Historians have chosen the discovery of America as a convenient date for dividing modern times from the Middle Ages, a conventional point for changing editors and attitudes. Yet the history of science, the history of ideas, and perhaps especially the history of the expansion of Europe all serve to remind us that the division is an arbitrary one. The world of Ptolemy did not suddenly become the world of Mercator. On the contrary, a traditional cosmography was gradually adjusted in the light of widening experience, and even Columbus's remarkable discovery forms part of a long process that has its origins deeply hidden in the Middle Ages. Behind his venture across the Atlantic lies the whole range of the Portuguese discoveries of the fifteenth century leading up to the finding of the sea-route to India. At their head stands the conquest of Ceuta in 1415, when the Portuguese established their first overseas possession and thus launched the movement of European expansion. This expansion in turn is the inversion of the Muslim conquest of the Iberian peninsula. The main phases of peninsular medieval history thus provide the background of the discoveries—the collapse of the ‘Ummaiyad caliphate after 1002, which opened the centre of the peninsula immediately and the south ultimately to the Christian advance; the conquest of Lisbon in 1147, the first Atlantic seaport where the Gothic north met the Mozarabic south; the capture of Seville and the opening of the straits of Gibraltar to the trade of northern and southern Europe; the intervention of the peninsular states in the affairs of Muslim North Africa; the expansion of Italian commerce from the Mediterranean into the Atlantic, and the confluence of Italian and northern European enterprise and capital in Portugal.