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37-652: The Minaean people were one of four ancient Yemeni groups mentioned by Eratosthenes . The others were the Sabaeans , Ḥaḑramites and Qatabānians . Each of these had regional kingdoms in ancient Yemen, with the Minaeans in the north-west (in Wādī al-Jawf ), the Sabaeans to the south-east of them, the Qatabānians to the south-east of the Sabaeans, and the Ḥaḑramites further east still. Nothing

74-500: A during 360 BCE, while Kenneth A. Kitchen dates it to c. 190–175 BCE) Minaean rule reached as far as Dedan . The extent of their long-distance trade is also shown by the presence of Minaean merchants in the Aegean . With the expansion of Ma’īn as far as the Red Sea they were also able to carry out sea trade. At the end of the 2nd century BCE Ma’īn found itself under the rule of Qatabān, but after

111-452: A given prime are generated starting from that prime, as a sequence of numbers with the same difference, equal to that prime, between consecutive numbers. This is the sieve's key distinction from using trial division to sequentially test each candidate number for divisibility by each prime. Eratosthenes was one of the most pre-eminent scholarly figures of his time, and produced works covering a vast area of knowledge before and during his time at

148-563: A number of major caravan stations along the trading route, including Yathrib (Medina) and Gaza ; there is also a brief account of how war between the Egyptians and Syrians interrupted the trade for a while. The Minaeans had a different social structure to the rest of the Old South Arabians. Their king was the only one involved in lawmaking, along with a council of elders, who in Ma'īn represented

185-459: Is known about the early history of this north Yemeni kingdom. The region later to be known as Ma’īn first enters history at the time of the Sabaean mukarrib Karib’il Watar I , and at that time consisted of a number of small city-states, which were under very strong Sabaean influence. The inscriptions from the city-state of Ḥaram , which date from this time, exhibit Minaean linguistic features, alongside

222-451: Is known in mathematics as the Sieve of Eratosthenes . In mathematics, the sieve of Eratosthenes (Greek: κόσκινον Ἐρατοσθένους), one of a number of prime number sieves , is a simple, ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite, i.e. , not prime, the multiples of each prime, starting with the multiples of 2. The multiples of

259-667: Is the first recorded instance of many terms still in use today, including the name of the discipline geography . He placed grids of overlapping lines over the surface of the Earth. He used parallels and meridians to link together every place in the world. It was now possible to estimate one's distance from remote locations with this network over the surface of the Earth. In the Geography the names of over 400 cities and their locations were shown, which had never been achieved before. However, his Geography has been lost to history, although fragments of

296-512: The Library of Pergamum . Eratosthenes created a whole section devoted to the examination of Homer , and acquired original works of great tragic dramas of Aeschylus , Sophocles and Euripides . Eratosthenes made several important contributions to mathematics and science , and was a friend of Archimedes . Around 255 BC, he invented the armillary sphere . In On the Circular Motions of

333-563: The Trojan War . This work was highly esteemed for its accuracy. George Syncellus was later able to preserve from Chronographies a list of 38 kings of the Egyptian Thebes . Eratosthenes also wrote Olympic Victors , a chronology of the winners of the Olympic Games . It is not known when he wrote his works, but they highlighted his abilities. These works and his great poetic abilities led

370-608: The Celestial Bodies , Cleomedes credited him with having calculated the Earth's circumference around 240 BC, with high accuracy. Eratosthenes believed there was both good and bad in every nation and criticized Aristotle for arguing that humanity was divided into Greeks and barbarians , as well as for arguing that the Greeks should keep themselves racially pure. As he aged, he contracted ophthalmia , becoming blind around 195 BC. Losing

407-471: The Earth , which he did by using the extensive survey results he could access in his role at the Library. His calculation was remarkably accurate (his error margin turned out to be less than 1%). He was also the first person 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

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444-416: The Earth is the distance between the two cities divided by the difference in shadow angles expressed as a fraction of one turn . Eratosthenes now continued from his knowledge about the Earth. Using his discoveries and knowledge of its size and shape, he began to sketch it. In the Library of Alexandria he had access to various travel books, which contained various items of information and representations of

