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4 turn derived from μέγιστη σύνταξις) was a subject in which he was particularly interested, and during his stay at Vienna as Papal Nuncio he succeeded in communicating to Purbach his own anxiety to make Ptolemy better known in the scientific world. Purbach was on the point of starting for Italy for the purpose of collecting Greek manuscripts, when he died suddenly in 1461, but Regiomontanus succeeded to his place in the Cardinal's friendship, and set out for Italy with Bessarion in the following year.

Regiomontanus stayed about seven years in Italy, visiting the principal cities, and losing no chance of studying the Greek language and collecting Greek manuscripts. At Venice he wrote a treatise on trigonometry, which branch of mathematics he also, during the remainder of his life, continued to develop, so that he constructed a table of tangents (tabula fecunda), and probably only was prevented by his early death from completing his treatise by introducing the use of tangents therein. After his return to Germany, he settled, in 1471, at Nürnberg. This city was one of the chief centres of German industry and literary life, and no other German city had such regular commercial communication with Italy, from whence the produce of the East was brought into the market, and nowhere did the higher classes of citizens use their wealth so willingly in support of art and science. The new art of printing had recently been introduced at Nürnberg, where a regular printing-press was now working—a circumstance of particular importance to the collector of Greek writings. A wealthy citizen, Bernhard Walther (born 1430, died 1504), became at once the friend and disciple of Regiomontanus,