doV moi pou sto

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doV moi pou sto Kai kinw thn ghn ArcimedhV Give
me a place where I may stand and I will move the
earth. Archimedes
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Eratosthenes (276 194 BCE) (Beta) Eratosthenes,
upon the death of Callimachus in 240 BCE, became
the third librarian of the Museon, a library in
the temple of the muses said to house several
hundred thousand manuscripts.
Alexandria
Syene (Aswan)
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Well at Syene Eratosthenes knew, probably from
manuscripts at the Museon, that there was a deep
vertical well at Syene where the sun shown
straight down the well on one day of the year.
Alexandria
Syene (Aswan)
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Camel caravans Eratosthenes also knew that it
took, probably from the cameleers, that it took
fifty days for the camel caravans to travel from
Syene to Alexandria, at an estimated hundred
stades per day.
Alexandria
Syene (Aswan)
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Camel caravans Stades varied in length in
different Greek cities. Pliny cites a length that
would be 157.2 meters. The stade that
Eratosthenes used may have been as long as 166.7
meters.
Alexandria
Syene (Aswan)
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Gnomon Eratosthenes gnomon was a hemispherical
bowl with horizontal lines inscribed at equal
angular intervals.
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Gnomon Eratosthenes gnomon was a hemispherical
bowl with horizontal lines inscribed at equal
angular intervals. A staphe is a vertical rod
placed on the central axis of the gnomon
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Gnomon When the gnomon is leveled the staphe is
vertical. Eratosthenes used the gnomon and
staphe to measure the angular altitude of the sun
at local noon by observing the shadow that the
staphe cast.
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Gnomon Eratosthenes measured the angle of the
sun from the zenith as 1/50th of a circle.
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Syene, 26 June 225 BCE, zenith transit, local noon
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Alexandria, 26 June 225 BCE, zenith transit,
local noon
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1/50
Alexandria
Staphe
5,000 stades
1/50
Syene
Sunlight
The circumference of the earth is therefore 50 X
5,000 stades or 250,000 stades
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The circumference of the earth is 250,000
stades At Plinys stade of 157.2 meters
Eratosthenes estimate would be 39,300
kilometers. At the larger value of 166.7 meters
the estimate would be 41,675 kilometers. Current
measurements of the equatorial circumference are
40,075 kilometers and of the polar circumference
are 40,008 kilometers. Thus Eratosthenes
estimates are between 98.15 and 104.08 of the
currently accepted mean of the equatorial and
polar circumferences.
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Eratosthenes measurement of the Zenith angle of
the Summer Solstice sun at Alexandria was 1/50th
of a circle, 7.2. The program SkyMap computes
the angle for 250 BCE as 7.5. Alexandria is
not due north of Syene, an assumption of
Erastosthenes. It is about three degrees of
Longitude west of Syene. The straight line
distance from Syene to Alexandria is 837
kilometers, the northing component of that
distance is 783 kilometers. Eratosthenes
calculation, depending upon the value of the
stade, is 786 to 833 kilometers.
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