THEODOSIUS, Greek geometer and astronomer, was the author of three works included in the collection of treatises known as the "Little Astronomy" or "Astronomer" (6 gtKpos p,evos or He was not "of Tripolis," but came from Bithynia, as we gather from Strabo, who mentions, among natives of Bithynia famous for their learning, "Hipparchus, Theodosius and his sons, mathematicians"; he is also evidently the Theodosius mentioned by Vitruvius as the inventor of a universal sun-dial (horologiunt rpos rav at,ua). He lived, therefore, not later than the ist century B.C.
His chief work, the Sphaerica, in three books, is a tolerably com plete treatise on the pure geometry of the sphere, and was still the classical book on the subject in Pappus's time. It does not con tain (except for a faint suggestion in iii. 11-12) any trace of spherical trigonometry, which, on the other hand, was the special subject of the work with the same title by Menelaus of Alexandria, who lived at the end of the ist century.
From the fact that both Autolycus of Pitane in his Moving Sphere and Euclid in his Phaenomena assume without proof vari ous propositions given by Theodosius, we conclude that already in the 4th century B.C. there existed a textbook on Sphaerica scarcely
differing, in its essential contents, from Theodosius's work; the role of Theodosius was therefore mainly that of editor and elabo rator of previously existing material. The Sphaerica was trans lated into Arabic in the 9th century, in part by Qusta b. Lucia, and in part by Thabit b. Qurra. Latin translations were made from the Arabic in the 12th century by Plato of Tivoli (Tiburtinus) and Gherard of Cremona, and various editions in Latin appeared from 1518 onwards, including one by Barrow (Theodosii Sphaerica, Metkodo Novo Illustrata et Succincte demonstrate, London, 1675). We now have a definitive Greek text (with Latin translation) by J. L. Heiberg (Berlin, 1927).
The two other works of Theodosius which have come down to us were first published in a Latin translation by Joseph Auria, On Days and Nights, in two books (with scholia, etc.) in 1591, and the tract On Habitations (IIepi oiKflo&ov) in 1587 (Rome) ; a critical edition of the Greek text of both (with Latin translation) by Ru dolf Fecht appeared in Berlin in 1927. (T. L. H.)