Among Thale's other accomplishments is included the accurate prediction the valid of solar eclipses, the follo probably based on his knowledge of records of previous eclipses from Babylonia. Legend also has it that he was able to apply notions of indirect measurement to calculate the distance between two ships at sea. This was probably accomplished by using a combination of some of the five geo- metric theorems referred to earlier. The name and legend of Pythagoras (580? -500? BC) appear next in this account of early Greece. Pythagoras, a native of Samos, was a philosopher, a mathematician, and a religious mystic who spent much of his life in the Greek cities of Italy. A cult of ardent followers surrounded him, established an academy at Croton, and came to be known as Py- thagoreans. Pythagoras himself became known as a religious prophet who advocated vegetarianism, taught immortality of man's soul, and declared that the union of man's soul with God took place by means of mathematics Mathematics became an important part of the Pythagorean's beliefs to the extent that natural numbers,. 1, 2, 3, 4, 5 were considered the most fundamental elements of nature, the number was the origin of all things; all things could be reduced to numbers; 10 was the best of all num bers; and 17 was a number to be greatly feared. The five pointed star formed by the diagonals of a regular pentagon was the or mark by the Babylonians.