In the third book he treats of the quan tity of the year, and of the unequal mo tion of the sun through the zodiac : lie here gives the method of computing the mean motion of the sun, with tables of the same ; and likewise treats of the in equality of days and nights.
In the fourth book he treats of the lu nar motions, and their various phenome na; he gives tables for finding the moon's mean motions, with her latitude and lon gitude ; he discourses largely concerning lunar epicycles ; and by comparing the times of a great number of eclipses men tioned by Hipparcus, Calippus, and others, he has computed the places of the sun and moon, according to their mean motions, from the first year of Na bonazar, king of Egypt, to his own time.
In the fifth book he treats of the instru ment called the astrolabe , he treats also of the eccentricity of the lunar orbit, and the inequality of the moon's motion ac cording to her distance from the sun ; he also gives tables and an universal canon for the inequality of the lunar motions : he then treats of the different aspects or phases of the moon, and gives a com putation of the diameter of the sun and moon, with the magnitude of the sun, moon, and earth, compared together ; he states also the different measures of the distance of the sun and moon, accordin,g as they are determined by ancient mathe maticians and philosophers.
In the sixth book he treats of the con junctions and oppositions of the sun and moon, with tables for computing the mean time when they happen ; of the boundaries of solar and lunar eclipses ; of the tables and methods of computing the eclipses of the sun and moon, with many other particulars.
In the seventh book he treats of the fixed stars, and shows the methods of de scribing them, in their various constella tions, on the surface of an artificial sphere or globe ; he rectifies the places of the stars to his own time, and shows how dif ferent those places were then, from what they had been in the times of Timocharis, Hipparcus, Calippus, and o thers : he then lays down a catalogue of the stars in each of the northern constel lations, with their latitude, longitude, and magnitudes.
In the eighth book he gives a like ca talogue of the stars in the constellations of the southern hemisphere, and in the twelve signs or constellations of the zo diac. This is the first catalogue of the stars now extant, and forms the most va luable part of Ptolemy's works. He then treats of the galaxy, or milky-way ; also of the planetary aspects, with the rising and setting of the sun, moon, and stars.
In the ninth book lie treats of the or der of the sun, moon, and planets, with the periodical revolutions of the five planets ; then he gives tables of the mean motions, beginning with the theory of Mercury, and showing its various phe nomena with respect to the earth.
The tenth book begins with the theory of the planet Venus, treating of its great est distance from the sun ; of its epicycle, eccentricity, and periodical motions ; it then treats of the same particulars in the planet Mars.
The eleventh book treats of the same circumstances in the theory of the pla nets Jupiter and Saturn. It also corrects all the planetary motions, from observa tions made from the time of Nabonazar to his own.
The twelfth book treats of the retro gressive motion of the several planets, giving also tables of their stations, and of the greatest distances of Venus and Mer cury from the sun.
The thirteenth book treats of the se veral hypotheses of the latitude of the five planets ; of the greatest latitude or inclination of the orbits of the five pla nets, which are computed and disposed in tables ; of the rising and setting of the planets, with tables of them. Then fol lows a conclusion or winding-up of the whole work.
This great work of Ptolemy will al ways be valuable, on account of the ob servations he gives of the places of the stars and planets in former times, and according to ancient philosophers and as tronomers, that were then extant ; but principally on account of the Large and curious catalogue of the stars, which be ing compared with their places at pre sent, we thence deduce the true quantity of their slow progresSive motion, accord ing to the order of the signs, or of the precession of the equinoxes.