Theodosius' Spherics

Several of the definitions and theorems in the Spherics were used without mention in Euclid's Phenomena and two extant works by Autolycus concerning motions of the celestial sphere, all written about two centuries before Theodosius.

It has been speculated that this tradition of Greek "spherics" – founded in the axiomatic system and using the methods of proof of solid geometry exemplified by Euclid's Elements but extended with additional definitions relevant to the sphere – may have originated in a now-unknown work by Eudoxus, who probably established a two-sphere model of the cosmos (spherical Earth and celestial sphere) sometime between 370–340 BC.

The Spherics follows the general presentation style of the Elements, with definitions followed by a list of theorems (propositions), each of which is first stated abstractly as prose, then restated with points lettered for the proof.

It also differs from the approach taken in Menelaus' Spherics, a treatise of the same title written 3 centuries later, which treats the geometry of the sphere intrinsically, analyzing the inherent structure of the spherical surface and circles drawn on it rather than primarily treating it as a surface embedded in three-dimensional space.

Other works in the collection included Aristarchus' On the Sizes and Distances, Autolycus' On Rising and Settings and On the Moving Sphere, Euclid's Catoptrics, Data, Optics, and Phenomena, Hypsicles' On Ascensions, Theodosius' On Geographic Places and On Days and Nights, and Menelaus' Spherics.