Auto'lycus（*)Autolu/kos), a mathematician, who is said to have been a native of Pitane in Aeolis, and the first instructor of the philosopher Arcesilaus. (D. L. 4.29.) From this, it would follow, that he lived about the middle of the fourth century B. C., and was contemporary with Aristotle. We know nothing more of his history.
WorksAutolycus wrote two astronomical treatises, which are still extant, and are the most ancient existing specimens of the Greek mathematics.
the Motion of the Sphere (περὶ κινουμένης σφαῖρας). It contains twelve propositions concerning a sphere which with its principal circles is supposed to revolve uniformly about a fixed diameter, whilst a fixed great circle (the horizon) always divides it into two hemispheres (the visible and invisible). Most of them are still explicitly or implicitly included amongst the elements of astronomy, and they are such as would naturally result from the first systematic application of geometrical reasoning to the apparent motion of the heavens.
The Motion of the Sphere may be considered as introductory to the second, which is on the risings and settings of the fixed stars, περὶ ἐπιτολῶν καὶ δύσεων in two books. Autolycus first defines the true risings and settings, and then the apparent. The former happen when the sun and a star are actually in the horizon together ; and they cannot be observed, because the sun's light makes the star invisible. The latter happen when the star is in the horizon, and the sun just so far below it that the star is visible, and there are in general four such phaenomena in the year in the case of any particular star; namely, its first visible rising in the morning, its last visible rising in the evening, its first visible setting in the morning, and last visible setting in the evening. In a favourable climate, the precise day of each of these occurrences might be observed, and such observations must have constituted the chief business of practical astronomy in its infancy; they were, moreover, of some real use. because these phaenomena afforded a means of defining the seasons of the year. A star when rising or setting is visible according to its brilliance, if the sun be from 10 to 18 degrees below the horizon. Autolycus supposes 15 degrees, but reckons them along the ecliptic instead of a vertical circle; and he proceeds to establish certain general propositions concerning the intervals between these apparent risings and settings, taking account of the star's position with respect to the ecliptic and equator. It was impossible, without trigonometry, to determine beforehand the absolute time at which any one of them would happen; but one having been observed, the rest might be roughly predicted, for the same star, by the help of these propositions. The demonstrations, and even the enunciations, are in some cases not easily understood without a globe; but the figures used by Autolycus are simple. There is nothing in either treatise to shew that he had the least conception of spherical trigonometry.