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The exact dates of Ptolemy's life are not known, but his recorded observations extend to the year 151 A.D. He was a working astronomer, and he made at least one original discovery of some significance namely, the observation of a hitherto unrecorded irregularity of the moon's motion, which came to be spoken of as the moon's evection.
His life was short, but he accomplished a great deal, and rightly ascribed the lunar inequality called evection to variations in the value of the eccentricity and in the direction of the line of apses, at the same time correctly assigning the disturbing force of the Sun as the cause.
It then gives Ptolemy's own great discovery that which has made his name immortal the discovery of the moon's evection or second inequality, reducing it to the epicyclic theory. It attempts the determination of the distances of the sun and moon from the earth with, however, only partial success.
Moreover, such observations as the precession of the equinoxes and the moon's evection are as yet unexplained, and measurements of the earth's size, and of the sun's size and distance, are so crude and imperfect as to be in one case only an approximation, and in the other an absurdly inadequate suggestion. But with all these defects, the total achievement of the Greek astronomers is stupendous.
It then gives Ptolemy's own great discovery that which has made his name immortal the discovery of the moon's evection or second inequality, reducing it to the epicyclic theory. It attempts the determination of the distances of the sun and moon from the earth, with, however, only partial success, since it makes the sun's distance but one-twentieth of the real amount.
In pure mathematics he gave methods for solving all triangles plane and spherical: he also constructed a table of chords. In astronomy, besides his capital discovery of the precession of the equinoxes just mentioned, he also determined the first inequality of the moon, the equation of the centre, and all but anticipated Ptolemy in the discovery of the evection.
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. This he called the evection, and introduced another epicycle to represent it.
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