Autolycus of Pitane

He is known today for his two surviving works On the Moving Sphere and On Risings and Settings, both about spherical geometry.

Autolycus' two surviving works are about spherical geometry with application to astronomy: On the Moving Sphere and On Risings and Settings (of stars).

While the obvious application is the diurnal motion of the stars as the celestial sphere appears to rotate about an immobile Earth (as modeled at the time), Autolycus' treatise never explicitly discusses this application: its content consists entirely of elementary theorems about the arcs of great circles and parallel small circles on an abstract sphere.

[1] Two hundred years later Theodosius wrote the Spherics, a treatise establishing the fundamental definitions and constructions in spherical geometry whose content is believed to have a common origin with On the Moving Sphere in some pre-Euclidean textbook, possibly written by Eudoxus.

In contrast to later astronomical analyses by Hipparchus (2nd century BC) and Ptolemy (2nd century AD), but similarly to the planar geometry of Euclid's Elements, both Autolycus's work and Theodosius' does not involve concrete quantification or trigonometry: spherical arcs are compared in size, but not given any numerical measure.