These did not require such marvellous mathematical powers as made Kepler and Newton immortal,the equals of Ptolemy and Hipparchus in mathematical demonstration,but only accuracy and perseverance in observations.

He was acquainted with the writings of all the previous astronomers, but accepted Hipparchus as his guide.

In the case of the moon, however, Ptolemy traced the variable inequality noticed sometimes by Hipparchus at first and last quarter, which vanished when the moon was in apogee or perigee.

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.