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17.

Alexandrine mathematic: *

Alexandria hosted some of the greatest mathematical minds of the Hellenistic world: Euclid, Hipparchus, Eratosthenes.  Their home was the Alexandrian Musaeum, an institution founded by Ptolemy I Soter (367-283 BC), a Macedonian general & successor to Alexander the Great.  It  included the famous Library (largest library of the Classical world) and was supported by the patronage of the Ptolemies. 

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A Greek Musaeum was a place of music, poetry, philosophy, libraries.  Over 1,000 scholars lived In the Alexandrian Musaeum; staff members & scholars were salaried & paid no taxes, received free meals, room & board & servants.  They conducted scientific research, published, lectured & collected as much literature as possible from the known world; foreign texts were collected & translated from Assyrian, Persian, Jewish, Indian, and other sources. The edited versions of the Greek literary canon, from Homer and Hesiod forward, were collated & corrected by these scholars.  

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Luminaries associated with the Musaeum included the father of geometry & number-theorist Euclid; the astronomers Hipparchus (founder of trigonometry) & Eratosthenes, who argued for a spherical earth, famous for calculating Earth's circumference & for his algorithm for finding prime numbers- he became head librarian.  It also attracted the following notables, who studied, wrote or performed experiments here: Archimedes – father of engineering; Aristarchus of Samos – proposed the first heliocentric system of the universe; Pappus – mathematician; Hero – father of mechanics.

18.

Persian-Babylonian schools: * 

This map shows the Persian-Babylonians Schools consisting of the cities of Edessa, Gundisapora and Ctesiphon (in yellow).  The Sasanian king Khosrau I (531 to 579 AD) had Plato and Aristotle translated into Pahlavi (the Iranian language), taught at Gundishapur & read them himself.  Under him, many historical annals were compiled;   when Justinian I closed the schools of Athens (529 AD), 7 professors fled to Persia & where they found refuge.

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The map on the right shows the Sasanian Empire at its greatest extent c. 620 AD, under Khosrau II; the western region shows territories gained in the Byzantine–Sasanian War (602–628 AD).

19.

Gundisapora: * 

In 489 AD, the Nestorian theological and scientific centre in Edessa was closed and transferred to become the School of Nisibis with secular faculties at Gundeshapur where research was done in medicine, astronomy & mathematics.  The city also hosted a teaching hospital & library.   Under Khosrau I the Academy of Gundishapur (founded 5th century AD) became the greatest intellectual center of the time (especially famous for medicine), drawing students & teachers from across the known world.  It gave refuge to Greek philosophers, Nestorian Assyrians & Neo-Platonists fleeing religious persecution in the Byzantine Empire.  The king commissioned them to translate Greek and Syriac texts (covering medicine, astronomy, astrology, philosophy & useful crafts) into Pahlavi.  Many Assyrians settled here during the 5th century AD, most of them medical doctors from Urfa (a the leading medical center).  Teaching in the Academy was done in Syriac.

20.

Chaldean circle division: *

Late the 5th century BC, Babylonian astronomers divided the ecliptic into 12 equal "signs", by analogy to 12 schematic months of 30 days each. Each sign contained 30 degrees of celestial longitude, thus creating the first known celestial coordinate system.  Babylonian astronomers fixed the zodiac in relation to stars, placing the beginning of Cancer at the "Rear Twin Star") and the beginning of Aquarius at the "Rear Star of the Goat-Fish".  Because the division was made into equal arcs, 30° each, they constituted an ideal system of reference for predictions about a planet's longitude.  Babylonian techniques of observational measurements were rudimentary and they measured the position of a planet in reference to a set of "normal stars" close to the ecliptic as observational reference points to help positioning a planet within this ecliptic coordinate system.

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In Babylonian astronomical diaries, a planet position was given with respect to a sign of the Zodiac alone, occasionally in specific degrees within a sign; when the degrees of longitude were given, they were expressed with reference to the 30° of the Zodiac sign, not with the 360° ecliptic.

Decline of the West, Chapter II: The Meaning of Numbers
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