Misplaced Pages

#149850

87-506: He is best known for being the first person known to calculate the circumference of 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

174-493: A circle ; assuming the Earth to be perfectly spherical, he concluded that its circumference was 50 times the known distance from Alexandria to Syene (5,000 stadia, a figure that was checked yearly), i.e. 250,000 stadia . Depending on whether he used the "Olympic stade" (176.4 m) or the Italian stade (184.8 m), this would imply a circumference of 44,100 km (an error of 10%) or 46,100 km, an error of 15%. A value for

261-526: A belfry in Dunkerque and Montjuïc castle in Barcelona to estimate the length of the meridian arc through Dunkerque. The length of the first prototype metre bar was based on these measurements, but it was later determined that its length was short by about 0.2 millimetres because of miscalculation of the flattening of the Earth, making the prototype about 0.02% shorter than the original proposed definition of

348-559: A deep well at that time in Syene blocked the reflection of the Sun on the water. Eratosthenes then measured the Sun's angle of elevation at noon in Alexandria by measuring the length of another gnomon's shadow on the ground. Using the length of the rod, and the length of the shadow, as the legs of a triangle, he calculated the angle of the sun's rays. This angle was about 7°, or 1/50th the circumference of

435-452: 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

522-582: A group of Galatian mercenaries rebelled against him but is likely to have supported him more tacitly throughout his conflict with Seleucus II. He offered similar support to Attalus I , the dynast of Pergamum , who took advantage of this civil conflict to expand his territories in northwestern Asia Minor. When the Seleucid general Achaeus was sent in 223 BC to reconquer the territories in Asia Minor that had been lost to Attalus, Ptolemy III sent his son Magas with

609-415: A group of Muslim astronomers led by Al-Khwarizmi to measure the distance from Tadmur ( Palmyra ) to Raqqa , in modern Syria . They calculated the Earth's circumference to be within 15% of the modern value, and possibly much closer. How accurate it actually was is not known because of uncertainty in the conversion between the medieval Arabic units and modern units, but in any case, technical limitations of

696-548: A military force to aid Attalus, but he was unable to prevent Attalus' defeat. Ptolemy III maintained his father's hostile policy to Macedonia . This probably involved direct conflict with Antigonus II during the Third Syrian War, but after the defeat at Andros in c. 245 BC, Ptolemy III seems to have returned to the policy of indirect opposition, financing enemies of the Antigonids in mainland Greece. The most prominent of these

783-473: A nautical mile as 6,080 feet, the length of one minute of arc at 48 degrees latitude. In 1793, France defined the metre so as to make the polar circumference of the Earth 40,000 kilometres. In order to measure this distance accurately, the French Academy of Sciences commissioned Jean Baptiste Joseph Delambre and Pierre Méchain to lead an expedition to attempt to accurately measure the distance between

870-564: A new deme named Berenicidae in honour of Queen Berenice II. The Athenians instituted a state religious cult in which Ptolemy III and Berenice II were worshipped as gods, including a festival, the Ptolemaia. The centre of the cult was the Ptolemaion, which also served as the gymnasium where young male citizens undertook civic and military training. Cleomenes III suffered serious defeats in 223 BC and Ptolemy III abandoned his support for him in

957-430: A new length unit based on the length of the meridian, as stated by Pliny, who writes about the stadion "according to Eratosthenes' ratio". Posidonius calculated the Earth's circumference by reference to the position of the star Canopus . As explained by Cleomedes , Posidonius observed Canopus on but never above the horizon at Rhodes , while at Alexandria he saw it ascend as far as 7 + 1 ⁄ 2 degrees above

SECTION 10

#1732851824150

1044-450: A single person from a single location. From the top of the mountain, he sighted the dip angle which, along with the mountain's height (which he determined beforehand), he applied to the law of sines formula. This was the earliest known use of dip angle and the earliest practical use of the law of sines. However, the method could not provide more accurate results than previous methods, due to technical limitations, and so al-Biruni accepted

1131-407: A son, Seleucus II , who was about 19 years old in 246 BC. However, in 253 BC, he had agreed to repudiate Laodice and marry Ptolemy III's sister Berenice . Antiochus II and Berenice had a son named Antiochus, who was still an infant when his father died. A succession dispute broke out immediately after Antiochus II's death. Ptolemy III quickly invaded Syria in support of his sister and her son, marking

