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The accomplishments of Greek mathematicians survived throughout Late Antiquity and the Middle Ages through a long and indirect history. Much of the work of Euclid, Archimedes, and Apollonius, along with later authors such as Hero and Pappus, were copied and studied in both Byzantine culture and in Islamic centers of learning. Translations of these works began already in the 12th century, with the work of translators in Spain and Sicily, working mostly from Arabic and Greek sources into Latin. Two of the most prolific were Gerard of Cremona and William of Moerbeke. The greatest of all translation efforts, however, took place in the 15th and 16th centuries in Italy, as attested by the numerous manuscripts dating from this period currently found in European libraries. Virtually all leading mathematicians of the era were obsessed with the need for restoring the mathematical works of the ancients. Not only did humanists assist mathematicians with the retrieval of Greek manuscripts, they also took an active role in translating these work into Latin, often commissioned by religious leaders such as Nicholas V and Cardinal Bessarion. Some of the leading figures in this effort include Regiomontanus, who made a copy of the Latin Archimedes and had a program for printing mathematical works; Commandino (15091575), who likewise produced an edition of Archimedes, as well as editions of works by Euclid, Hero, and Pappus; and Maurolyco (14941575), who not only translated the work of ancient mathematicians but added much of his own work to these. Their translations ensured that the next generation of mathematicians would be in possession of techniques far in advance of what it was generally available during the Middle Ages. It must be borne in mind that the mathematical output of the 15th and 16th centuries was not exclusively limited to the works of the ancient Greeks. Some mathematicians, such as Tartaglia and Luca Paccioli, welcomed and expanded on the medieval traditions of both Islamic scholars and people like Jordanus and Fibonnacci. Giordano Bruno was also one to critique the works of people like Aristotle, whom he believed to have a flawed logic and developed a mathematical doctrine for the computation of partial physics, with Bruno attempting to transform theories of nature.

=== Physics === The progress being made in mathematics was complemented by advancements in physics, with people attempting to bridge the gap between the two fields and question Aristotelian ideas. The revived investigation of physics opened up many opportunities in subfields like mechanics, optics, navigation, and cartography. Mechanical theories had originated with the Greeks, especially Aristotle and Archimedes. Mechanics and philosophy had been related disciplines in ancient Greece, and only in the Renaissance did the two subjects begin to split. A lot of the work of developing new mechanical ideas and theories was carried out by Italians such as Rafael Bombelli, though the Fleming Simon Stevin also provided many ideas. Navigation was an important topic of the time, and many innovations were made that, with the introduction of better ships and applications of the compass, would later lead to geographical discoveries. The calculations involved in navigation proved to be difficult, with the technology of the time unable to accuately predict weather or determine one's geographic position. Determining one's longitude proved especially challenging, since one's local time need to be calculated on the basis of an astronomical observation. One theory that was tested was to record the time of an eclipse and use Regiomontanus' Ephemerides to compare it with Nuremberg time or Zacuto's Almanach perpetuum to compare it with Salamanca time, though the margin of error in such calculations was unacceptably great (around 25.5 degrees). Until longitude could be accurately determined, navigators had to rely on dead reckoning, with its many uncertainties.

=== Medicine ===

With the Renaissance came an increase in experimental investigation, principally in the field of dissection and body examination, thus advancing our knowledge of human anatomy. The development of modern neurology began in the 16th century with Andreas Vesalius, who described the anatomy of the brain and other organs; he had little knowledge of the brain's function, thinking that it resided mainly in the ventricles. Understanding of medical sciences and diagnosis improved, but with little direct benefit to health care. Few effective drugs existed, beyond opium and quinine. William Harvey provided a refined and complete description of the circulatory system. The most useful tomes in medicine, used both by students and expert physicians, were materiae medicae and pharmacopoeiae.

== See also == Continuity thesis The Copernican Question Renaissance magic Renaissance technology

== Notes ==

== References == Dear, Peter. Revolutionizing the Sciences: European Knowledge and Its Ambitions, 15001700. Princeton: Princeton University Press, 2001. Debus, Allen G. Man and Nature in the Renaissance. Cambridge: Cambridge University Press, 1978. Grafton, Anthony, et al. New Worlds, Ancient Texts: The Power of Tradition and the Shock of Discovery. Cambridge: Belknap Press of Harvard University Press, 1992. Grant, Edward (1971). Physical Science in the Middle Ages. Cambridge University Press. ISBN 9780521292948. Hall, Marie Boas. The Scientific Renaissance, 14501630. New York: Dover Publications, 1962, 1994.