481-448: The Greek suffix, "graphy", meaning "description", so a geographer is someone who studies the earth. The word "geography" is a Middle French word that is believed to have been first used in 1540. Although geographers are historically known as people who make maps , map making is actually the field of study of cartography , a subset of geography. Geographers do not study only the details of

518-538: The Library. He wrote on many topics – geography, mathematics, philosophy, chronology, literary criticism, grammar, poetry, and even old comedies. There are no documents left of his work after the destruction of the Library of Alexandria . Geographer A geographer is a physical scientist, social scientist or humanist whose area of study is geography , the study of Earth's natural environment and human society, including how society and nature interacts. The Greek prefix "geo" means "earth" and

555-478: 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 the age of 82 in Alexandria. The measurement of Earth's circumference is the most famous among the results obtained by Eratosthenes, who estimated that the meridian has a length of 252,000 stadia (39,060 to 40,320 kilometres (24,270 to 25,050 mi)), with an error on

592-452: 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 1183 BC. In number theory , he introduced the sieve of Eratosthenes , an efficient method of identifying prime numbers and composite numbers. He was a figure of influence in many fields who yearned to understand

629-423: 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 accurately 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

666-655: The collapse of the Qatabānian Empire a few centuries later, the Minaean kingdom fell too. The area was under Sabaean rule at the latest by the time the Roman general Aelius Gallus waged a military campaign in the area in 25/24 BCE. The Minaeans, like some other Arabian and Yemenite kingdoms of the same period, were involved in the extremely lucrative spice trade , especially frankincense and myrrh . Inscriptions found in Qanāwu mention

703-518: The complexities of the entire world. 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 (a 10th-century encyclopedia), some critics scorned him, calling him Number 2 because he always came in second in all his endeavours. The son of Aglaos, Eratosthenes

740-420: The following table presents the reconstruction of Kenneth A. Kitchen. It should however be pointed out that the reconstruction of Hermann von Wissmann deviates from this considerably, and is just as probable. Eratosthenes Eratosthenes of Cyrene ( / ɛr ə ˈ t ɒ s θ ə n iː z / ; Ancient Greek : Ἐρατοσθένης [eratostʰénɛːs] ; c.  276 BC  – c.  195/194 BC )

777-589: The founder of the Ptolemaic Kingdom . Under Ptolemaic rule the economy prospered, based largely on the export of horses and silphium , a plant used for rich seasoning and medicine. Cyrene became a place of cultivation, where knowledge blossomed. Like any young Greek at the time, Eratosthenes would have studied in the local gymnasium , where he would have learned physical skills and social discourse as well as reading, writing, arithmetic, poetry, and music. Eratosthenes went to Athens to further his studies. There he

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814-418: The king Ptolemy III Euergetes to seek to place him as a librarian at the Library of Alexandria in the year 245 BC. Eratosthenes, then thirty years old, accepted Ptolemy's invitation and traveled to Alexandria, where he lived for the rest of his life. Within about fifty years he became Chief Librarian, a position that the poet Apollonius Rhodius had previously held. As head of the library Eratosthenes tutored

851-532: The natural environment or human society, but they also study the reciprocal relationship between these two. For example, they study how the natural environment contributes to human society and how human society affects the natural environment. In particular, physical geographers study the natural environment while human geographers study human society and culture. Some geographers are practitioners of GIS ( geographic information system ) and are often employed by local, state, and federal government agencies as well as in

888-411: The priesthood as well as families of high social class. The Minaeans were divided into groups of various sizes, led by a very high official called the kabīr , appointed once every two years, who was in charge of one or sometimes all of the trading posts. The reason for this difference in social structure is unknown. The order of succession and the dates of individual Minaean kings is extremely uncertain;

925-546: The private sector by environmental and engineering firms. The paintings by Johannes Vermeer titled The Geographer and The Astronomer are both thought to represent the growing influence and rise in prominence of scientific enquiry in Europe at the time of their painting in 1668–69. Subdividing geography is challenging, as the discipline is broad, interdisciplinary, ancient, and has been approached differently by different cultures. Attempts have gone back centuries, and include

