**Theodosius of Bithynia** (Greek : Θεοδόσιος; c. 169 BC –c. 100 BC) was a Greek astronomer and mathematician who wrote the * Sphaerics *, a book on the geometry of the sphere.

Born in Tripolis, in Bithynia, Theodosius was mentioned by Strabo as among the residents of Bithynia distinguished for their learning, and one whose sons were also mathematicians. He was cited by Vitruvius as having invented a sundial suitable for any place on Earth.^{ [1] }

His chief work, the *Sphaerics* (Greek : σφαιρικά), provided the mathematics for spherical astronomy, and may have been based on a work by Eudoxus of Cnidus.^{[ citation needed ]} It is reasonably complete, and remained the main reference on the subject at least until the time of Pappus of Alexandria (4th century AD).^{ [1] } The work was translated into Arabic in the 10th century, and then into Latin in the early 16th century, but these versions were faulty. Francesco Maurolico translated the works later in the 16th century.^{ [1] }

In addition to the *Sphaerics*, 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. Both were published in Latin in the 16th century.^{ [2] }

- 1 2 3 Heath 1911, p. 771.
- ↑ Heath 1911, pp. 771–772.

**Diophantus of Alexandria** was an Alexandrian mathematician, who was the author of a series of books called *Arithmetica*, many of which are now lost. His texts deal with solving algebraic equations. While reading Claude Gaspard Bachet de Méziriac's edition of Diophantus' *Arithmetica,* Pierre de Fermat concluded that a certain equation considered by Diophantus had no solutions, and noted in the margin without elaboration that he had found "a truly marvelous proof of this proposition," now referred to as Fermat's Last Theorem. This led to tremendous advances in number theory, and the study of Diophantine equations and of Diophantine approximations remain important areas of mathematical research. Diophantus coined the term παρισότης (parisotes) to refer to an approximate equality. This term was rendered as *adaequalitas* in Latin, and became the technique of adequality developed by Pierre de Fermat to find maxima for functions and tangent lines to curves. Diophantus was the first Greek mathematician who recognized fractions as numbers; thus he allowed positive rational numbers for the coefficients and solutions. In modern use, Diophantine equations are usually algebraic equations with integer coefficients, for which integer solutions are sought.

**Euclid**, sometimes called **Euclid of Alexandria** to distinguish him from Euclid of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry". He was active in Alexandria during the reign of Ptolemy I. His *Elements* is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics from the time of its publication until the late 19th or early 20th century. In the *Elements*, Euclid deduced the theorems of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory, and mathematical rigour.

**Eudoxus of Cnidus** was an ancient Greek astronomer, mathematician, scholar, and student of Archytas and Plato. All of his works are lost, though some fragments are preserved in Hipparchus' commentary on Aratus's poem on astronomy. *Sphaerics* by Theodosius of Bithynia may be based on a work by Eudoxus.

**Bithynia** was an ancient region, kingdom and Roman province in the northwest of Asia Minor, adjoining the Sea of Marmara, the Bosporus, and the Black Sea. It bordered Mysia to the southwest, Paphlagonia to the northeast along the Pontic coast, and Phrygia to the southeast towards the interior of Asia Minor.

**Aratus** was a Greek didactic poet. His major extant work is his hexameter poem *Phenomena*, the first half of which is a verse setting of a lost work of the same name by Eudoxus of Cnidus. It describes the constellations and other celestial phenomena. The second half is called the *Diosemeia*, and is chiefly about weather lore. Although Aratus was somewhat ignorant of Greek astronomy, his poem was very popular in the Greek and Roman world, as is proved by the large number of commentaries and Latin translations, some of which survive.

**Theodosius** is a given name. It may take the form **Teodósio**, **Teodosie**, **Teodosije** etc.

The * Elements* is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC. It is a collection of definitions, postulates, propositions, and mathematical proofs of the propositions. The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines.

