316 On the Systems of Numerical Signs 



well distinguished by the name of " Indian and ancient-Indian 

 language," because in that country many more very ancient lan- 

 guages are found which do not derive their origin from the San- 

 scrit ; so Hkewise the expression, " Indian and ancient-Indian 

 figures,*" is too indefinite, not only as far as it regards the form 

 of the figures, but also respecting the spirit of the methods. 

 For in India the principal groups of n, n^, n^, and their mul- 



tipla, 2n,3n are sometimes expressed by juxtaposition, 



sometimes by coefficients, and sometimes merely by the place 

 of the figures. Even the existence of a distinct figure for the 

 cypher, is, in the Indian system, no necessary condition of the 

 method of expressing value by position, as it is proved by the 

 scholion of the monk Neophy tus. In India within the Ganges 

 the most extended languages are the Tamul and the Teloogou, 

 The tribes who speak the first use figures different from their 

 alphabet, of which only two, the two and the eight, exhibit a 

 slight similarity with the Indian (Devanagari) figures of two 

 and five*. Much more different from the Indian figures 

 are those of the Cingalese f . In both the Tamul and the 

 Cingalese languages the different value of the figures is not 

 indicated by position, they have also no distinct figure for the 

 cypher, but distinct hieroglyphics for the groups n, n*, ri^ , . . , 

 The Cingalese make use of juxtaposition, the Tamuls of co- 

 efficients. In India without the Ganges, in the empire of the 

 Burmese, we find the value expressed by position, and a dis- 

 tinct figure for the cypher, but the figures *used by them do 

 not resemble the Arabic, Persian, and Devanagari Indian 

 figures ;};. The Persian figures, used also by the Arabs, are all 

 of them quite different from the Devanagari figures § ; 7 is 

 like a Roman 5; 8 like a Tuscan 5. Among the figures 

 which we call Arabic, only 1 , 2, 3, resemble the figures of the 

 Devanagari of the same value -, the 4 of the Devanagari is our 

 8 ; our 9 is the 7 of the Devanagari. Our 7 is the Persian C. 



* Robert Anderson, Rudiments of Tamul Grammar, 1821„p. 135. 



f James Chater, Grammar of the Cingalese Language. Colombo, 1815, p. 135. 



+ Carey, Grammar of the Burman Language, 1814, p. 196. Only the Bur- 

 mese figures of 3, 4, and 7, resemble in some manner those of 2, 5, and 7. 



^ Compare John Shakespear, Grammar of the Hindustani Language, 1813, 

 p. 95, and PI. L William Jones, Grammar of the Persian Language, 1809, p. 93. 

 Silvestre do Sacy, Grammaire Arabe. PI. VIII. 



