remained as conquerors. The power of the Goths, who had held Spain for three centuries, was shattered at the battle of Jerez de la Frontera in 711, and almost immediately the Moors became masters of Spain and so remained for five hundred years, and masters of Granada for a much longer period. Until 850 the Christians were absolutely free as to religion and as to holding political office, so that priests and monks were not infrequently skilled both in Latin and Arabic, acting as official translators, and naturally reporting directly or indirectly to Rome. There was indeed at this time a complaint that Christian youths cultivated too assiduously a love for the literature of the Saracen, and married too frequently the daughters of the infidel.[[396]] It is true that this happy state of affairs was not permanent, but while it lasted the learning and the customs of the East must have become more or less the property of Christian Spain. At this time the ġobār numerals were probably in that country, and these may well have made their way into Europe from the schools of Cordova, Granada, and Toledo.
Furthermore, there was abundant opportunity for the numerals of the East to reach Europe through the journeys of travelers and ambassadors. It was from the records of Suleimān the Merchant, a well-known Arab trader of the ninth century, that part of the story of Sindbād the Sailor was taken.[[397]] Such a merchant would have been particularly likely to know the numerals of the people whom he met, and he is a type of man that may well have taken such symbols to European markets. A little later,
Abū 'l-Ḥasan ‛Alī al-Mas‛ūdī (d. 956) of Bagdad traveled to the China Sea on the east, at least as far south as Zanzibar, and to the Atlantic on the west,[[398]] and he speaks of the nine figures with which the Hindus reckoned.[[399]]
There was also a Bagdad merchant, one Abū 'l-Qāsim ‛Obeidallāh ibn Aḥmed, better known by his Persian name Ibn Khordāḍbeh,[[400]] who wrote about 850 A.D. a work entitled Book of Roads and Provinces[[401]] in which the following graphic account appears:[[402]] "The Jewish merchants speak Persian, Roman (Greek and Latin), Arabic, French, Spanish, and Slavic. They travel from the West to the East, and from the East to the West, sometimes by land, sometimes by sea. They take ship from France on the Western Sea, and they voyage to Farama (near the ruins of the ancient Pelusium); there they transfer their goods to caravans and go by land to Colzom (on the Red Sea). They there reëmbark on the Oriental (Red) Sea and go to Hejaz and to Jiddah, and thence to the Sind, India, and China. Returning, they bring back the products of the oriental lands.... These journeys are also made by land. The merchants, leaving France and Spain, cross to Tangier and thence pass through the African provinces and Egypt. They then go to Ramleh, visit Damascus, Kufa, Bagdad, and Basra, penetrate into Ahwaz, Fars, Kerman, Sind, and thus reach India and China." Such travelers, about 900 A.D., must necessarily have spread abroad a knowledge of all number
systems used in recording prices or in the computations of the market. There is an interesting witness to this movement, a cruciform brooch now in the British Museum. It is English, certainly as early as the eleventh century, but it is inlaid with a piece of paste on which is the Mohammedan inscription, in Kufic characters, "There is no God but God." How did such an inscription find its way, perhaps in the time of Alcuin of York, to England? And if these Kufic characters reached there, then why not the numeral forms as well?
Even in literature of the better class there appears now and then some stray proof of the important fact that the great trade routes to the far East were never closed for long, and that the customs and marks of trade endured from generation to generation. The Gulistān of the Persian poet Sa‛dī[[403]] contains such a passage:
"I met a merchant who owned one hundred and forty camels, and fifty slaves and porters.... He answered to me: 'I want to carry sulphur of Persia to China, which in that country, as I hear, bears a high price; and thence to take Chinese ware to Roum; and from Roum to load up with brocades for Hind; and so to trade Indian steel (pûlab) to Halib. From Halib I will convey its glass to Yeman, and carry the painted cloths of Yeman back to Persia.'"[[404]] On the other hand, these men were not of the learned class, nor would they preserve in treatises any knowledge that they might have, although this knowledge would occasionally reach the ears of the learned as bits of curious information.
There were also ambassadors passing back and forth from time to time, between the East and the West, and in particular during the period when these numerals probably began to enter Europe. Thus Charlemagne (c. 800) sent emissaries to Bagdad just at the time of the opening of the mathematical activity there.[[405]] And with such ambassadors must have gone the adventurous scholar, inspired, as Alcuin says of Archbishop Albert of York (766-780),[[406]] to seek the learning of other lands. Furthermore, the Nestorian communities, established in Eastern Asia and in India at this time, were favored both by the Persians and by their Mohammedan conquerors. The Nestorian Patriarch of Syria, Timotheus (778-820), sent missionaries both to India and to China, and a bishop was appointed for the latter field. Ibn Wahab, who traveled to China in the ninth century, found images of Christ and the apostles in the Emperor's court.[[407]] Such a learned body of men, knowing intimately the countries in which they labored, could hardly have failed to make strange customs known as they returned to their home stations. Then, too, in Alfred's time (849-901) emissaries went
from England as far as India,[[408]] and generally in the Middle Ages groceries came to Europe from Asia as now they come from the colonies and from America. Syria, Asia Minor, and Cyprus furnished sugar and wool, and India yielded her perfumes and spices, while rich tapestries for the courts and the wealthy burghers came from Persia and from China.[[409]] Even in the time of Justinian (c. 550) there seems to have been a silk trade with China, which country in turn carried on commerce with Ceylon,[[410]] and reached out to Turkestan where other merchants transmitted the Eastern products westward. In the seventh century there was a well-defined commerce between Persia and India, as well as between Persia and Constantinople.[[411]] The Byzantine commerciarii were stationed at the outposts not merely as customs officers but as government purchasing agents.[[412]]