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 of the fixed stars round the axis of the ecliptic, which is called the Precession of the Equinoxes,—­one of the greatest discoveries in astronomy.  He maintained that the precession was not greater than fifty-nine seconds, and not less than thirty-six seconds.  Hipparchus also framed a catalogue of the stars, and determined their places with reference to the ecliptic by their latitudes and longitudes.  Altogether he seems to have been one of the greatest geniuses of antiquity, and his works imply a prodigious amount of calculation.

Astronomy made no progress for three hundred years, although it was expounded by improved methods.  Posidonius constructed an orrery, which exhibited the diurnal motions of the sun, moon, and five planets.  Posidonius calculated the circumference of the earth to be two hundred and forty thousand stadia, by a different method from Eratosthenes.  The barrenness of discovery from Hipparchus to Ptolemy,—­the Alexandrian mathematician, astronomer, and geographer in the second century of the Christian era,—­in spite of the patronage of the royal Ptolemies of Egypt, was owing to the want of instruments for the accurate measure of time (like our clocks), to the imperfection of astronomical tables, and to the want of telescopes.  Hence the great Greek astronomers were unable to realize their theories.  Their theories however were magnificent, and evinced great power of mathematical combination; but what could they do without that wondrous instrument by which the human eye indefinitely multiplies its power?  Moreover, the ancients had no accurate almanacs, since the care of the calendar belonged not so much to the astronomers as to the priests, who tampered with the computation of time for sacerdotal objects.  The calendars of different communities differed.  Hence Julius Caesar rendered a great service to science by the reform of the Roman calendar, which was exclusively under the control of the college