1218-451: 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

1305-617: 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

1392-718: The Aegean , Ptolemy III suffered a major setback when his fleet was defeated by the Antigonids at the Battle of Andros around 246 BC, but he continued to offer financial support to their opponents in mainland Greece for the rest of his reign. At his death, Ptolemy III was succeeded by his eldest son, Ptolemy IV . Ptolemy III was born some time around 280 BC, as the eldest son of Ptolemy II and his first wife Arsinoe I , daughter of King Lysimachus of Thrace . His father had become co-regent of Egypt in 284 BC and sole ruler in 282 BC. Around 279 BC,

1479-695: The Demetrian War against Macedon with Ptolemaic financial support. However, in 229 BC, the Cleomenean War (229–222 BC) broke out between the Achaian League and Cleomenes III of Sparta . As a result, in 226 BC, Aratos of Sicyon the leader of the Achaian League forged an alliance with the Macedonian king Antigonus III . Ptolemy III responded by immediately breaking off relations with the Achaian League and redirecting his financial support to Sparta. Most of

1566-720: The Egyptian calendar of 365 days, and instituted related changes in festivals. Ptolemy III's infant daughter Berenice died during the synod and the stele arranges for her deification and ongoing worship. Further decrees would be issued by priestly synods under Ptolemy III's successors. The best-known examples are the Decree of Memphis passed by his son Ptolemy IV in about 218 BC and the Rosetta Stone erected by his grandson Ptolemy V in 196 BC. The Ptolemaic kings before Ptolemy III, his grandfather Ptolemy I and his father Ptolemy II, had followed

1653-511: 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

1740-541: The Musaeum was supplemented by a second library built in the Serapeum . He was said to have had every book unloaded in the Alexandria docks seized and copied, returning the copies to their owners and keeping the originals for the Library. Galen attests that he borrowed the official manuscripts of Aeschylus , Sophocles , and Euripides from Athens and forfeited the considerable deposit he paid for them in order to keep them for

1827-669: The Third Syrian War (246–241 BC), Ptolemy III invaded the Seleucid empire and won a near total victory, but was forced to abandon the campaign as a result of an uprising in Egypt. In the aftermath of this rebellion, Ptolemy forged a closer bond with the Egyptian priestly elite, which was codified in the Canopus decree of 238 BC and set a trend for Ptolemaic power in Egypt for the rest of the dynasty. In

SECTION 20

#1732851824150

1914-563: 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

2001-479: 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 1183 BC. In number theory , he introduced the sieve of Eratosthenes , an efficient method of identifying prime numbers and composite numbers. He

2088-538: The monsoon pattern at the time, resulting from a volcanic eruption which took place in 247 BC. After his return to Egypt and suppression of the revolt, Ptolemy III made an effort to present himself as a victorious king in both Egyptian and Greek cultural contexts. Official propaganda, like OGIS 54, an inscription set up in Adulis and probably the copy of an inscription in Alexandria, vastly exaggerated Ptolemy III's conquests, claiming even Bactria among his conquests. At

2175-416: The poles , the circumference is 40,007.863 km (24,859.734 mi). Measurement of Earth's circumference has been important to navigation since ancient times. The first known scientific measurement and calculation was done by Eratosthenes , by comparing altitudes of the mid-day sun at two places a known north–south distance apart. He achieved a great degree of precision in his computation. Treating

2262-605: 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

2349-521: The Circular Motions of the Celestial Bodies , around 240 BC, Eratosthenes calculated the circumference of the Earth in Ptolemaic Egypt . Using a vertical rod known as a gnomon and under the previous assumptions, he knew that at local noon on the summer solstice in Syene (modern Aswan , Egypt), the Sun was directly overhead, as the gnomon cast no shadow. Additionally, the shadow of someone looking down

2436-510: The Cleomenian War would in fact be the last time that the Ptolemies intervened in mainland Greece. In November or December 222 BC, shortly after Cleomenes' arrival in Egypt and Magas' failure in Asia Minor, Ptolemy III died of natural causes. He was succeeded by his son Ptolemy IV without incident. Ptolemy III built on the efforts of his predecessors to conform to the traditional model of

2523-436: The Earth as a sphere , its circumference would be its single most important measurement. Earth deviates from spherical by about 0.3%, as characterized by flattening . In modern times, Earth's circumference has been used to define fundamental units of measurement of length: the nautical mile in the seventeenth century and the metre in the eighteenth. Earth's polar circumference is very near to 21,600 nautical miles because

