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| He is credited by ] in ''On the Circular Motions of the Celestial Bodies'' with having calculated the Earth's ] ca. ], using ] and knowledge of the angle of ] of the ] at noon in Alexandria and ] (now ], Egypt). | He is credited by ] in ''On the Circular Motions of the Celestial Bodies'' with having calculated the Earth's ] ca. ], using ] and knowledge of the angle of ] of the ] at noon in Alexandria and ] (now ], Egypt). | ||
| Eratosthenes |
Eratosthenes results, that make the degree 700 stadia, imply the circumference of the earth is 252,000 stadia and would be off by 1 part in 6 if the stadia he were using were Greek or Roman ] of 185 m. | ||
| If his results were acurate his stadia would have measured 158.57 m. As it happens this works out to 302 Egyptian ]. | |||
| He also knew, from measurement, that in his hometown of Alexandria, the angle of elevation of the Sun would be 1/50th of a circle (7.2°) south of the zenith at the same time. Assuming that Alexandria was due ] of Syene — Alexandria is in fact on a more westerly ] — he concluded that the distance from Alexandria to Syene must be 7/360 of the total circumference of the Earth. | |||
| The Egyptians had a very well documented standard of measure called the ] which was 100 royal cubits in length and was the side of an ] or field called a ]. In Greek and Roman times the ] were generally farmed in clusters of three with one left fallow, one plowed and sowed in grain and another planted in hay for the plow animal. | |||
| ⚫ | The distance between the cities was |
||
| This means the Egyptians clusters of fields would have been surveyed by a standard of 300 royal cubits that Eratosthenes could have found useful in his work. | |||
| From the information compiled in his library Eratosthenes would have known that the last time the experiment had been performed, on the ] at local ] on the ], the Sun would have appeared at the ], directly overhead — though Syene was in fact slightly north of the tropic and the same conditions as previously recorded were no longer true in his time. | |||
| He also would have discovered in his reading, measurements such as those recorded by Herodotus giving the distance between Alexandria and Syene and information to the effect that the last time the experiment had been performed in his hometown of Alexandria, the angle of elevation of the Sun had been 7° south of the zenith at the same time although that also was no longer true in his time. | |||
| Assuming that Alexandria was due ] of Syene- Alexandria is in fact on a more westerly ]- and knowing from his reading that the distance from Alexandria to Syene was 5000 stadia of 300 Egyptian royal cubits of which there were 700 to a degree he would have known that the distance was a little over 7/360 of the great circle of the Earth | |||
| ⚫ | The distance between the cities was about 5,000 ] or 7 degrees, 1 itrw, and 7 khet | ||
| This recognized that the Egyptian itrw of 70 stadia was 1/10 a value of 700 stadia per degree, with a great circle circumference of 252,000 stadia. The methods discovered by Eratosthenes' were used again by ]to check the results about 150 years later. | |||
| Much confusion has existed because the Attic Greeks used a stadion of 600 pous of 304.8 mm = 185 m which doesn't agree with the reported calculations. Similarly the Roman Stadium of 625 pes of 296 mm which also equals 185m has to be rejected. Its worth observing that Eratosthenes was not an Attic Greek but rather a resident of Alexandria in Egypt which had since its conquest by the Persians and incorporation in their empire used a stadia of 300 Egyptian royal cubits or 157.5 m. | |||
| Many otherwise knowledgable people have convinced themselves that Eratosthenes' reported value was in error because of this discrepancy. Archimedes, Posidonius, Marinus and Ptolemy also used stadia which were different from the Attic, Ionian and Athenia stadia. | |||
| Marinus and Ptolemy used a stadia composed of 600 remen which were 5/4 the pous or pes and 5/6 the mh t3 or land cubit and measured 500 to a degree making 1 degree 112.5 km by their reckoning. | |||
| He established a final value of 700 stadia per degree, which implies a circumference of 252,000 stadia. The exact size of the ''stadion'' he used is no longer known (the common Attic ''stadion'' was about 185 m), but it is generally believed that Eratosthenes' value corresponds to between 39,690 ] and 46,620 km. The circumference of the Earth around the poles is now measured at around 40,008 km. Eratosthenes' method was used by ] about 150 years later. | |||
| About ] Eratosthenes is thought to have coined or to have adopted the word '']'', the descriptive study of the Earth. | About ] Eratosthenes is thought to have coined or to have adopted the word '']'', the descriptive study of the Earth. | ||
Revision as of 00:32, 24 August 2005
Eratosthenes (Ερατοσθένης) (276 BC - 194 BC) was a Greek mathematician, geographer and astronomer. His contemporaries nicknamed him 'Beta' because he was the second best in the world in many subjects.
He was born in Cyrene (now in Libya), but worked and died in Ptolemaic Alexandria. He is noted for devising a system of latitude and longitude and computing the size of the Earth.
