Early Greek Math & Astronomy

The History of Western Philosophy
Bertrand Russell

Ch. XXIV Early Greek Mathematics and Astronomy

The Greeks took a little from the Egyptians and a little from the Babylonians and then developed some sound mathematics.

Euclid was still regarded as the sole textbook on geometry when Bertrand Russell was a schoolboy. 

"Euclid Elements is certainly one of the greatest books ever written, and one of the most perfect
monuments of the Greek intellect. It has, of course, the typical Greek limitations: the method is
purely deductive, and there is no way, within it, of testing the initial assumptions. These
assumptions were supposed to be unquestionable, but in the nineteenth century non-Euclidean
geometry showed that they might be in part mistaken, and that only observation could decide
whether they were so" (Russell, 211)

Like Plato, Euclid had a contempt for the practical utility of his work.

The Buridan's ass argument: two bundles of hay were placed at equal distances to the right and left of the donkey. Therefore, he died of hunger. That could be mined for an interesting short story idea.

In astronomy the Greeks made leaps and strides, with some even moving away from an anthropocentric universe. Of course, it wasn't quite heliocentric yet, but the notion of earth being just one of the planets moving in space paved the way from a heliocentric theory.

Heraclides, a pupil of Plato's school postulated that the earth rotates once on its own axis every twenty-four hours and discovered that Venus and Mercury revolve around the son.

Aristarchus of Samos (310 - 230 BC) "is the most interesting of all ancient astronomers, because he advanced the complete Copernican hypothesis, that all the planets, including the earth, revolve in circles around the sun, and that the earth rotates on its axis once in twenty-four hours" (Russell, 214).
Seleucus, Aristarchus' successor fully adhered to this theory as well, but then was not adopted by any other ancient astronomer.

Eratosthenes estimated the earth's diameter within 50 miles of the actual diameter.