2610-416: 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

2697-562: The Egyptian pharaoh . He was responsible for the first known example of a series of decrees published as trilingual inscriptions on massive stone blocks in Ancient Greek , Egyptian hieroglyphs , and demotic . Earlier decrees, like the Satrap stele and the Mendes stele , had been in hieroglyphs alone and had been directed at single individual sanctuaries. By contrast, Ptolemy III's Canopus decree

Eratosthenes - Misplaced Pages Continue

2784-509: The Elder mentions Posidonius among his sources and—without naming him—reported his method for estimating the Earth's circumference. He noted, however, that Hipparchus had added some 26,000 stadia to Eratosthenes's estimate. The smaller value offered by Strabo and the different lengths of Greek and Roman stadia have created a persistent confusion around Posidonius's result. Ptolemy used Posidonius's lower value of 180,000 stades (about 33% too low) for

2871-517: The Levantine coast encountering minimal resistance. The cities of Seleucia and Antioch surrendered to him without a fight in late autumn. At Antioch, Ptolemy III went to the royal palace to plan his next moves with Berenice in person, only to discover that she and her young son had been murdered. Rather than accept defeat in the face of this setback, Ptolemy III continued his campaign through Syria and into Mesopotamia , where he conquered Babylon at

2958-414: The Library rather than returning them. The most distinguished scholar at Ptolemy III's court was the polymath and geographer Eratosthenes , most noted for his remarkably accurate calculation of the circumference of the world . Other prominent scholars include the mathematicians Conon of Samos and Apollonius of Perge . Ptolemy III's reign was also marked by trade with other contemporaneous polities. In

3045-521: 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 . Circumference of the Earth Earth's circumference is the distance around Earth . Measured around the equator , it is 40,075.017 km (24,901.461 mi). Measured passing through

3132-507: The Ptolemaic dynasty; the main temple was finished in the reign of Ptolemy IV in 231 BC, and the full complex was only completed in 142 BC, during the reign of Ptolemy VIII , while the reliefs on the great pylon were finished in the reign of Ptolemy XII . Other construction work took place at a range of sites, including (from north to south): Ptolemy III continued his predecessor's sponsorship of scholarship and literature. The Great Library in

3219-625: The Seleucids had recaptured Mesopotamia. The Egyptian revolt is significant as the first of a series of native Egyptian uprisings which would trouble Egypt for the next century. One reason for this revolt was the heavy tax-burdens placed on the people of Egypt by Ptolemy III's war in Syria. Furthermore, papyri records indicate that the inundation of the Nile river failed in 245 BC, resulting in famine. Climate proxy studies suggest that this resulted from changes of

3306-478: The Son was a son of Arsinoe II by Lysimachus. Around the time of the rebellion, Ptolemy II legitimised the children of Arsinoe I by having them posthumously adopted by Arsinoe II. In the late 250s BC, Ptolemy II arranged the engagement of Ptolemy III to Berenice , the sole child of Ptolemy II's half-brother King Magas of Cyrene . The decision to single Ptolemy III out for this marriage indicates that, by this time, he

3393-423: 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

3480-526: The agreement and invited an Antigonid prince, Demetrius the Fair , to Cyrene to marry Berenice instead. With Apame's help, Demetrius seized control of the city, but he was assassinated by Berenice. A republican government, led by two Cyrenaeans named Ecdelus and Demophanes, controlled Cyrene for four years. It was only with Ptolemy III's accession in 246 BC, that the wedding of Ptolemy III and Berenice seems to have actually taken place. Ptolemaic authority over Cyrene

3567-425: The basis for a unit of measurement for distance and proposed the nautical mile as one minute or one-sixtieth ( ⁠ 1 / 60 ⁠ ) of one degree of latitude. As one degree is ⁠ 1 / 360 ⁠ of a circle, one minute of arc is ⁠ 1 / 21600 ⁠ of a circle – such that the polar circumference of the Earth would be exactly 21,600 miles. Gunter used Snellius's circumference to define

Eratosthenes - Misplaced Pages Continue

3654-464: The beginning of the Second Syrian War and was removed from the co-regency. Some scholars have identified Ptolemy the Son with Ptolemy III. This seems unlikely, since Ptolemy III was probably too young to lead forces in the 260s and does not seem to have suffered any of the negative consequences that would be expected if he had revolted from his father in 259 BC. Chris Bennett has argued that Ptolemy

