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110 equinox, the earth has reached (fig. 41), the sun is again in the plane of the equator, and the day is everywhere equal to the night.

83. Coppernicus devotes the first eleven chapters of the first book to this preliminary sketch of his system; the remainder of this book he fills with some mathematical propositions and tables, which, as previously mentioned (§ 74), had already been separately printed by Rheticus. The second book contains chiefly a number of the usual results relating To the celestial sphere and its apparent daily motion, treated much as by earlier writers, but with greater mathematical skill. Incidentally Coppernicus gives his measurement of the obliquity of the ecliptic, and infers from a comparison with earlier observations that the obliquity had decreased, which was in fact the case, though to a much less extent than his imperfect observations indicated. The book ends with a catalogue of stars, which is Ptolemy's catalogue, occasionally corrected by fresh observations, and rearranged so as to avoid the effects of precession. When, as frequently happened, the Greek and Latin versions of the Almagest gave, owing to copyists' or printers' errors, different results, Coppernicus appears to have followed sometimes the Latin and sometimes the Greek version, without in general attempting to ascertain by fresh observations which was right.

84. The third book begins with an elaborate discussion of the precession of the equinoxes (chapter, § 42). From a comparison of results obtained by Timocharis, by later Greek astronomers, and by Albategnius, Coppernicus infers that the amount of precession has varied, but that its average value is 50"⋅2 annually (almost exactly the true value), and accepts accordingly Tabit ben Korra's unhappy suggestion of the trepidation (chapter, § 58). An examination of the data used by Coppernicus shews that the erroneous or fraudulent observations of Ptolemy (chapter , § 50) are chiefly responsible for the perpetuation of this mistake.