Eratosthenes
Eratosthenes of Cyrene was an Ancient Greek polymath: a philosopher, scholar, mathematician, geographer, poet, astronomer, and music theorist. Eratosthenes eventually became the chief librarian at the Library of Alexandria. His work was the precursor to the modern discipline of geography, and he introduced some of its terminology, coining the terms geography and geographer.
He is best remembered as the first known person to calculate the Earth's circumference. He was also the first to calculate Earth's axial tilt, which similarly proved to have remarkable accuracy. He created the first global projection of the world incorporating parallels and meridians based on the available geographic knowledge of his era. Eratosthenes was the founder of scientific chronology; he used Egyptian and Persian records to estimate the dates of the main events of the Trojan War, dating the sack of Troy to 1184 BC. In number theory, he introduced the sieve of Eratosthenes, an efficient method of identifying prime numbers and composite numbers.
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. Yet, according to an entry in the Suda, some critics scorned him, calling him Beta '' because he always came in second in all his endeavors.
Life
The son of Aglaos, Eratosthenes was born in 276 BC in Cyrene. Now part of modern-day Libya, Cyrene had been founded by Greeks during the second half of the 7th century BCE, and its proximity to the sea, its defensible position, its abundant water sources and its rich soil all contributed to its status as a capital city in the region. Cyrene came under the rule of Alexander the Great in 332 BC, and following his death in 323 BC, after a local civil war, it was seized by one of his generals, Ptolemy I Soter, the founder of the Ptolemaic Kingdom. When Cyrene came under Ptolemaic rule, it had a rich economy, based largely on the export of horses and silphium, and was long known as a prosperous hub of Greek culture.According to Roller, the rarity of both Eratosthenes' and his father's names are indicative of his humble origins, though due to the possibilities of upward mobility in the Hellenistic world he was not limited by them. However, Matthew suggests that his name, meaning "lovely strength" suggests noble upbringing, as does his education from a young age, which could imply his belonging to the aristocracy of Cyrene. Like any young Greek at the time, Eratosthenes would have studied in the local gymnasium, where he would have learned physical skills as well as reading, writing, arithmetic, poetry, and music.
By the late 260s BCE, Eratosthenes went to Athens to further his studies. According to Strabo, he was taught Stoicism there by the school's founder, Zeno of Citium, though their interaction would have been minimal, since Zeno died shortly after Eratosthenes arrived. Strabo also lists the little-known Apelles of Chios among his teachers. Eratosthenes is said to have studied under the cynic Aristo of Chios, and from the eclectic Bion of Borysthenes. He was further taught by the recently appointed head of the Platonic Academy, Arcesilaus of Pitane. Eratosthenes' later mathematical work implies that he received mathematical training there. According to the Suda Eratosthenes was also a student of Lysanias of Cyrene, a philologist and grammarian who focused on Homer. The poet, scholar, and librarian Callimachus likely crossed paths with Eratosthenes in local debates and scholarly discourse, even though he was likely never his formal teacher.
Strabo complained that Eratosthenes did not pay enough respect to Zeno, and criticized Eratosthenes for his association with such varied schools of thought, believing that he was unwilling to commit to philosophy and had learned only enough to appear as a philosopher, seeing it as nothing more than a distraction from his regular work. Later authors may have shared this view to some extent: The Suda states that Eratosthenes was referred to as Beta, because he was not seen as the leading expert in any given field. Others dubbed him Pentathlos, given his various skills and areas of knowledge; Pentathlos, however, is also the title of an athlete who competes in many events but comes in second in all of them. Strabo described Eratosthenes as a mathematician among geographers and a geographer among mathematicians.
The majority of Eratosthenes' studies focused on philosophy; mathematics was less prominent, and philology even less so. Despite his later contributions to the field, Eratosthenes could not formally study geography, as such a discipline did not exist at the time. Eratosthenes was however exposed to extensive geographic literature, such as the works of Homer, who he considered the first geographer, Hecataeus of Miletus, Aeschylus, Herodotus and others. Additionally, Eratosthenes was born forty years after the death of Alexander the Great, and he would have also encountered the works of Alexander's travel companions, Androsthenes, Nearchos, Onesikratos, Ptolemy I and others, who wrote about their journeys with him, and whose conquests cleared the path for Hellenistic explorers.
