used b]f different NaHon9,i ^^^ 327 



Illative position of the strings, could lead men to invent tha^ 

 system, in which value is expressed by position. 



Whether the simple Indian system, expressing value by 

 position, was brought into the west by the learned astronomer, 

 Rihan Muhammed eben Ahmet Albiruni*, who remained a 

 long time in India, or by Moorish custom-house officers in 

 the ports of North Africa, and their intercourse with th« 

 Italian merchants, I do not presume to decide. Further^ 

 though mental culture was doubtless very early disseminate4 

 in India, it remains doubtful whether the numerical systen^ 

 expressing value by position, which has so powerfully affected 

 the progress of the mathematical sciences, had already been 

 invented and adopted by that nation, when the Macedonian 

 conqueror invaded their country. In how different a con- 

 dition, in how much more perfect a state would the mathe- 

 matical sciences have been transmitted to the learned epoch 

 of the Hashimides by Archimedes, Apollonius of Perga and 

 piophantus, if the western countries of the old continent had 

 received the Indian numerical system twelve or thirteen cen- 

 turies sooner, at the time of Alexander"'s expedition. But 

 that part of upper India, which was then overrun by the 

 Greeks, the Penjab, as far as Palibothra, was, according to the 

 learned researches of M. Lassen, inhabited by nations very 

 little advanced in civilization. Those who lived farther to 

 the east, called them even barbarians. Seleucus Nicator was 

 the first who passed the river Sarasvatis, and by doing so, 

 the limits that separated the civilized and uncivilized tribes ; 

 and then he advanced towards the Gangesf. 



The old Indian numerical figures of the Tamul language, 

 which express the quantities 2n, Sn^ .... by the addition of 

 multiplicators, and consequently besides the figures for the first 

 nine unities, have distinct ones for n, n^, w^, . . . . prove evidently 

 that, in India, besides that system which exclusively has ob- 

 tained the name of Indian (or Arabic) figures, and in which 

 value is expressed by position, there yet, at the same time, 



* According to an observation of the orientalist Sedillot, not less acquainted 

 with the Greek, than with the Arabian astronomy. 

 t Lassen, Comment. Geog. de Pentap., p. 58. 