**Apollonius of Perga** was an Ancient Greek geometer and astronomer known for his work on conic sections. Beginning from the contributions of Euclid and Archimedes on the topic, he brought them to the state prior to the invention of analytic geometry. His definitions of the terms ellipse, parabola, and hyperbola are the ones in use today.

**Theon of Alexandria** was a Greek scholar and mathematician who lived in Alexandria, Egypt. He edited and arranged Euclid's *Elements* and wrote commentaries on works by Euclid and Ptolemy. His daughter Hypatia also won fame as a mathematician.

**Phlegon of Tralles** was a Greek writer and freedman of the emperor Hadrian, who lived in the 2nd century AD.

**Pappus of Alexandria** was one of the last great Greek mathematicians of antiquity, known for his *Synagoge* (Συναγωγή) or *Collection*, and for Pappus's hexagon theorem in projective geometry. Nothing is known of his life, other than what can be found in his own writings: that he had a son named Hermodorus, and was a teacher in Alexandria.

**Autolycus of Pitane** was a Greek astronomer, mathematician, and geographer. The lunar crater Autolycus was named in his honour.

**Scholia** are grammatical, critical, or explanatory comments — original or copied from prior commentaries — which are inserted in the margin of the manuscript of ancient authors, as glosses. One who writes scholia is a **scholiast**. The earliest attested use of the word dates to the 1st century BC.

**Greek mathematics** refers to mathematics texts written during and ideas stemming from the Archaic through the Hellenistic periods, extant from the 7th century BC to the 4th century AD, around the shores of the Eastern Mediterranean. Greek mathematicians lived in cities spread over the entire Eastern Mediterranean from Italy to North Africa but were united by Greek culture and the Greek language. The word "mathematics" itself derives from the Ancient Greek: μάθημα, romanized: *máthēma*Attic Greek: [má.tʰɛː.ma]Koine Greek: [ˈma.θi.ma], meaning "subject of instruction". The study of mathematics for its own sake and the use of generalized mathematical theories and proofs is an important difference between Greek mathematics and those of preceding civilizations.

**Geminus** of Rhodes, was a Greek astronomer and mathematician, who flourished in the 1st century BC. An astronomy work of his, the *Introduction to the Phenomena*, still survives; it was intended as an introductory astronomy book for students. He also wrote a work on mathematics, of which only fragments quoted by later authors survive.

**Plato Tiburtinus** was a 12th-century Italian mathematician, astronomer and translator who lived in Barcelona from 1116 to 1138. He is best known for translating Hebrew and Arabic documents into Latin, and was apparently the first to translate information on the astrolabe from Arabic.

**Greek astronomy** is astronomy written in the Greek language in classical antiquity. Greek astronomy is understood to include the ancient Greek, Hellenistic, Greco-Roman, and Late Antiquity eras. It is not limited geographically to Greece or to ethnic Greeks, as the Greek language had become the language of scholarship throughout the Hellenistic world following the conquests of Alexander. This phase of Greek astronomy is also known as **Hellenistic astronomy**, while the pre-Hellenistic phase is known as **Classical Greek astronomy**. During the Hellenistic and Roman periods, much of the Greek and non-Greek astronomers working in the Greek tradition studied at the Musaeum and the Library of Alexandria in Ptolemaic Egypt.

**Qusta ibn Luqa** (820–912) was a Syrian Melkite Christian physician, philosopher, astronomer, mathematician and translator. He was born in Baalbek. Travelling to parts of the Byzantine Empire, he brought back Greek texts and translated them into Arabic.

**Nicomedes** was an ancient Greek mathematician.

* Sphaerics* was a set of three volumes on spherical geometry written by Theodosius of Bithynia in the 2nd century BC. These proved essential in the restoration of Euclidean geometry to Western civilization, when brought back from the Islamic world during the crusades and translated back from Arabic into Latin.

- 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 .
- Heath, Thomas Little (1911). . In Chisholm, Hugh (ed.).
*Encyclopædia Britannica*.**26**(11th ed.). Cambridge University Press. pp. 771–772.

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