troduction into Europe. From what has been said of the trade relations between the East and the West, and of the probability that it was the trader rather than the scholar who carr

London, Hamburg, and Rotterdam to-day, customs that no scholar has yet described in print and that may not become known for many years, if ever. And if this be so now, how much more would it have been true

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 t

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 l

ransfer their goods to caravans and go by land to Colzom (on the Red Sea). They there re?mbark 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., mus

t the great trade routes to the far East were never closed for long, and that the customs and marks of trade

hinese ware to Roum; and from Roum to load up with brocades for Hind; and so to trade Indian steel (p?lab) to Halib. From Halib I will convey its glass to Yeman, and carry the painted cloths of Yeman back to Persia.'"[404] On the

h 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 fu

n to have been partly understood in Italy, at the opening of the eleventh century, one Constantine, an African, traveled from Italy through a great part of Africa and Asia, even on to India, for the

a princess from Constantinople. This monarch was in touch with the Moors of Spain and invited to his court numerous scholars f

nd in only a slight degree among their Jewish predecessors in the annual pilgrimage to Jerusalem, and almost wholly wanting in other pre-Christian peoples. Chief among these early pilgrims were the two Placentians, John and Antonine the Elder (c. 303), who, in their wanderings

uer Syracuse, they soon held a good part of the island, and a little later they successfully besieged the city. Before Syracuse fell, however, they had plundered the shores of Italy, even to the walls of Rome itself; and had not Leo IV, in 849, repaired the neglected fortifications, the effects of the Moslem raid of that year might have been very far-reaching. Ibn Khordā?beh, who left Bagdad in the latter part of the ninth century, gives a picture of the great commercial activity at that time in the Saracen city of Palermo. In this same century they

gorgeous E

safeguard

oa had become her p

d thence to the court of Kublai Khan, penetrating China, and returning by way of Acre in 1269 with a commission which required them to go back to China two years later. This time they

company of missionaries was large, converts were numerous, churches and Franciscan convents had been organized in the East, travelers were appealing for the truth of their accounts to the "many"

ecome acquainted with such numerals of the Orient as merchants may have used for warehouse or price marks. And the fact that Gerbert seems to hav

to Kiev and Novgorod, and thence to the East. Constantinople was a great clearing-house of commerce with the Orient,[423] and the Byzantine merchants must have been entirely familiar with the various numerals of the Eastern peoples. In the eleventh century the Italian town of Amalfi established a factory[424] in Constantinople, and had trade relations with Antioch and Egypt. Venice, as early as the ninth century, had a valuable trade with Syria and Cairo.[425] Fifty years after Gerbert died, in the time of Cnut, the Dane and the

rabs: species

oleum palmaru

bylon: Nilus la

i, varium gri

eas vestes: G

stones save only the turquoise, the Chinese (Seres) may have sent their purple vestments, and the north her s

lf in the songs of the troubadours, and the baudekin,[428] the canopy of Bagdad,[429] became common in the churches of Italy. In

numerals must of necessity have been known to many traders in a country like Italy at least as early as the ninth century, and probably even earlier, but there was no reason for preserving them

967 in company with Count Borel,[435] remaining there three years, and studying under Bishop Hatto of Vich,[436] a city in the province of Barcelona,[437] then entirely under Christian rule. Indeed, all of Gerbert's testimony is as to the influence of the Christian civilization upon his education. Thus he speaks often of his study of Boethius,[438] so that if the latter knew the numerals Gerbert would have learned them from him.[439] If Gerbert had studied in any Moorish schools he would, under the decree of the emir Hishām (787-822), have been obl

s, and became archbishop of that diocese in 991. For political reasons he returned to Italy in 996, became archbishop of Ravenna in 998, and the following year was elected to the papal chair. Far ahead of his age in wisdom, he suffered as many such scholars have even in times not so remote by being accused of heresy and witchcraft. As late as 1522, in a biography

n name of "caracteres," a word used by Radulph of Laon in the same sense a century later.[447] It is probable that Gerbert was the first to describe th

the lines between Christian and Moor at that time were sharply drawn.[451] Writers fail, however, to recognize that a commercial numeral system would have been more likely to be made known by merchants than by scholars. The itinerant peddler knew no forbidden pale in Spain, any more than he has known one in other lands. If the ?obār numerals were used for marking wares or keeping simple accounts, it was he who would have known them, and who would have been the one rather than any Arab scholar to bring them to the inquiring mind of the young French monk. The facts that Gerbert knew them only imperfectly, that he used them solely for calculati

art, and his exalted position led to the preservation of his letters to a degree that would not have been vouchsafed even by their classic excellence.[453] Richer was a monk at St. Remi de Rheims, and was doubtless a pupil of Gerbert. The latter, when archbishop of Rheims, asked Richer to write a hist

