Greaves enrolled at University of Leyden in 1633, where he became friends with Jacob Golius, professor of Arabic at Leyden. He enrolled at the University of Padua in 1635 along with George Ent, meeting the Dane Johan Rode (John Rhodius), an expert on ancient weights and measures, who also made a commentary on Celsus. A brief return to England was followed by a second European journey; in 1636 he sailed via Livorno (Leghorn) to Rome, dining with Ent on 5 October at the English College, Rome; he also met William Harvey, who was entertained at the college on the 12th, Gasparo Berti, Lucas Holstenius and Athanasius Kircher.