its surface.”  Aristarchus also, according to Plutarch, explained the apparent annual motion of the sun in the ecliptic by supposing the orbit of the earth to be inclined to its axis.  There is no evidence that this great astronomer supported his heliocentric theory with any geometrical proof, although Plutarch maintains that he demonstrated it.  This theory gave great offence, especially to the Stoics; and Cleanthes, the head of the school at that time, maintained that the author of such an impious doctrine should be punished.  Aristarchus left a treatise “On the Magnitudes and Distances of the Sun and Moon;” and his methods to measure the apparent diameters of the sun and moon are considered theoretically sound by modern astronomers, but practically inexact owing to defective instruments.  He estimated the diameter of the sun at the seven hundred and twentieth part of the circumference of the circle which it describes in its diurnal revolution, which is not far from the truth; but in this treatise he does not allude to his heliocentric theory.

Archimedes of Syracuse, born 287 B.C., is stated to have measured the distance of the sun, moon, and planets, and he constructed an orrery in which he exhibited their motions.  But it was not in the Grecian colony of Syracuse, but of Alexandria, that the greatest light was shed on astronomical science.  Here Aristarchus resided, and also Eratosthenes, who lived between the years 276 and 196 B.C.  The latter was a native of Athens, but was invited by Ptolemy Euergetes to Alexandria, and placed at the head of the library.  His great achievement was the determination of the circumference of the earth.  This was done by measuring on the ground the distance between Syene, a city exactly under the tropic, and Alexandria, situated on the same meridian.  The distance was found to be five thousand stadia.  The meridional distance of the sun from the zenith of Alexandria he estimated to be 7 deg. 12’, or a fiftieth part of the circumference of the meridian.  Hence the circumference of the earth was fixed at two hundred and fifty thousand stadia,—­which is not very different from our modern computation.  The circumference being known, the diameter of the earth was easily determined.  The moderns have added nothing to this method.  He also calculated the diameter of the sun to be twenty-seven times greater than that of the earth, and the distance of the sun from the earth to be eight hundred and four million stadia, and that of the moon seven hundred and eighty thousand stadia,—­a close approximation to the truth.

Astronomical science received a great impulse from the school of Alexandria, the greatest light of which was Hipparchus, who flourished early in the second century before Christ.  He laid the foundation of astronomy upon a scientific basis.  “He determined,” says Delambre, “the position of the stars by right ascensions and declinations, and was acquainted with the obliquity of the ecliptic.