Sapiens, but who this Joseph the Wise of Spain may have been we do not know. Possibly it was he who contributed the morsel of knowledge so imperfectly assimilated by the young French monk.[457] Within a few years after Gerbert's visit two young Spanish monks of lesser fame, and doubtless with not that keen interest in mathematical matters whic

bscure documents in the history of science."[460] The most complete information in regard to this and the

prepare for him.[467] Instead of putting eight counters in say the tens' column, Gerbert would put a single counter marked 8, and so for the other places, leaving the column empty where we would place a zero, but where he, lacking the zero, had no counter to place. These counters he possibly called caracteres, a name which adhered also to the figures themselves. It is an inte

ill remain a mystery. The Semitic origin of several of the words seems probable. Wahud, thaneine, thalata, arba, kumsa, setta, sebba, timinia, taseud are given by the Rev. R. Pat

re often used, and it finally gave the name to notation.[472] Still more co

with the Roman characters, in contrast to Gerbert's use of the ?obār forms without the zero.[474] O'Creat uses three forms for zero, o, ō, and τ, as in Maximus Planudes. With this

e Hindu art of reckoning, there was strife between the abacists, the advocates of the abacus, and the algorists, those who favored the new numerals. The words cifra and algorismus cifra were used with a somewhat derisive significan

beast,

rismus-

who on such

brate the hol

t the new algorism employing the new numerals. Geoffrey C

e and bokes g

ie, longinge

stones laye

uched at his

es ther ben noumbres of augrim, that devyden thilke same degrees fro fyve to fyve," and "... the nombres ... ben writen in augrim," meaning in the way of the algorism. Thomas Usk about

reserved for fractions. Beginning with the units columns, each set of three columns (lineae is the word which Bernelinus uses) is grouped together by a semicircular arc placed above them, while a smaller arc is placed over the units column and another joins the tens and hundreds columns. Thus arose the designation arcus pictagore[482] or sometimes simply arcus.[483] The operations of addition, subtraction, and multiplication upon this form of the abacus required litt

the Roman numerals. Similarly Adelhard of Bath (c. 1130), in his work Regulae Abaci,[490] gives no reference to the new numerals, although it is certain that he knew them. Other writers on the abacu

and wished to apparel itself in a white robe of churches." And with this activity in religion came a corresponding interest in other lines. Algorisms began to appear, and knowledge from the outside world found interested listeners. Another Raoul, or Radulph, to whom we have referred as Radulph of Laon,[494] a teacher in the cloister school of his city, and the brother of Anselm of Laon[495] the celebrated theologian, wrote a treatise on music, extant but unpublished, and an arithmetic which Nagl

-mathematical literature. Jordan [497] cites numerous instances of such use from the wor

00] His interests were chiefly in the translation of Arabic works, especially such as bore upon the Aristotelian philosophy. From the standpoint of arithmetic, however, the chief interest centers about a manuscript entitled Joannis Hispalensis liber Algorismi de Practica Arismetrice which Boncompagni found in what is now the Bibliothèque nationale at Par

t erroneously, with Gernardus,[505] the author of a work on algorism. He was a physician, an astronomer, and a mathematician,

ury for the purpose of studying mathematics and Arabic. Adelhard of Bath made translations from Arabic into Latin of Al-Khowārazmī's astronomical tables[507] and of Euclid's Elements,[508] while Ro

or and bearing the date given. It contains chapters "De additione," "De diminutione," "De mediatione," "De divisione," and part of a chapter on multiplication. The numerals are in the usual

England. He died in 1167. The probability is that he acquired his knowledge of the Hindu arithmetic[514] in his native town of Toledo, but it is also likely that the knowledge of other systems which he acquired on travels increased his appreciation of this one. We have mentioned the fact that he used the first letters