**Theodosius** was a Greek mathematician and astronomer who worked on the geometry of the sphere.

- Theodosius wrote verses on the spring and other types of works.
- We are indeed interested in this article in the Theodosius who wrote Sphaerics in three books.
- It would now appear that, apart from the work on Theudas and Skeptical Chapters which was almost certainly written by the same person (one assumes another author by the name of Theodosius), the rest of the entry is correct except for the final two sentences "Theodosius wrote verses on the spring and other types of works.
- He was from Tripolis." which must refer to what one has to assume is yet a third author called Theodosius.
- So Theodosius was the author of Sphaerics, a book on the geometry of the sphere, written to provide a mathematical background for astronomy.
- Theodosius defines a sphere to be a solid figure with the property that any point on its surface is at a constant distance from a fixed point (the centre of the sphere).
- The second book of Theodosius's work considers touching circles on a sphere.
- For example Theodosius proves that for a spherical triangle with angles A,B,CA, B, CA,B,C (CCC a right angle) and sides a,b,ca, b, ca,b,c where side aaa is opposite angle AAA, etc.
- Two other works by Theodosius have survived in the original Greek.
- Theodosius considers the length of the night and day at various points on the earth and claims that the day lasts for seven months at the north pole and the night for five months.
- Of course this is very strange and partly explained by Theodosius's definition of night as period of darkness and day as a period of light.
- Theodosius considered that it was 'day' if the sun was less than 15° below the horizon for then no stars were visible and he seemed to fail to understand that in the polar regions the sun can move almost parallel to the horizon.
- Theodosius also considers the two possibilities, that the length of the year is a rational multiple of the length of the day and that it is an irrational multiple.
- Of the other works mentioned in the Suda we have no reason to doubt that Theodosius wrote a commentary on the Method by Archimedes but there is no other evidence to prove whether this is correct or not.
- Theodosius is also reported to have invented a sundial suitable for all regions but nothing is known about it.

Born about 160 BC, Bithynia, Anatolia (now Turkey). Died about 90 BC.

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Ancient Arab, Ancient Greek, Applied Maths, Astronomy, Geography, Origin Turkey

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive