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The mathematics and astronomy of the Greeks had been known in medieval western Europe only through often imperfect translations, some of them made from Arabic intermediary texts rather than the Greek originals. The papal curia became a center for the recovery of the original Greek manuscripts, often very old and remarkably elegant, and the production of new translations of these works. Ptolemy's "Geography" -- the book which inspired Columbus to attempt his voyage, and remains the model of all systematic atlases -- was dedicated to Popes Gregory XII and Alexander V by its first translator, the apostolic secretary Jacopo Angeli. Illustrated texts of this elegant atlas found readers everywhere in Europe. Nicholas V supported translations of the greatest of Greek mathematicians, Archimedes, and the greatest of Greek astronomers, Ptolemy. Cardinal Bessarion collected a vast range of Greek texts (which eventually wound up in Venice, as the nucleus of another great Renaissance library). A scholar whom he helped in many ways, Joannes Regiomontanus, became the first western European in centuries really to master Ptolemy's astronomy, which had been preserved and improved in the Islamic world. His work done in and for the curia laid the essential foundations on which Copernicus and other innovators built a new astronomy in the sixteenth century, using the Greek texts as their basic source of data and methods.