3741-605: The beginning of the Third Syrian War (also known as the Laodicean War). An account of the initial phase of this war, written by Ptolemy III himself, is preserved on the Gurob papyrus . At the outbreak of war, Laodice I and Seleucus II were based in western Asia Minor , while the widowed Queen Berenice was in Antioch . The latter quickly seized control of Cilicia to prevent Laodice I from entering Syria. Meanwhile, Ptolemy III marched along

3828-423: 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

3915-430: The circumference has improved since then, but the physical length of each unit of measure had remained close to what it was determined to be at the time, so the Earth's circumference is no longer a round number in metres or nautical miles. The measure 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 , with an error on

4002-474: The collapse of Lysimachus' kingdom led to the return to Egypt of Ptolemy II's sister Arsinoe II , who had been married to Lysimachus. A conflict quickly broke out between Arsinoe I and Arsinoe II. Sometime after 275 BC, Arsinoe I was charged with conspiracy and exiled to Coptos . When Ptolemy II married Arsinoe II probably in 273/2 BC, her victory in this conflict was complete. As children of Arsinoe I, Ptolemy III and his two siblings seem to have been removed from

4089-724: The earth's circumference in his Geography . This was the number used by Christopher Columbus in order to underestimate the distance to India as 70,000 stades. Around AD 525, the Indian mathematician and astronomer Aryabhata wrote Aryabhatiya , in which he calculated the diameter of earth to be of 1,050 yojanas . The length of the yojana intended by Aryabhata is in dispute. One careful reading gives an equivalent of 14,200 kilometres (8,800 mi), too large by 11%. Another gives 15,360 km (9,540 mi), too large by 20%. Yet another gives 13,440 km (8,350 mi), too large by 5%. Around AD 830, Caliph Al-Ma'mun commissioned

4176-508: The end of 246 or beginning of 245 BC. In light of this success, he may have been crowned 'Great King' of Asia. Early in 245 BC, he established a governor of the land 'on the other side' of the Euphrates , indicating an intention to permanently incorporate the region into the Ptolemaic kingdom. At this point however, Ptolemy III received notice that a revolt had broken out in Egypt and he was forced to return home to suppress it. By July 245 BC,

4263-420: The fact that Eratosthenes' measure corresponds precisely to 252,000 stadia (according to Pliny) might be intentional, since it is a number that can be divided by all natural numbers from 1 to 10: some historians believe that Eratosthenes changed from the 250,000 value written by Cleomedes to this new value to simplify calculations; other historians of science, on the other side, believe that Eratosthenes introduced

4350-587: 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

4437-503: The half-brother of Ptolemy III, captured Ephesus from the Seleucids in 246 BC. At an uncertain date around 245 BC, he fought a sea-battle at Andros against King Antigonus II of Macedon , in which the Ptolemaic forces were defeated. It appears that he then led an invasion of Thrace, where Maroneia and Aenus were under Ptolemaic control as of 243 BC. Ptolemy Andromachou was subsequently assassinated at Ephesus by Thracian soldiers under his control. The only further action known from

SECTION 50

#1732851824150

4524-421: The horizon (the meridian arc between the latitude of the two locales is actually 5 degrees 14 minutes). Since he thought Rhodes was 5,000 stadia due north of Alexandria, and the difference in the star's elevation indicated the distance between the two locales was 1/48 of the circle, he multiplied 5,000 by 48 to arrive at a figure of 240,000 stadia for the circumference of the earth. It is generally thought that

4611-418: 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

4698-607: The kingship from his father's hand Ptolemy III Euergetes ( Greek : Πτολεμαῖος Εὐεργέτης , romanized :  Ptolemaîos Euergétēs , "Ptolemy the Benefactor "; c. 280 – November/December 222 BC ) was the third pharaoh of the Ptolemaic dynasty in Egypt from 246 to 222 BC. The Ptolemaic Kingdom reached the height of its military and economic power during his kingship, as initiated by his father Ptolemy II Philadelphus . Ptolemy III

4785-589: The lead of Alexander the Great in prioritising the worship of Amun , worshipped at Karnak in Thebes among the Egyptian deities. With Ptolemy III the focus shifted strongly to Ptah , worshipped at Memphis . Ptah's earthly avatar, the Apis bull came to play a crucial role in royal new year festivals and coronation festivals. This new focus is referenced by two elements of Ptolemy III's Pharaonic titulary : his nomen which included

4872-522: The methods and tools would not permit an accuracy better than about 5%. A more convenient way to estimate was provided in Al-Biruni 's Codex Masudicus (1037). In contrast to his predecessors, who measured the Earth's circumference by sighting the Sun simultaneously from two locations, al-Biruni developed a new method of using trigonometric calculations, based on the angle between a plain and mountain top, which made it possible for it to be measured by

