498 THE POPULAR SCIENCE MONTHLY 



tan patrons of learning, the Caliph Amiansur, who reigned during the 

 second half of the eighth century. 



For a period of five hundred years the intellectual activity of the 

 Mediterranean countries was well nigh confined to the Arabs. With 

 what extraordinary diligence the pursuit of foreign learning was made 

 by these erstwhile wanderers is evidenced by the thousands upon 

 thousands of Arabic manuscripts. The library of Hakam at Cordova 

 in Spain contained 400,000 manuscripts; the catalogue alone is in 44 

 volumes. Original work in science and mathematics did not come from 

 Arabic hands, but the debt of civilization is none the less great as they 

 were long the conservors of the learning of the Greeks and Hindus. 

 The revival of Euclid was brought about by translations made from the 

 Arabic; indeed many important Greek works in all the sciences have 

 come to us only from Arabic sources. 



The points of contact of Europeans and the Ottomans were numer- 

 ous. From Asia Minor at the east to Greece was a well-traveled route ; 

 Sicily, Sardinia and Africa were in constant communication with Italy. 

 Moorish Spain was for centuries a meeting place of English, French, 

 Polish and German scholars. 



The church played an important role in the spread of the Hindu 

 numerals over Europe, and at the beginning of the thirteenth century 

 in England, France, Germany, Italy and Poland, the arithmetic of the 

 far east was explained by churchmen who had learned of Moorish 

 teachers. However, it remained for a commercial traveler (line he 

 handled is not known) to write the epoch-making work explaining the 

 new doctrine. Leonard of Pisa traveled for business purposes in Africa, 

 Syria, Egypt, Greece and Sicily and incidentally he acquired enough 

 mathematics to make him the greatest mathematician since Archimedes. 

 His Liber Abaci, or book of the abacus, first edition written in 1202, 

 gave the first masterful exposition of the better way to reckon. It was 

 for four centuries the great work of reference in this field. 



With the knowledge of the Hindu method spread over all Europe 

 at the beginning of the thirteenth century the acceptance of the im- 

 provement might be presupposed, but as late as 1520 arithmetics were 

 published entirely in Eoman numerals. The logically self-evident step 

 to the right, to decimal fractions, required further centuries for its 

 completion. The step up, to exponents to base ten, was made rather 

 quickly, but has not yet taken its proper place in commercial work. 



It is not too much to say that the present development of modern 

 science would be impossible without our number system, yet how slow 

 the world was to accept the reform. Is not the same story being re- 

 peated in the United States and England with the decimal system of 

 weights and measures ? But the optimistic soul regards chiefly the final 

 acceptance with the comfortable assurance that the forward movement 

 is as sure as it is slow. 



