Theodosius of Bithynia
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Born in Tripolis, in Bithynia, Theodosius is cited by Vitruvius as having invented a sundial suitable for any place on Earth. His Sphaerics provided the mathematics for spherical astronomy, and may have been based on a work by Eudoxus of Cnidus. Francesco Maurolico translated his works in the 16th century. In addition to the Sphaerics, two other works by Theodosius have survived: On Habitations, describing the appearances of the heavens at different climes, and On Days and Nights, a study of the apparent motion of the Sun.
Born in Tripolis, in Bithynia. Bithynia is a place located in Turkey along the northwestern coast of the Aegean. Theodosius is cited by Vitruvius as having invented a sundial suitable for any place on Earth. His Sphaerics provided the mathematics for spherical astronomy, and may have been based on a work by Eudoxus of Cnidus. Francesco Maurolico translated his works in the 16th century. It contains about 60 propositions in total and many definitions. In addition to the Sphaerics, two other works by Theodosius have survived: On Habitations (De Habitationibus), describing the appearances of the heavens at different climes, and On Days and Nights (De Diebus et noctibus), a study of the apparent motion of the Sun. All of his works can be tied back to the works of others such as Euclid, Autolycus, Hipparchus, and Menelaus. Ultimately most of his works were incorporated into textbooks which is why they still exist today. Theodosius of Bithynia lived most likely during the first or second century BC. He is most famously known for the Sphaerics, a textbook on the geometry of the sphere and minor astronomical and astrological aspects  . It is Menelaus, a Greek mathematician and astronomer who is famous for conceiving and defining a spherical triangle, who is quoted saying that Theodosius is the author of the Sphaerics. His works were translated by Naṣīr al-Dīn al-Ṭūsī, Qusṭā ibn Lūqā in Bagdad . The three books translated were the Sphaerics, On days and nights, and On hanitations  . These works become known as The intermediates and the purpose was to teach students in schools . The collection was at one point edited by al-Ṭūsī  . All of these works would become a part of The little astronomy, an intermediate after Euclid’s Elements and before the Almagest .
Theodosius most recognized work was a compilation of three-volume text on spherical geometry, Sphaerica (translated Sphaerics), which satisfied the need for astronomers of the time to tackle the subject of sphericity. There have been many debates over the success and credibility of this book because while it does provide valuable information on everything spherical, many would argue that it contains almost no original philosophy from Theodosius. The Mathematician, T. Heath called him a “laborious compiler” and Otto Neugebauer pointed out that his theories seldom treat more than what is obvious and his proofs do little more than reword the conjecture.12 Another notable fact is that Theodosius left out the great-circle triangle, which was an important structure at the time and still remains as so today. Throughout the compilation, he rarely admits to the assumptions used and the composition of the ideas. Nonetheless, despite criticism, this text did exactly what Theodosius aimed for it to and that was explain the phenomenon of spherical geometry. The thoughts he compiles are well-organized and serve the purpose of responding to the need of one text that contains all information about this science.
He is also noted as the inventor of a sundial suitable for any specific region, as noted by Vitruvius, a Roman architect, engineer and author most famous for treatise On Architecture  . While there are no details of Theodosius every creating a sundial, there is little information discrediting what Vitruvius stated. Theodosius’ contributions consist of three works that make up the Sphaerics. The book contains to trigonometry and it was written to aid Euclid’s Elements in making up for the lack of results on the geometry if the sphere . The works are named Sphaerica, De habitationibus and De diebus  . It was Sphaerica and De habitationibus that were translated from Arabic into Latin by Gerard of Cremona in the twelfth century  . The Greek manuscripts were translated into Arabic around the tenth century  . In 1518 a Latin version was printed . It was not long after that in 1529 Johannes Vögelin improved the translation of the Spherics . Again in 1586, Christoph Clavius produced his own translation and commentary of the works  . It was not until 1721 that an English version was produced  . In his writings Theodosius defines a sphere to be a solid figure with the property that an point on its surface is a constant distance from the center of the sphere . In his works he is also cited as proving that for a spherical triangle with angles A, B, C, and sides with a, b, c, side a is opposite angle A . This is equivalent to the tangent of a equals sin of b times tangent of A.
