NOTES. 



presses units by nine diameters, and all other values by group-signs for 10, 

 100, and 1000, having multipliers added to the left. I draw the same infer- 

 ence from the singular aptfljiiot eySt/cot in a scholium of the monk Neophytos, 

 discovered by Prof. Brandis in the library of Paris, and kindly communicated 

 to me for publication. The nine characters of Neophytos are, with the ex. 

 ceptiou of the 4, quite similar to the present Persian ; but these nine units are 

 raised to 10, 100, 1000 times their value by writing one, two, or three 



o o oo 



ciphers (o) above them ; as 2 for twenty, 2 4 for twenty-four, 5 for five hun 







dred, and 3 6 for three hundred and six. If we suppose points to be used 

 instead of ciphers, we have the Arabic dust writing, Gobar ; As my brother 

 Wilhelm von Humboldt has often remarked of the Sanscrit, that it is very in 

 appropriately designated by the terms "Indian" and "ancient Indian" 

 language, since there are in the Indian peninsula several very ancient lan- 

 guages not at all derived from the Sanscrit, so the expression Indian, 01 

 ancient Indian, system of notation is also vague, both in respect to the form 

 of the characters and also to the spirit of the method, which latter sometimes 

 consists in simple juxta-position, sometimes in the use of Coefficients and 

 Indicators, and sometimes in proper " position-value." Even the existence 

 of the cipher, or character for 0, is not a necessary condition of the simple 

 position-value in Indian notation, as the scholium of Neophytos shews. The 

 Indians who speak the Tamul language have numerical characters which 

 appear to differ from their alphabetic characters. The 2 and the 8 have a 

 faint resemblance to the 2 and the 5 of the Devanagari figures, (Rob. Anderson, 

 Rudiments of Tamul Grammar, 1821, p. 135) ; and yet an accurate com- 

 parison shews that the Tamul numerical characters are derived from the 

 Tamul alphabetical writing. Still more different from the Devanagari figures 

 are, according to Carey, the Cingalese. In the latter, and in the Tamul, we 

 find neither position-value nor zero sign, but symbols for tens, hundreds, and 

 thousands. The Cingalese work, like the Romans, by juxta-position ; the 

 Tamuls by coefficients. Ptolemy, in his Almagest and in his Geography, 

 nses the present zero sign to represent the descending or negative scale in 

 degrees and minutes. The zero sign is, consequently, of more ancient use in 

 the West than the epoch of the invasion of the Arabs. (See my work above 

 cited, and the memoir printed in Crelle's Mathematical Journal, S. 215, 219, 

 223, and 227.) 



(3 60 ) p. 228. Wilhelm von Humboldt, fiber die Kawi-Sprache, Bd. i. 

 S. cclxii. Compare also the excellent description of the Arabians, in Herder's 

 Ideen zur Gesch. der Menscheit, Book xix. 4 and 5. 



