Theodosius of Bithynia (Ancient Greek:ΘεοδόσιοςTheodosios; 2nd–1st century BC) was aHellenisticastronomer andmathematician fromBithynia who wrote theSpherics, a treatise aboutspherical geometry, as well as several other books on mathematics and astronomy, of which two survive,On Habitations andOn Days and Nights.
Little is known about Theodosius' life. TheSuda (10th-centuryByzantine encyclopedia) mentioned him writing a commentary onArchimedes'Method (late 3rd century BC),[1] andStrabo'sGeographica mentioned mathematiciansHipparchus (c. 190 –c. 120 BC) and "Theodosius and his sons" as among the residents of Bithynia distinguished for their learning.[2]Vitruvius (1st century BC) mentioned a sundial invented by Theodosius. Thus Theodosius lived sometime after Archimedes and before Vitruvius, likely contemporaneously with or after Hipparchus, probably sometime between 200 and 50 BC.[3]
Historically he was calledTheodosius of Tripolis due to a confusing paragraph in theSuda which probably fused the entries about separate people named Theodosius,[4][1] and was interpreted to mean that he came either from theTripolis in Phoenicia orthe one in Africa.[5] Some sources claim he moved from Bithynia to Tripolis,[6] or came from a hypothetical city called Tripolis in Bithynia.[7]
Theodosius' chief work, theSpherics (Ancient Greek:τὰ σφαιρικάtá sphairiká), aboutspherical geometry, establishes a formal foundation for the mathematics of Greekspherical astronomy similar to the foundationEuclid'sElements provides for geometry in general. Euclid'sPhenomena andAutolycus'sOn the Moving Sphere, both dating from two centuries prior, make use of geometric relationships proven inSpherics, so it has been speculated that they may have expected readers to be familiar with a treatise on elementary spherical geometry, perhaps byEudoxus of Cnidus (4th century BC), on which theSpherics may have been based.[8] However, no mention of this hypothetical earlier work or its author remains today, and it is also plausible that Theodosius was the first to formalize material which had been previously justified by informal physical demonstrations on a globe or armillary sphere.
In addition to theSpherics, two other works by Theodosius have survived:On Habitations, describing the appearances of the heavens at differentclimes and different times of the year, andOn Days and Nights, a study of the apparent motion of the Sun.
Theodosius was cited byVitruvius as having invented asundial suitable for any place on Earth, but nothing else is known about it.[9]
All three of Theodosius' extant treatises were transmitted together, as part of a collection now called theLittle Astronomy, an assortment of shorter works on geometry and astronomy building on Euclid'sElements. During theIslamic Golden Age, the books in theLittle Astronomy were translated intoArabic, and with the addition of a few new works, were known as theMiddle Books, intended to fit between theElements andPtolemy'sAlmagest.[10]Spherics was translated into Arabic byQusṭā ibn Lūqā andThābit ibn Qurra, and translated from Arabic into Latin in the 12th century byPlato Tiburtinus andGerard of Cremona.[8] Theodosius' works were published in Latin in the 16th century.[11]
TheSpherics was widely copied and highly influential, serving as a theoretical foundation for spherical geometry and astronomy for millennia.Menelaus of Alexandria (c. 100 AD) extended it with his ownSpherics, which proved many additional theorems of spherical geometry.Pappus of Alexandria (4th century) commented extensively on Theodosius'Spherics andOn Days and Nights in hisCollection,Book VI.[8]Spherics was continuously copied and studied in Greek manuscript throughout the Byzantine period, and was a foundational text for medieval Islamic astronomy and for European astronomy starting in the 12th century.
Theodosius, philosopher, wroteSphaerics in three books, a commentary on the chapter of Theudas, two booksOn Days and Nights, a commentary on theMethod of Archimedes,Descriptions of Houses in three books,Skeptical Chapters, astrological works,On Habitations. Theodosius wrote verses on the spring and other types of works. He was from Tripolis.Θεοδόσιος, φιλόσοφος. ἔγραψε Σφαιρικὰ ἐν βιβλίοις γ', ̔Υπόμνημα εἰς τὰ Θευδα̂ κεφάλαια, Περὶ ἡμερω̂ν καὶ νυκτω̂ν δύο, ̔Υπόμνημα εἰς τὸ ̓Αρχιμήδους ̓Εφόδιον, Διαγραφὰς οἰκιω̂ν ἐν βιβλίοις τρισί, Σκεπτικὰ κεφάλαια, ̓Αστρολογικά, Περὶ οἰκήσεων. Θεοδόσιος: ἔγραψε δι' ἐπω̂ν εἰς τὸ ἔαρ, καὶ ἕτερα διάφορα. ἠ̂ν δὲ Τριπολίτης.
This text was historically taken to refer to a single person, but the sentences about the Theodosius from Tripoli who wrote verses about the spring were likely intended to represent a separate entry. Furthermore,Theudas lived after Theodosius of Bithynia; the commentary on Theudas andSkeptical Chapters were written by someone else, perhaps a different Theodosius. The other listed works were by the Theodosius who wrote theSpherics, including presumably the (now-lost) commentary on Archimedes'Method. It is unclear whetherDescriptions of Houses is a mangled reference toOn Habitations, a separate now-lost work on astronomy, or perhaps a lost work on architecture.
Men notable for theirpaideia from Bithynia have been the philosopherXenocrates, thedialecticusDionysius, the mathematicians Hipparchus and Theodosius and his sons, and therhetor Cleophanes from Myrleia and the doctorAsclepiades from Prusias.ἄνδρες δ’ ἀξιόλογοι κατὰ παιδείαν γεγόνασιν ἐν τῇ Βιθυνίᾳ Ξενοκράτης τε ὁ φιλόσοφος καὶ Διονύσιος ὁ διαλεκτικὸς καὶ Ἵππαρχος καὶ Θεοδόσιος καὶ οἱ παῖδες αὐτοῦ μαθηματικοὶ Κλεοφάνης τε ῥήτωρ ὁ Μυρλεανὸς Ἀσκληπιάδης τε ἰατρός ὁ Προυσιεύς. Older edition:Strabo (1852).Meineke, August (ed.).Strabonis Geographica (in Greek). Vol. 2. Leibzig: Teubner. p. 795 lines 13–14.
