Through Alexandria then was one source:  but the special development of the Greek science and of medicine took place in the ninth century under the Eastern Caliphates.  Let me quote here a couple of sentences from Leclerc (Tome I, pp. 91-92): 

“The world has but once witnessed so marvellous a spectacle as that presented by the Arabs in the ninth century.  This pastoral people, whose fanaticism had suddenly made them masters of half of the world, having once founded their empire, immediately set themselves to acquire that knowledge of the sciences which alone was lacking to their greatness.  Of all the invaders who competed for the last remains of the Roman Empire they alone pursued such studies; while the Germanic hordes, glorying in their brutality and ignorance, took a thousand years to re-unite the broken chain of tradition, the Arabs accomplished this in less than a century.  They provoked the competition of the conquered Christians—­a healthy competition which secured the harmony of the races.

“At the end of the eighth century, their whole scientific possessions consisted of a translation of one medical treatise and some books on alchemy.  Before the ninth century had run to its close, the Arabs were in possession of all the science of the Greeks; they had produced from their own ranks students of the first order, and had raised among their initiators men who, without them, would have been groping in the dark; and they showed from this time an aptitude for the exact sciences, which was lacking in their instructors, whom they henceforward surpassed.”

It was chiefly through the Nestorians that the Arabs became acquainted with Greek medicine, and there were two famous families of translators, the Bakhtishuas and the Mesues, both Syrians, and probably not very thoroughly versed in either Greek or Arabic.  But the prince of translators, one of the finest figures of the century, was Honein, a Christian Arab, born in 809, whose name was Latinized as Joannitius.  “The marvellous extent of his works, their excellence, their importance, the trials he bore nobly at the beginning of his career, everything about him arouses our interest and sympathy.  If he did not actually create the Oriental renaissance movement, certainly no one played in it a more active, decided and fruitful part."(10) His industry was colossal.  He translated most of the works of Hippocrates and Galen, Aristotle and many others.  His famous “Introduction” or “Isagoge,” a very popular book in the Middle Ages, is a translation of the “Microtegni” of Galen, a small hand-book, of which a translation is appended to Cholmeley’s “John of Gaddesden."(11) The first printed edition of it appeared in 1475 (see Chapter iv) at Padua.

     (10) Leclerc:  Histoire de la medecine arabe, Tome I, p. 139.