4959-545: The metre. Regardless, this length became the French standard and was progressively adopted by other countries in Europe. This is why the polar circumference of the Earth is actually 40,008 kilometres, instead of 40,000. Ptolemy III Euergetes Second Horus name: ḥkn-nṯrw-rmṯ-ḥr.f m-šsp.f-nsyt-m-Ꜥ-jt.f Hekenetjeruremetj-heref emshesepefnesytemaitef The one over whom gods and people have rejoiced when he has received

5046-427: The nautical mile was intended to express one minute of latitude (see meridian arc ), which is 21,600 partitions of the polar circumference (that is 60 minutes × 360 degrees). The polar circumference is also close to 40,000 kilometres because the metre was originally defined to be one ten millionth (i.e., a kilometre is one ten thousandth) of the arc from pole to equator ( quarter meridian ). The accuracy of measuring

5133-609: The new year in 243 BC, Ptolemy III incorporated himself and his wife Berenice II into the Ptolemaic state cult, to be worshipped as the Theoi Euergetai (Benefactor Gods), in honour of his restoration to Egypt of statues found in the Seleucid territories, which had been seized by the Persians . There may also have been a second theatre to this war in the Aegean. The general Ptolemy Andromachou, ostensibly an illegitimate son of Ptolemy II and

5220-419: The next year – probably as a result of an agreement with Antigonus. The Egyptian king seems to have been unwilling to commit actual troops to Greece, particularly as the threat of renewed war with the Seleucids was looming. Cleomenes III was defeated and forced to flee to Alexandria, where Ptolemy III offered him hospitality and promised to help restore him to power. However, these promises were not fulfilled, and

5307-607: The phrase Mery-Ptah (beloved of Ptah), and his golden Horus name , Neb khab-used mi ptah-tatenen (Lord of the Jubilee-festivals as well as Ptah Tatjenen). Ptolemy III financed construction projects at temples across Egypt. The most significant of these was the Temple of Horus at Edfu , one of the masterpieces of ancient Egyptian temple architecture and now the best-preserved of all Egyptian temples. The king initiated construction on it on 23 August 237 BC. Work continued for most of

SECTION 60

#1732851824150

5394-457: The place where he made landfall was not Asia , but rather a New World . In 1617 the Dutch scientist Willebrord Snellius assessed the circumference of the Earth at 24,630 Roman miles (24,024 statute miles). Around that time British mathematician Edmund Gunter improved navigational tools including a new quadrant to determine latitude at sea. He reasoned that the lines of latitude could be used as

5481-399: The priesthood, his military success in defending Egypt and in restoring religious artefacts supposedly held by the Seleucids, and his good governance, especially an incident when Ptolemy III imported, at his own expense, a vast amount of grain to compensate for a weak inundation . The rest of the decree consists of reforms to the priestly orders ( phylai ). The decree also added a leap day to

5568-468: 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

5655-549: The real value between −2.4% and +0.8% (assuming a value for the stadion between 155 and 160 metres; the exact value of the stadion remains a subject of debate to this day; see stadion ). Eratosthenes described his technique in a book entitled On the measure of the Earth , which has not been preserved; what has been preserved is the simplified version described by Cleomedes to popularise the discovery. Cleomedes invites his reader to consider two Egyptian cities, Alexandria and Syene (modern Aswan ): According to Cleomedes ' On

5742-462: The rest of the Greek states were brought under the Macedonian umbrella in 224 BC when Antigonus established the "Hellenic League". However Aetolia and Athens remained hostile to Macedon and redoubled their allegiance to Ptolemy III. In Athens, in 224 BC, extensive honours were granted to Ptolemy III to entrench their alliance with him, including the creation of a new tribe named Ptolemais in his honour and

5829-407: 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

5916-405: The stadion of 157.7 metres has even been posited by L.V. Firsov, which would give an even better precision, but is plagued by calculation errors and false assumptions. In 2012, Anthony Abreu Mora repeated Eratosthenes's calculation with more accurate data; the result was 40,074 km, which is 66 km different (0.16%) from the currently accepted polar circumference. Eratosthenes' method

6003-461: The stadion used by Posidonius was almost exactly 1/10 of a modern statute mile. Thus Posidonius's measure of 240,000 stadia translates to 24,000 mi (39,000 km), not much short of the actual circumference of 24,901 mi (40,074 km). Strabo noted that the distance between Rhodes and Alexandria is 3,750 stadia, and reported Posidonius's estimate of the Earth's circumference to be 180,000 stadia or 18,000 mi (29,000 km). Pliny

