Who was the first person to measure the diameter of the Earth with any degree of accuracy and how did they do?

Question

it. Best answer gets ten points in five minutes.

Answer 1

A chap named Eratosthenes. He was the curator of the great library at Alexandria about 250 BC. While traveling in the south of Egypt one summer at the town of Syene (now Aswan), he noticed that the midday sun at the solstice shone directly down a well, illuminating the bottom. He had noticed that this did not happen at home. He measured the distance between Syene and Alexandria, and noted that at Alexandria the sun was off vertical by 7.2 degrees - 1/50 of a circle. Multiplying the distance from Syene to Alexandria by 50, he came up with a number which was nearly correct. We don't know exactly how close he was, because the exact length of his unit of measurement has been lost. But his method was sound and his measurement was good.

Answer 2

Eratostheses as the first person to make a good measurement of the Earth's diameter. Eratosthenes was the librarian of the great Library of Alexandria around 250 BC. He had access to one of the largest collections of knowledge ever available up to that time (sort of like an early World Wide Web...).
While reading in the library, Eratosthenes discovered that, on a certain day in the year, the sun was directly overhead Syene, a city in the far south of Egypt. He knew the distance to Syene from other books in the library. By measuring the angle of the sun in Alexandria on the right day, he found that the Earth is about 7850 miles in diameter, very close to our modern number of 7900 miles.

Answer 3

Measurement of the Earth
Eratosthenes knew that on the summer solstice at local noon in the town of Syene on the Tropic of Cancer, the sun would appear at the zenith, directly overhead.

He also knew, from measurement, that in his hometown of Alexandria, the angle of elevation of the Sun would be 7.2° south of the zenith at the same time. Assuming that Alexandria was due north of Syene he concluded that the distance from Alexandria to Syene must be 7.2/360 of the total circumference of the Earth. The distance between the cities was known from caravan travellings to be about 5000 stadia: approximately 800 km. 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 39,690 km.

Although his method was correct, some of his assumptions and measurements were not. Syene is not exactly on the Tropic of Cancer but rather slightly north of it, and is not directly south of Alexandria; nor is the Sun at infinite distance. (Eratosthenes knew the latter, but we are not told he corrected for it.) More seriously, angles in antiquity could be measured only to degrees or quarter-degrees, and measurement of overland distances was worse. The circumference of the Earth around the poles is now measured at around 40,008 km.

Eratosthenes' method was used by Posidonius about 150 years later.

About 200 BC Eratosthenes is thought to have coined or to have adopted the word geography, the descriptive study of the Earth.