The work of Theodosius is similar to the two works of Autylocus and both of their findings resemble those discussed in Euclid’s Elements. Books 1 and 2.1-10 of the Spherics are a strict translation of book 3 of the elements from the circle to the sphere.13
Sphaerics: Many would say that this work is closely tied to Euclid’s Elements because of the first three definitions he uses in this text. The definitions define a center of a sphere, diameter of a sphere, and the poles of a sphere and these three definitions alone are in Euclid’s book. He not only has many similarities with Euclid, but also has his own original thoughts within his text as well. For example, he thought of spheres as a bunch of circles intersecting each other at angles. De Habitationibus: A written text that predated Ptolemaic spherical astronomy. It was composed of over 30 propositions and was translated from Greek to Arabic in the late ninth century. It literally describes the lengths of the day and night times which were observed through the sun with respect to the tropics. De Diebus et noctibus: This book also predates Ptolemaic astronomy and was also translated from Greek to Arabic in the late ninth century. It also talked about the lengths of day and night with respect to the tropics Other claims Theodosius makes in his works, particularly On days and nights, are that the day last for seven months at the north pole and night last five months  . His work On days and nights aims to explain how the rotation of the Earth affects the universe. The work is divided into two books with the first being composed of thirteen propositions and the second having nineteen propositions . In On days and nights, Theodosius explains his beliefs how the views of the stars and lengths of night and day are all affected by the location of the observer. Theodosius believed that it was day if the sun was less than 15 degrees below the horizon  . Theodosius came to the conclusion in his book that if the year equals an irrational number of days than stellar phases show not annual pattern  . Theodosius is also credited with a work on astronomy in which he gives a commentary on Archimedes’ Mechanics  . These works have been deemed lost but little fragments have survived as seen in Description of Houses, a piece of work that deals with problems in architecture.
Spherical Geomoetry Spherical geometry was used mainly in the Middle Ages and Renaissance. In comparison to Euclid’s Elements of Geometry, Theodosius work satisfied the need for spherical geometry. With his three volume Spherics. Spherics is not given much praise by modern writers. Mathematician T. Heath describes Theodosius as, “simply a laborious compiler.”  He backs up this claim be explaining that there was hardly any original information in his work. Otto Negebauer, an Austrian American mathematician known for research on the history of astronomy as well as other sciences, explains that Theodosius never recognizes the significance of the great circle triangle, his theorems only explain the obvious and he seldom admits his own assumptions  . A misconception of Theodosius is that he wrote s commentary on the chapter of Theudas and Skeptical Cahpters . This was not the Theodosius of Bithynia but rather a sceptic philosopher of the second century AD with the same name who wrote both works .
- Ivor Bulmer-Thomas, "Theodosius of Bithynia," Dictionary of Scientific Biography 13:319–320.
- also on line  "Theodosius of Bithynia." Complete Dictionary of Scientific Biography. 2008. Encyclopedia.com. 25 Mar. 2015 .
- Chisholm, Hugh, ed. (1911). Encyclopædia Britannica. 26 (11th ed.). Cambridge University Press. .
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- 1 Kwan A. (2014) Theodosius of Bithynia. In: Hockey T. et al. (eds) Biographical Encyclopedia of Astronomers. Springer, New York, NY
- 2 file:///home/chronos/u-abdca5bc4753bcf58032da23c909d68395ca5c2f/Downloads/25991-Article%20Text-57821-1-10-20151116.pdf
- 3 file:///home/chronos/u-abdca5bc4753bcf58032da23c909d68395ca5c2f/Downloads/25991-Article%20Text-57821-1-10-20151116.pdf
- 4 file:///home/chronos/u-abdca5bc4753bcf58032da23c909d68395ca5c2f/Downloads/25991-Article%20Text-57821-1-10-20151116.pdf
- 5 file:///home/chronos/u-abdca5bc4753bcf58032da23c909d68395ca5c2f/Downloads/25991-Article%20Text-57821-1-10-20151116.pdf
- 6 file:///home/chronos/u-abdca5bc4753bcf58032da23c909d68395ca5c2f/Downloads/25991-Article%20Text-57821-1-10-20151116.pdf
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- 10 Theodosius, De diebus et noctibus
Paul Kunitzsch, Richard Lorch
- 11 Theodosius, De diebus et noctibus
Paul Kunitzsch, Richard Lorch
- 12 Kwan, A. (1970, January 01). Theodosius of Bithynia. Retrieved November 12, 2018.
- 13 Berggren, L. (2012). Book Review: The Spherics of Theodosius, Theodosius, Sphaerica: Arabic and Medieval Latin TranslationsTheodosius, Sphaerica: Arabic and Medieval Latin Translations. Edited by KunitzschPaul and LorchRichard (Boethius, lxii; Franz Steiner Verlag, Stuttgart, 2010). Pp. 431. €64. ISBN 978-3-515-09288-3. Journal for the History of Astronomy, 43(2), 250-252. doi:10.1177/002182861204300214