Final answer:
Eratosthenes's calculation of the Earth's circumference was based on the angle of the Sun's rays and the known distance between Syene and Alexandria. His method concluded that the Earth's circumference was 250,000 stadia. The claim that a degree of longitude on the equator is about 128 km is false according to his findings.
Step-by-step explanation:
The statement that Eratosthenes estimated the size of the degree of longitude on the equator to be about 128 km (79.5 mi) is false. Eratosthenes, the ancient Greek mathematician and astronomer accurately calculated the Earth's circumference using geometric principles and observations of the Sun. His calculation was based on the observation that in Syene (modern Aswan, Egypt) the Sun was directly overhead at noon on the summer solstice while at the same time in Alexandria there was an angle of 7° to the vertical.
Knowing the distance between Syene and Alexandria was approximately 5000 stadia, and the angle of the Sun's shadow suggested the cities were 1/50 of the full 360° around the Earth, he multiplied 5000 by 50 to get a total Earth circumference of 250,000 stadia. Although the exact length of a stadium is debated, the commonly used conversion is around 157.5 meters which would make a single degree of longitude much less than 128 km.