Eratosthenes remained in Athens for 20 years, studying and writing. During this period he wrote Platonikos, inquiring into the mathematics and music in Plato's philosophy, as well as the poetic works of Hermes and Erigone. His Chronographies focused on the important dates of the Trojan War, and his Olympic Victors compiled a list of the winners of the Olympic games. Little more is known about this period of his life.
In 246 BCE, Ptolemy III succeeded his father, Ptolemy II. Over the next twenty-five years, the Ptolemaic empire reached its greatest extent and Alexandria attained its zenith as an intellectual center. The post of librarian, which included the position of royal tutor to Ptolemy IV Philopator, became the most prestigious academic appointment. The reigning librarian, Apollonius of Rhodes, was forced into retirement by the new king, and Eratosthenes, who by this time was gaining fame as a scholar and a poet in the tradition of Callimachus, was summoned from Athens to replace him. Roller suggests that Eratosthenes' roots in Cyrene, the native city of Callimachus, and more importantly Queen Berenike, contributed favorably to his appointment.
The beginning of Eratosthenes' career in Alexandria was focused on mathematics. He was closely affiliated with Archimedes, who sent him material for comment and praised him enthusiastically for his contributions; his Method of Mechanical Theorems was written as a letter to Eratosthenes, and he sent Eratosthenes the famous Cattle Problem to be presented to the mathematicians of Alexandria. Eratosthenes subsequently wrote compositions on geography, philosophy, rhetoric, literary criticism, grammar, poetry and star lore. D. R. Dicks suggests that his astronomical contributions were hardly notable, and it was said that his poetry strangely contained the very didactic elements which he condemned.
Toward the end of his days, he served as an advisor and companion to Arsinoe, sister and wife of Ptolemy IV. According to the Suda, as he aged his eyesight began to fail. Losing the ability to read and to observe nature plagued and depressed him, leading him to voluntarily starve himself to death. He died at the age of 80 in Alexandria around 196 BCE. Roller notes that Dionysios of Kyzikos recorded the genuine epitaph of Eratosthenes, bemoaning the fact that he was buried in a foreign land, with "the shore of Proteus" being a Homeric allusion to the land of Egypt:
A softening old age with no darkening through disease quenched you and put you to deserved sleep pondering great things, Eratosthenes. Mother Kyrene did not receive you into the paternal tombs, son of Aglaos, but you are buried as a friend in a foreign land, here on the edge of the shore of Proteus.
The Suda records four students of Eratosthenes: Aristophanes of Byzantium, his successor as Librarian of Alexandria, the geographer Mnaseus of Patara in Lycia, the historian Menander, probably of Ephesos, and Aristis, who was otherwise unknown.
Contributions
Astronomy
Measurement of Earth's circumference
The Earth's circumference is the most famous measurement obtained by Eratosthenes. He described his arc measurement technique in his book , which has not been preserved. However, a simplified version of the method as described by Cleomedes was preserved.The simplified method works by considering two cities along the same meridian, and the difference in angles of the shadows cast by the sun on a vertical rod. The two cities used by Eratosthenes were Alexandria and Syene. At noon on the summer solstice, there were still shadows in Alexandria. However, in Syene, rods cast no shadows, and the Sun's rays shone straight down into the city-center well.
According to Cleomedes, Eratosthenes then measured the shadow's angle to be about 7.2 degrees, which is 1/50 of a full circle, and reasoned using alternate interior angles that this angle represented the portion of Earth's curvature between the two cities. The distance between Alexandria and Syene was reported to be about 5,000 stadia, as measured by professional bematists. Eratosthenes multiplied this number by 50 and arrived at a total of roughly 250,000 stadia for the Earth's circumference.
This calculation is expressed algebraically as
where is the Earth's circumference, is the distance between the two cities, and is the difference in the two cities' shadow angles.
According to Matthew, the result of Eratosthenes calculation is approximately, while the modern day measurement of the circumference around the equator is ; passing through the poles the circumference is.