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. He determined the
inequality of the sun and the place of its apogee, as well as its mean
motion; the mean motion of the moon, of its nodes and apogee; the
equation of the moon's centre, and the inclination of its orbit. He
calculated eclipses of the moon, and used them for the correction of his
lunar tables, and he had an approximate knowledge of parallax." His
determination of the motions of the sun and moon, and his method of
predicting eclipses evince great mathematical genius. But he combined
with this determination a theory of epicycles and eccentrics which
modern astronomy discards. It was however a great thing to conceive of
the earth as a solid sphere, and to reduce the phenomena of the heavenly
bodies to uniform motions in circular orbits. "That Hipparchus should
have succeeded in the first great steps of the resolution of the
heavenly bodies into circular motions is a circumstance," says Whewell,
"which gives him one of the most distinguished places in the roll of
great astronomers." But he did even more than this: he discovered that
apparent motion