Halley supplies corrections to some of the observations recorded in De Motu Stellarum.
Of the eight books which made up his original treatise, only seven are certainly known, the first four in the original Greek, the next three are found in Arabic translations, and the eighth was restored by Edmund Halley in 1710 from certain introductory lemmas of Pappus.
The fifth book contains properties of normals and their envelopes, thus embracing the germs of the theory of evolutes, and also maxima and minima problems, such as to draw the longest and shortest lines from a given point to a conic; the sixth book is concerned with the similarity of conics; the seventh with complementary chords and conjugate diameters; the eighth book, according to the restoration of Edmund Halley, continues the subject of the preceding book.
The Conics of Apollonius was translated into Arabic by Tobit ben Korra in the 9th century, and this edition was followed by Halley in 1710.
But Edmund Halley found, by a comparison of ancient eclipses with modern observations, that the mean motion had been accelerated.