reading, arithmetic and music.
Eratosthenes went to Athens to further his studies. There he was taught Stoicism by its founder, Zeno of Citium, in philosophical lectures on living a virtuous life, he studied under Aristo of Chios, who led a more cynical school of philosophy. He studied under the head of the Platonic Academy, Arcesilaus of Pitane, his interest in Plato led him to write his first work at a scholarly level, inquiring into the mathematical foundation of Plato's philosophies. Eratosthenes investigated the art of poetry under Callimachus, he was a imaginative poet. He wrote poems: one in hexameters called Hermes, illustrating the god's life history, he wrote Chronographies, a text that scientifically depicted dates of importance, beginning with the Trojan War. This work was esteemed for its accuracy. George Syncellus was able to preserve from Chronographies a list of 38 kings of the Egyptian Thebes. Eratosthenes wrote Olympic Victors, a chronology of the winners of the Olympic Games, it is not known when he wrote his works.
These works and his great poetic abilities led the pharaoh Ptolemy III Euergetes to seek to place him as a librarian at the Library of Alexandria in the year 245 BC. Eratosthenes thirty years old, accepted Ptolemy's invitation and traveled to Alexandria, where he lived for the rest of his life. Within about five years he became Chief Librarian, a position that the poet Apollonius Rhodius had held; as head of the library Eratosthenes tutored the children of Ptolemy, including Ptolemy IV Philopator who became the fourth Ptolemaic pharaoh. He expanded the library's holdings: in Alexandria all books had to be surrendered for duplication, it was said that these were copied so that it was impossible to tell if the library had returned the original or the copy. He sought to maintain the reputation of the Library of Alexandria against competition from the Library of Pergamum. Eratosthenes created a whole section devoted to the examination of Homer, acquired original works of great tragic dramas of Aeschylus and Euripides.
Eratosthenes made several important contributions to mathematics and science, was a friend of Archimedes. Around 255 BC, he invented the armillary sphere. In On the Circular Motions of the Celestial Bodies, Cleomedes credited him with having calculated the Earth's circumference around 240 BC, using knowledge of the angle of elevation of the Sun at noon on the summer solstice in Alexandria and on Elephantine Island near Syene. Eratosthenes believed there was good and bad in every nation and criticized Aristotle for arguing that humanity was divided into Greeks and barbarians, that the Greeks should keep themselves racially pure; as he aged he contracted ophthalmia, becoming blind around 195 BC. Losing the ability to read and to observe nature plagued and depressed him, leading him to voluntarily starve himself to death, he died in 194 BC at 82 in Alexandria. Eratosthenes calculated the Earth's circumference without leaving Alexandria, he knew that at local noon on the summer solstice in Syene (modern Asw