OF TUB UNIVERSE. THE ARABIANS. 227 



The present work is not the place for entering more fully 

 on. this subject, which was treated by me many years ago in 

 two memoirs presented in 1819 and in 1829 to the Aca- 

 demic des Inscriptions at Paris, and the Akademie deir> 

 Wissenschaften at Berlin ; ( 359 ) but in an historical problem, 

 in which much still remains to be discovered, the question 

 arises, whether the highly ingenious artificial idea of value 

 b) position, which appears both in the Tuscan Abacus and> 

 in the Suan-pan of the interior of Asia, was separately dis- 

 covered in the East and in the West ; or whether, through 

 the direction of the commerce of the world under the Lagidse, 

 it. made its way from the western peninsula of India to 

 Alexandria, and subsequently, in the renewal of the dreams 

 of the Pythagoreans, was represented as a discovery of 

 their founder. We need not dwell on the mere possibility 

 of ancient relations with which we are entirely unacquainted ,> 

 having subsisted prior to the 60th Olympiad. Why may 

 we not suppose that, under a sense of similar wants, the 

 same combinations of ideas may have presented themselves 

 separately to highly-gifted nations of different races ? 



The algebra of the Arabians, including what they had 

 received from the Greeks and the Indians and what they 

 had themselves originated, notwithstanding its great defi- 

 ciency in symbolic notation, exercised a beneficial influence 

 during the brilliant period of the Italian mathematicians of the 

 middle ages; the Arabians have also the merit of having by 

 their writings, and by their extensive commercial intercourse, 

 accelerated the use of the Indian system of numbers from 

 Bagdad in the East to Cordova in the West. Both cir- 

 cumstances contributed powerfully, although in different 



