THE HINDU-ARABIC NUMERALS 609 



tion at Gwalior, 876 a.d. Fifty and two hundred and seventy are 

 written respectively 



So at last the decimal system was complete, and it had been worked 

 cut in the Hindu numerals. It remained now to carry them from 

 India into the countries nearby. 



The introduction of the Hindu numerals into Europe is one of the 

 obscurest matters in history. Most probably the truth can never be 

 completely discovered. This is as it should be, since the adoption of 

 these numerals was natural and slow, and not premeditated or arti- 

 ficial. After a while they were in use among the merchants of the east, 

 who carried them along the highways of the world's commerce It may 

 be that they entered into countries upon bales of goods or in the 

 accounts of traders, and so would be unnoticed by the scholars. Per- 

 haps for a long time the local mathematicians would know nothing of 

 them, and would continue to use the symbols and the systems of their 

 forefathers. It may be said, however, that the fame of the Hindu 

 characters was spreading into the countries near by even before the 

 addition of the zero. In 662 Sebocht, a Syrian ecclesiastic, writing in 

 a monastery on the Euphrates, refers to the " science of the Hindus 

 ... and of the easy method of their calculations, and of their com- 

 putation, which surpasses words. I mean that made with nine symbols." 

 No doubt there were others in the neighboring lands who came to know 

 of this wondrous art. 



Of one thing there is no doubt : the Arabs soon adopted the Hindu 

 numerals, and when they spread their conquest across the world they 

 carried these numerals with them. In the ninth century a group of 

 brilliant mathematicians were employing them at Bagdad, while a long 

 line of scholars used them in a slightly different form, the Gobar 

 numerals, in Spain. Erom the Arabs these numbers were taken by 

 Christian Europe, and for this reason came to be known for a long 

 time as Arabic numbers. 



There will always be the question whether in some form these 

 numerals were known and used in southern Europe before the coming 

 of the Arabs. It is not likely that this matter can ever be entirely 

 determined. In an eleventh century manuscript of the "Geometry 

 of Boethius there is a passage where certain numerals are introduced, 

 curiously like the Hindu symbols : 



1 t ?a2q i3 ^ 8 ? 9 



As Boethius wrote at the beginning of the sixth century this was at 

 one time thought to indicate an early introduction of the symbols, or 



