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The article is about the Continental Army but it has a sub section titled Flag that does not fit into the article. There are also incorrect dates referenced in the article. The article begins stating that is wishes to depict the relationship between congress and the continental army. The article itself only gives facts on the Continental Army and does little to establish a relationship with Congress. The citations in the article are few and far between. The links that are available lead to un-updated pages that no longer work. There are also links to user but no information supporting what they wrote in the article. those who are talking on the page are highlighting the issues with the article. Incorrect dates mis information and flat out wrong ideas are key issues with the article.

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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 [1] . It is Menelaus, a Greek mathematician and astronomer who is famous for conceiving and defining a spherical triangle[2], who is quoted saying that Theodosius is the author of the Sphaerics[3]. His works were tranated by Naṣīr al-Dīn al-Ṭūsī, Qusṭā ibn Lūqā in Bagdad [4]. 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[4] . The collection was at one point edited by al-Ṭūsī [4] . All of these works would become a part of The little astronomy, an intermediate after Euclid’s Elements and before the Almagest [4].

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 [4] . 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 [5]. The works are named Sphaerica, De habitationibus and De diebus [6] . It was Sphaerica and De habitationibus that were translated from Arabic into Latin by Gerard of Cremona in the twelfth century [7] . The Greek manuscripts were translated into Arabic around the tenth century [8] . In 1518 a Latin version was printed[9] . It was not long after that in 1529 Johannes Vögelin improved the translation of the Spherics [10]. Again in 1586, Christoph Clavius produced his own translation and commentary of the works [11] . It was not until 1721 that a English version was produced [12] . 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[13] . 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[14] . This is equivalent to the tangent of a equals sin of b times tangent of A.

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 [15] . 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[16] . 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[17].  Theodosius believed that it was day if the sun was less than 15 degrees below the horizon [18] . 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 [19] . Theodosius is also credited with a work on astronomy in which he gives a commentary on Archimedes’ Mechanics [20] . 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 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.” [21] 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 [22] . A misconception of Theodosius is that he wrote s commentary on the chapter of Theudas and Skeptical Cahpters [23]. 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 [24].

Theon of Smyrna

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Works

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Many of Theon's works have been lost. He has been mentioned in Ibn al-Nadīm’s Fihrist [25]. In the work Ibn al-Nadīm, mentions a treatise Theon wrote about Plato's writings and the exact order they should be read in.

Theon is most famous for the Expositio. It provides citations from earlier works. The book helps explain the connection between arithmetic, geometry, stereometry, music, and astronomy for philosophy students [25]. Theon explains in his work how music is divided into three distinct parts: instrumental, musical intervals expressed numerically, and the harmony of the universe [25]. Theon claims in his work to not have invented any specific musical property but he only means to expand on his predecessors such as: Thrasyllus, Adrastus, Aristoxenus, Hippasus, Eudoxus, and Plato [25]. Theon discusses the following topics within his text: Eratosthenes’ Platonikos, Adrastus ideas are talked about in the astronomical portion of the writing, Hipparchos considered the onventor of the epicyclic hypothesis by Theon, and fragments from Eudemus on pre-Socratic astronomy [25].


  1. ^ </nowiki> "Theodosius of Bithynia | Encyclopedia.com". www.encyclopedia.com.
  2. ^ "Menelaus of Alexandria | Greek mathematician". Encyclopedia Britannica.
  3. ^ "Theodosius of Bithynia | Encyclopedia.com". www.encyclopedia.com.
  4. ^ a b c d e "OU Libraries Authentication Service". search-proquest-com.ezproxy.lib.ou.edu.
  5. ^ "Theodosius biography". www-groups.dcs.st-and.ac.uk.
  6. ^ Kunitzsch, Paul; Lorch, Richard (2011). "Theodosius, De diebus et noctibus". Suhayl. International Journal for the History of the Exact and Natural Sciences in Islamic Civilisation. pp. 9–46.
  7. ^ Kunitzsch, Paul; Lorch, Richard (2011). "Theodosius, De diebus et noctibus". Suhayl. International Journal for the History of the Exact and Natural Sciences in Islamic Civilisation. pp. 9–46.
  8. ^ Kwan, Alistair (2014). "Theodosius of Bithynia". Biographical Encyclopedia of Astronomers. Springer New York. pp. 2144–2145. doi:10.1007/978-1-4419-9917-7_1372.
  9. ^ Kwan, Alistair (2014). "Theodosius of Bithynia". Biographical Encyclopedia of Astronomers. Springer New York. pp. 2144–2145. doi:10.1007/978-1-4419-9917-7_1372.
  10. ^ Kwan, Alistair (2014). "Theodosius of Bithynia". Biographical Encyclopedia of Astronomers. Springer New York. pp. 2144–2145. doi:10.1007/978-1-4419-9917-7_1372.
  11. ^ Kwan, Alistair (2014). "Theodosius of Bithynia". Biographical Encyclopedia of Astronomers. Springer New York. pp. 2144–2145. doi:10.1007/978-1-4419-9917-7_1372.
  12. ^ Kwan, Alistair (2014). "Theodosius of Bithynia". Biographical Encyclopedia of Astronomers. Springer New York. pp. 2144–2145. doi:10.1007/978-1-4419-9917-7_1372.
  13. ^ http://www-groups.dcs.st-and.ac.uk/history/Biographies/Theodosius.html. {{cite web}}: Missing or empty |title= (help)
  14. ^ "Theodosius biography". www-groups.dcs.st-and.ac.uk.
  15. ^ "Theodosius biography". www-groups.dcs.st-and.ac.uk.
  16. ^ "Theodosius biography". www-groups.dcs.st-and.ac.uk.
  17. ^ Kwan, Alistair (2014). "Theodosius of Bithynia". Biographical Encyclopedia of Astronomers. Springer New York. pp. 2144–2145. doi:10.1007/978-1-4419-9917-7_1372.
  18. ^ "Theodosius biography". www-groups.dcs.st-and.ac.uk.
  19. ^ Kwan, Alistair (2014). "Theodosius of Bithynia". Biographical Encyclopedia of Astronomers. Springer New York. pp. 2144–2145. doi:10.1007/978-1-4419-9917-7_1372.
  20. ^ Kwan, Alistair (2014). "Theodosius of Bithynia". Biographical Encyclopedia of Astronomers. Springer New York. pp. 2144–2145. doi:10.1007/978-1-4419-9917-7_1372.
  21. ^ Kwan, Alistair (2014). "Theodosius of Bithynia". Biographical Encyclopedia of Astronomers. Springer New York. pp. 2144–2145. doi:10.1007/978-1-4419-9917-7_1372.
  22. ^ Kwan, Alistair (2014). "Theodosius of Bithynia". Biographical Encyclopedia of Astronomers. Springer New York. pp. 2144–2145. doi:10.1007/978-1-4419-9917-7_1372.
  23. ^ Kwan, Alistair (2014). "Theodosius of Bithynia". Biographical Encyclopedia of Astronomers. Springer New York. pp. 2144–2145. doi:10.1007/978-1-4419-9917-7_1372.
  24. ^ Kwan, Alistair (2014). "Theodosius of Bithynia". Biographical Encyclopedia of Astronomers. Springer New York. pp. 2144–2145. doi:10.1007/978-1-4419-9917-7_1372.
  25. ^ a b c d e "Theon of Smyrna | Encyclopedia.com". www.encyclopedia.com. Retrieved 2018-12-04.