962-471: The real value between −2.4% and +0.8% (assuming a value for the stadion between 155 and 160 metres (509 and 525 ft)). Eratosthenes described his arc measurement technique, in a book entitled On the Measure of the Earth , which has not been preserved. However, a simplified version of the method has been preserved, as described by Cleomedes . The simplified method works by considering two cities along

999-408: The same meridian and measuring both the distance between them and the difference in angles of the shadows cast by the sun on a vertical rod (a gnomon ) in each city at noon on the summer solstice . The two cities used were Alexandria and Syene (modern Aswan ), and the distance between the cities was measured by professional bematists . A geometric calculation reveals that the circumference of

1036-463: The same century ( c. 350–300 BCE). The next capital of the kingdom was Yathill (modern Baraqish ) and later Qarnāwu (near modern Ma’īn). The kingdom enjoyed its golden age in the 3rd century BCE when it was able to extend its influence all along the incense trail due to the conquest of Najrān , ‘Asīr and Ḥijāz . From the time of Waqah'il Sadiq I. (sources differ on when this golden age was, by as much as two centuries; Hermann von Wissmann has it

1073-403: The significant Sabaean impact. The Kingdom of Ma’īn emerged in the 6th century BCE, but then found itself under the rule of Saba’ . Only in about 400 BCE were the Minaeans able to ally themselves to Ḥaḑramawt and free themselves from direct Saba’ rule. In the 4th century both Ma’īn and Ḥaḑramawt were ruled by the same family, a close relationship that broke up again probably in the second half of

1110-539: The work can be pieced together from other great historians like Pliny , Polybius , Strabo , and Marcianus . While this work is the earliest we can trace certain ideas, words, and concepts in the historical record, earlier contributions may have been lost to history. According to Strabo, Eratosthenes argued against the Greek- Barbarian dichotomy. He says Alexander ignored his advisers by his regard for all people with law and government. Strabo says that Eratosthenes

1147-406: The world that needed to be pieced together in some organized format. In his three-volume work Geography ([Geographika] Error: {{Langx}}: invalid parameter: |script= ( help ) ), he described and mapped his entire known world, even dividing the Earth into five climate zones: two freezing zones around the poles, two temperate zones, and a zone encompassing the equator and the tropics. This book

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1184-454: Was a man of many perspectives and investigated the art of poetry under Callimachus . He wrote poems: one in hexameters called Hermes , illustrating the god's life history; and another in elegiacs , called Erigone , describing the suicide of the Athenian maiden Erigone (daughter of Icarius) . He wrote Chronographies , a text that scientifically depicted dates of importance, beginning with

1221-419: Was an Ancient Greek polymath : a mathematician , geographer , poet , astronomer , and music theorist . He was a man of learning, becoming the chief librarian at the Library of Alexandria . His work is comparable to what is now known as the study of geography , and he introduced some of the terminology still used today. He is best known for being the first person known to calculate the circumference of

1258-500: 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 (North Africa) , a country of five cities: Cyrene, Arsinoe , Berenice , Ptolemias , and Apollonia . Alexander the Great conquered Cyrene in 332 BC, and following his death in 323 BC, its rule was given to one of his generals, Ptolemy I Soter ,

1295-435: Was skilled in a variety of things; he was a true polymath. His opponents nicknamed him "Number 2" because he was great at many things and tried to get his hands on every bit of information but never achieved the highest rank in anything; Strabo accounts Eratosthenes as a mathematician among geographers and a geographer among mathematicians. Eratosthenes proposed a simple algorithm for finding prime numbers . This algorithm

1332-566: Was taught Stoicism by its founder, Zeno of Citium , in philosophical lectures on living a virtuous life. He then studied under Aristo of Chios , who led a more cynical school of philosophy. He also studied under the head of the Platonic Academy , who was Arcesilaus of Pitane . His interest in Plato led him to write his first work at a scholarly level, Platonikos , inquiring into the mathematical foundation of Plato's philosophies. Eratosthenes

1369-493: Was wrong to claim that Alexander had disregarded the counsel of his advisers. Strabo argues it was Alexander's interpretation of their "real intent" in recognizing that "in some people there prevail the law-abiding and the political instinct, and the qualities associated with education and powers of speech." Eratosthenes was described by the Suda Lexicon as a Πένταθλος (Pentathlos) which can be translated as "All-Rounded", for he

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