Eratosthenes studied at Alexandria and for some years in Athens. In 236 BC he was appointed by Ptolemy III Euergetes I as librarian of the Alexandrian library. He made several important contributions to mathematics and science, and was a good friend to Archimedes. Around 255 BC he invented the armillary sphere, which was widely used until the invention of the orrery in the 18th century.
He is credited by Cleomedes in On the Circular Motions of the Celestial Bodies with having calculated the Earth's circumference ca. 240 BC, using trigonometry and knowledge of the angle of elevation of the Sun at noon in Alexandria and Syene (now Aswan, Egypt).
Eratosthenes results, that make the degree 700 stadia, imply the circumference of the earth is 252,000 stadia and would be off by 1 part in 6 if the stadia he were using were Greek or Roman stadia of 185 m.
If his results were acurate his stadia would have measured 158.57 m. As it happens this works out to 302 Egyptian royal cubits.
The Egyptians had a very well documented standard of measure called the khet which was 100 royal cubits in length and was the side of an 3ht or field called a st3t. In Greek and Roman times the Egyptian fields were generally farmed in clusters of three with one left fallow, one plowed and sowed in grain and another planted in hay for the plow animal.
This means the Egyptians clusters of fields would have been surveyed by a standard of 300 royal cubits that Eratosthenes could have found useful in his work.
From the information compiled in his library Eratosthenes would have known that the last time the experiment had been performed, on the summer solstice at local noon on the Tropic of Cancer, the Sun would have appeared at the zenith, directly overhead — though Syene was in fact slightly north of the tropic and the same conditions as previously recorded were no longer true in his time.
He also would have discovered in his reading, measurements such as those recorded by Herodotus giving the distance between Alexandria and Syene and information to the effect that the last time the experiment had been performed in his hometown of Alexandria, the angle of elevation of the Sun had been 7° south of the zenith at the same time although that also was no longer true in his time.
Assuming that Alexandria was due north of Syene- Alexandria is in fact on a more westerly longitude- and knowing from his reading that the distance from Alexandria to Syene was 5000 stadia of 300 Egyptian royal cubits of which there were 700 to a degree he would have known that the distance was a little over 7/360 of the great circle of the Earth
The distance between the cities was about 5,000 stadia or 7 degrees, 1 itrw, and 7 khet
This recognized that the Egyptian itrw of 70 stadia was 1/10 a value of 700 stadia per degree, with a great circle circumference of 252,000 stadia. The methods discovered by Eratosthenes' were used again by Posidoniusto check the results about 150 years later.
Much confusion has existed because the Attic Greeks used a stadion of 600 pous of 304.8 mm = 185 m which doesn't agree with the reported calculations. Similarly the Roman Stadium of 625 pes of 296 mm which also equals 185m has to be rejected. Its worth observing that Eratosthenes was not an Attic Greek but rather a resident of Alexandria in Egypt which had since its conquest by the Persians and incorporation in their empire used a stadia of 300 Egyptian royal cubits or 157.5 m.
Many otherwise knowledgable people have convinced themselves that Eratosthenes' reported value was in error because of this discrepancy. Archimedes, Posidonius, Marinus and Ptolemy also used stadia which were different from the Attic, Ionian and Athenia stadia.
Marinus and Ptolemy used a stadia composed of 600 remen which were 5/4 the pous or pes and 5/6 the mh t3 or land cubit and measured 500 to a degree making 1 degree 112.5 km by their reckoning.
About 200 BC Eratosthenes is thought to have coined or to have adopted the word geography, the descriptive study of the Earth.
Eratosthenes' other contributions include:
- The Sieve of Eratosthenes as a way of finding prime numbers.
- The measurement of the Sun-Earth distance, now called the astronomical unit (804,000,000 stadia).
- The measurement of the distance to the Moon (780,000 stadia).
- The measurement of the inclination of the ecliptic with an angle error 7'.
- He compiled a star catalogue containing 675 stars, which was not preserved.
- A map of the Nile's route as far as Khartoum.
- A map of the entire known world, from the British Isles to Ceylon, and from the Caspian Sea to Ethiopia. Only Hipparchus, Strabo, and Ptolemy were able to make more accurate maps in the classical and post-classical world.
Eratosthenes was known under the name β, because he supposedly proved himself to be the second in the world in many fields. He was also reputedly known for his haughty character. In 195 BC he became blind and a year later he starved himself to death.
The fragmentary collection of Hellenistic sky-myths called Catasterismi (Katasterismoi) was given an attribution to Eratosthenes, a name to conjure with, to add to its credibility.
Named after Eratosthenes
- Eratosthenes crater on the Moon.
- Eratosthenian period in the lunar geologic timescale.