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In H. Eves Return to Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1988.
Eratosthenes and the Mystery of the Stades
Angle between shadow and staff in Alexandria
4. That the angle formed by the shadow and the staff in Alexandria at the summer solstice is equal to 1/50th of a circle [6, p.411 ].
This assumption states that the angle formed by the shadow cast by the staff in Alexandria is “1/50th of a circle”, meaning 1/50th of 360° degrees, or 7 1/5 °= 7° 12’. Although it was used by Babylonian civilizations as early as the fifth century BCE, division of a circle into the familiar 360 degrees was not introduced to Greek science until the second century BCE by Hipparchus of Rhodes (190-120 BCE) [2, p.149]. The system of angle measure used by Eratosthenes divided the circle into 60 parts, each called a hexacontade. As will be seen, this system provides one of the most compelling arguments as to the source of the additional 2000 stades. There is no way to know if Eratosthenes made this measurement himself, but many scholars argue that he probably did measure this angle using a hemispherical sundial, known as a scaphe, which was the best astronomical instrument of the day [5, pp.153-154].
Then based on his own observation, Eratosthenes is justified in assuming that the angle formed by the shadow in Alexandria is 1/50th of a circle.