Theodosius of Bithynia (Greek: Θεοδόσιος Theodosios; 2nd–1st century BC) was a Hellenistic astronomer and mathematician from Bithynia who wrote the Spherics, a treatise about spherical geometry, as well as several other books on mathematics and astronomy, of which two survive, On Habitations and On Days and Nights.


Little is known about Theodosius' life. The Suda (10th-century Byzantine encyclopedia) mentioned him writing a commentary on Archimedes' Method (late 3rd century BC),[1] and Strabo's Geographica mentioned mathematicians Hipparchus (c. 190c. 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 200–50 BC.[3]

Historically he was called Theodosius of Tripolis due to a confusing paragraph in the Suda which probably fused the entries about separate people named Theodosius,[4][1] and was interpreted to mean that he came either from the Tripolis in Phoenicia or the 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]


See also: Theodosius' Spherics

Theodosius' chief work, the Spherics (Greek: τὰ σφαιρικά tá sphairiká), about spherical geometry, establishes a formal foundation for the mathematics of Greek spherical astronomy similar to the foundation Euclid's Elements provides for geometry in general. Euclid's Phenomena and Autolycus's On the Moving Sphere, both dating from two centuries prior, make use of geometric relationships proven in Spherics, so it has been speculated that they may have expected readers to be familiar with a treatise on elementary spherical geometry, perhaps by Eudoxus of Cnidus (4th century BC), on which the Spherics 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 the Spherics, two other works by Theodosius have survived: On Habitations, describing the appearances of the heavens at different climes and different times of the year, and On Days and Nights, a study of the apparent motion of the Sun.

Theodosius was cited by Vitruvius as having invented a sundial suitable for any place on Earth, but nothing else is known about it.[9]

Transmission and influence

All three of Theodosius' extant treatises were transmitted together, as part of a collection now called the Little Astronomy, an assortment of shorter works on geometry and astronomy building on Euclid's Elements. During the Islamic Golden Age, the books in the Little Astronomy were translated into Arabic, and with the addition of a few new works, were known as the Middle Books, intended to fit between the Elements and Ptolemy's Almagest.[10] Spherics was translated into Arabic by Qusṭā ibn Lūqā and Thābit ibn Qurra, and translated from Arabic into Latin in the 12th century by Plato Tiburtinus and Gerard of Cremona.[8] Theodosius' works were published in Latin in the 16th century.[11]

The Spherics 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 own Spherics, which proved many additional theorems of spherical geometry. Pappus of Alexandria (4th century) commented extensively on Theodosius' Spherics and On Days and Nights in his Collection, 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.


  1. ^ a b Adler, Ada, ed. (1931). "Theodosius". Suidae Lexicon (in Greek). Vol. 2. p. 693, §Θ.142–143 (Translation from Dictionary of Scientific Biography): Theodosius, philosopher, wrote Sphaerics in three books, a commentary on the chapter of Theudas, two books On Days and Nights, a commentary on the Method 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 and Skeptical Chapters were written by someone else, perhaps a different Theodosius. The other listed works were by the Theodosius who wrote the Spherics, including presumably the (now-lost) commentary on Archimedes' Method. It is unclear whether Descriptions of Houses is a mangled reference to On Habitations, a separate now-lost work on astronomy, or perhaps a lost work on architecture.

  2. ^ Strabo (2004). Radt, Stefan (ed.). Strabons Geographika (in Greek). Vol. 3. Göttingen: Vandenhoeck & Ruprecht. IB ¶4.9, C.566, p. 490 lines 19–22. Men notable for their paideia from Bithynia have been the philosopher Xenocrates, the dialecticus Dionysius, the mathematicians Hipparchus and Theodosius and his sons, and the rhetor Cleophanes from Myrleia and the doctor Asclepiades 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.
    Translation from Bowie, Ewen (2022). "Greek High Culture in Hellenistic and Early Imperial Bithynia". Mnemosyne. 75 (1): 73–112. doi:10.1163/1568525X-bja10120.
  3. ^ Sidoli & Thomas 2023, "Theodosios's time and works", pp. 3–5.
  4. ^ Neugebauer 1975, p. 750.
  5. ^ Stone, Edmund (1721). Clavius's Commentary on the Sphericks of Theodosius Tripolitae: or, Spherical Elements. London: J. Senex. Preface. Translated from Clavius, Christopher (1586). Theodosii Tripolitae Sphaericorum Libri III (in Latin). Rome: Ex Typographia Dominici Basae.
  6. ^ Rozenfeld, Boris Abramovich (1988). A History of Non-Euclidean Geometry. Translated by Shenitzer, Abe. Springer. p. 3. ISBN 978-0-387-96458-4. Translated from Istoriya Neevklidovoi Geometrii (in Russian). Moscow: Nauka. 1976.
  7. ^ Tripolis, Greek for "three cities", was the name of several ancient cities. See Tripolis (disambiguation).
  8. ^ a b c Bulmer-Thomas 1976.
  9. ^ Heath 1911, p. 771.
  10. ^ Evans, James (1998). The History & Practice of Ancient Astronomy. Oxford University Press. "The Little Astronomy", pp. 89–91. ISBN 0-19-509539-1.
    Roughan, Christine (2023). The Little Astronomy and Middle Books between the 2nd and 13th Centuries CE: Transmissions of Astronomical Curricula (PhD thesis). New York University.
  11. ^ Heath 1911, pp. 771–772.