6090-504: The succession after their mother's fall. This political background may explain why Ptolemy III seems to have been raised on Thera in the Aegean, rather than in Egypt. His tutors included the poet and polymath Apollonius of Rhodes , later head of the Library of Alexandria . From 267 BC, a figure known as Ptolemy "the Son" was co-regent with Ptolemy II. He led naval forces in the Chremonidean war (267–261 BC), but revolted in 259 BC at

6177-408: The value calculated the previous century by the al-Ma'mun expedition. 1,700 years after Eratosthenes's death, Christopher Columbus studied what Eratosthenes had written about the size of the Earth. Nevertheless, based on a map by Toscanelli , he chose to believe that the Earth's circumference was 25% smaller. If, instead, Columbus had accepted Eratosthenes's larger value, he would have known that

6264-554: The war is some fighting near Damascus in 242 BC. Shortly after this, in 241 BC, Ptolemy made peace with the Seleucids, retaining all the conquered territory in Asia Minor and northern Syria. Nearly the whole Mediterranean coast from Maroneia in Thrace to the Syrtis in Libya was now under Ptolemaic control. One of the most significant acquisitions was Seleucia Pieria, the port of Antioch, whose loss

6351-538: 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

6438-403: 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

6525-582: Was a figure of influence in many fields who yearned to understand 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

6612-452: 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

6699-506: Was a significant economic and logistical set-back for the Seleucids. The conclusion of the Third Syrian War marked the end of military intervention in the Seleucid territories, but Ptolemy III continued to offer covert financial assistance to the opponents of Seleucus II. From 241 BC, this included Antiochus Hierax , the younger brother of Seleucus II, who rebelled against his brother and established his own separate kingdom in Asia Minor. Ptolemy III sent military forces to support him only when

6786-496: Was actually more complicated, as stated by the same Cleomedes, whose purpose was to present a simplified version of the one described in Eratosthenes' book. Pliny, for example, has quoted a value of 252,000 stadia. The method was based on several surveying trips conducted by professional bematists , whose job was to precisely measure the extent of the territory of Egypt for agricultural and taxation-related purposes. Furthermore,

6873-452: 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 ,

6960-467: Was forcefully reasserted. Two new port cities were established, named Ptolemais and Berenice (modern Tolmeita and Benghazi ) after the dynastic couple. The cities of Cyrenaica were unified in a League overseen by the king, as a way of balancing the cities' desire for political autonomy against the Ptolemaic desire for control. In July 246 BC, Antiochus II , king of the Seleucid empire , died suddenly. By his first wife Laodice I , Antiochus II had had

7047-434: 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

7134-564: 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

7221-621: Was the Achaian League , a federation of Greek city-states in the Peloponnese that were united by their opposition to Macedon. From 243 BC, Ptolemy III was the nominal leader ( hegemon ) and military commander of the League and supplied them with a yearly payment. After 240 BC, Ptolemy also forged an alliance with the Aetolian League in northwest Greece. From 238 to 234 BC, the two leagues waged

7308-513: Was the heir presumptive . On his father's death, Ptolemy III succeeded him without issue, taking the throne on 28 January 246 BC. Cyrene had been the first Ptolemaic territory outside Egypt, but Magas had rebelled against Ptolemy II and declared himself king of Cyrenaica in 276 BC. The aforementioned engagement of Ptolemy III to Berenice had been intended to lead to the reunification of Egypt and Cyrene after Magas' death. However, when Magas died in 250 BC, Berenice's mother Apame refused to honour

7395-405: Was the eldest son of Ptolemy II and Arsinoe I . When Ptolemy III was young, his mother was disgraced and he was removed from the succession. He was restored as heir to the throne in the late 250s BC and succeeded his father as king without issue in 246 BC. On his succession, Ptolemy III married Berenice II , reigning queen of Cyrenaica , thereby bringing her territory into the Ptolemaic realm. In

7482-423: Was the product of a special synod of all the priests of Egypt, which was held in 238 BC. The decree instituted a number of reforms and represents the establishment of a full partnership between Ptolemy III as pharaoh and the Egyptian priestly elite. This partnership would endure until the end of the Ptolemaic dynasty. In the decree, the priesthood praise Ptolemy III as a perfect pharaoh. They emphasise his support of

7569-492: 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

#149850