598 COSMOS. 



problem, concerning which much yet remains to be elucidated, 

 the question arises, whether position-value the ingenious 

 application of position which occurs in the Tuscan abacus, 

 and in the Suampan of Inner Asia, has been twice indepen- 



positions (strings) are occupied by units (3, 5, 6, and 8) as multipliers or 

 indicators. In both ways, whether by the figurative (the written) or by 

 the palpable arithmetic, we arrive at the value of position, and at the 

 ample use of nine numbers. If a string be without any ball the place 

 will be left blank in writing. If a group (a member of the progression) 

 be wanting, the vacuum is graphically filled by the symbol of a vacuum 

 (s&nya, sifron, tzuplira). In the " Method of Eutocius" I find in the 

 group of the myriads, the first trace of the exponential or indicational 

 system of the Greeks, which was so influential in the east: M a , M#, M?, 

 designate 10,000, 20,000, 30,000. That which is here alone applied to 

 the myriads, passes among the Chinese and the Japanese, who derived 

 their knowledge from the Chinese, two hundred years before the Chris- 

 tian era, through all the multiples of the groups. In the Gobar, the 

 Arabian " dust writing," (discovered by my deceased friend and teacher 

 Silvestre de Sacy, in a manuscript in the library of the old Abbey of St. 

 Germain des Pres) the group-signs are points therefore zeros or 

 ciphers; for in India, Thibet, and Persia, zeros and points are identical. 

 In the Gobar, 3' is written for 30; 4" for 400; and 6'"' for 6000. 

 The Indian numbers, and the knowledge of the value of position, must 

 "be more modern than the separation of the Indians and the Arians; for 

 the Zend nation only used the far less convenient Pehlwi numbers. The 

 conjecture of the successive improvements that have been made in the 

 Indian notation, appears to me to be supported by the Tamul system, 

 which expresses units by nine characters, and all other values by group- 

 signs for 10, 100, and 1000, with multipliers added to the left. The 

 singular doiQfioL ivciicoi in a scholium of the monk Neophytos, dis- 

 covered by Prof. Brandis in the library of Paris, and kindly communi- 

 cated to me for publication, appear to corroborate the opinion of such a 

 gradual process of improvement. The nine characters of Neophytos 

 are, with the exception of the 4, quite similar to the present Persian; 

 but the value of these nine units is raised 10, 100, 1000 fold by writing 

 one, two, or three ciphers or zero signs above them; as 2 for 20, 2 4 

 for 24, 5 for 500, and If 6 for 306. If we suppose points to be 

 used instead of zeros, we have the Arabic dust- writing, Gobar. As my 

 brother, Wilhelm von Humboldt, has often remarked of the Sanscrit, 

 that it is very inappropriately designated by the terms " Indian " and 

 "ancient Indian" language, since there are in the Indian peninsula 

 several very ancient languages not at all derived from the Sanscrit; so 

 the expression, Indian or ancient Indian arithmetical characters, is also 

 very vague, and this vagueness applies both to the form of the characters 

 and to the spirit of the methods, which sometimes consist in mere juxta- 

 position, sometimes in the employment of coefficients and indicators, 



