THE ARABS. 597 



Arabs to a knowledge of Indian algebra, enabled them also to 

 obtain, in the ninth century, Indian numerals from Persia and 

 the shores of the Euphrates. Persians were established at 

 that period as revenue-collectors on the Indus, and the 

 use of Indian numerals was gradually transmitted to the 

 revenue officers of the Arabs in Northern Africa, opposite the 

 shores of Sicily. Nevertheless, the important historical in- 

 vestigations of the distinguished mathematician Chasles,* 

 have rendered it more than probable, according to his correct 

 interpretation of the so-called Pythagorean table in the 

 Geometry of Boethius, that the Christians in the west were 

 familiar with Indian numerals even earlier than the Arabs, 

 and that they were acquainted with the use of nine figures or 

 characters, according to their position-value, under the 

 name of the system of the abacus. 



The present is not a fitting place to enter more fully into 

 the consideration of this subject, which I have already treated 

 of in two papers (written in 1819 and 1829,) and presented 

 to the Academic des Inscriptions at Paris, and the Academy 

 of Sciences at Berlin,f but in our attempts to solve a historical 



* Chasles, Apercu historique des Methodes en Geometric, 1837, 

 pp. 464-472; also in the Comptes rendus de I'Acad. des Sciences, 

 t. viii. 1839, p. 78; t. ix. 1839, p. 449; t. xvi. 1843, pp. 156-173, and 

 218--246; t. xvii. 1843, pp. 143-154. 



+ Humboldt, Ueber die bei verschiedenen Volkern ublichen Systeme 

 von Zalilezeichen und uber den Ursprung des Stellenwerthcs in den 

 indisclien Zalden, in CreWs Journal fur die reine und angewandte 

 Mathematik, bd. iv. (1829), s. 205-231 ; compare also my Examen crit. 

 de mist, de la Geographic, t. iv. p. 275. The simple enumeration of 

 the different methods which nations, to whom the Indian arithmetic by 

 position was unknown, employed for expressing the multiplier of the 

 fundamental groups, furnishes, in my opinion, an explanation of the 

 gradual rise or origin of the Indian system. If we express the number 

 3568, either perpendicularly or horizontally, by means of " indicators," 

 corresponding to the different divisions of the abacus, (thus, M 3 C X 6 ! 8 ), 

 we shall easily perceive that the group-signs (MCXI) might be omitted. 

 But our Indian numbers are, however, nothing more than these indi- 

 cators the multipliers of the different groups. We are also reminded 

 of this designation by indicators by the ancient Asiatic Suanpan 

 (the reckoning machine which the Moguls introduced into Russia), 

 which has successive rows of strings, to represent thousands, hundreds, 

 tens, and units. These strings would bear in the numerical example 

 just cited, 3, 5, 6, and 8 balls. In the Suanpan there is no apparent 

 group-sign; the group-signs are the positions themselves; and these 



