300 On the Systems of Numerical Signs 



On the Systems of Numerical Signs used by different Nations, 

 and on the Origin of the Expression of Value by Position 

 in the Indian Numbers, By Alexander von Humboldt. 



[Read in a Class-Session of the Royal Academy of Sciences, in Berlin, 

 the 2d of March, 1829.] 



Translated from the German, and commtmicated by J. W. 



In our researches upon numerical figures (the only hiero- 

 glyphics which, among the nations of the old continent, have 

 been preserved, besides the alphabetical figures used to express 

 the different sounds of spoken language,) our attention has, 

 hitherto, rather been directed to the characteristic physiognomy 

 of the figures and their peculiar formation, than to the spirit 

 of the methods by which human sagacity has succeeded in 

 expressing quantities with a greater or less degree of simplicity. 

 These researches have been entered into with views as narrow 

 and as contracted as those made on languages. The latter 

 have, for a length of time, been compared rather according to 

 the frequency of certain sounds and terminations, or to the 

 form of their roots, than to the organic formation of their 

 grammars. For many years I have been occupied constantly, 

 and with particular predilection, in endeavouring to bring 

 under a general view the different systems of numerical figures 

 used by the different nations of ancient and modern times, and in 

 this way I have succeeded in throwing some light on the origin 

 of what is called the Arabic numerical system. Many circum- 

 stances concurred to enable me to effect it. I myself have 

 acquired, on my travels, a knowledge of the numerical systems 

 of the Aztekes (Mexicans), and of the Muyscas* (the inha- 

 bitants of the elevated plain of Cundinamarca) ; Thomas 

 Young made the discovery of the Egyptian numerical figures, 

 which (as is now known) do not, all of them, express the 

 multipla of the groups by juxtaposition ; the Arabic Gobar, 

 or Dust-figures, were discovered by Silvestre de Sacy/in a 



* On the opinion that the numerical figures of the Muyscas (wliich at the 

 same time are the hieroglyphics of the moon-days of the increasing age of the 

 moon) have some connexion with the face of the moon, increasing by degrees 

 according to its diflferent phases, see Humboldt, Vties des Cord, et Mouumens 

 des Peuples indigenes de TAm^rique, t. ii., p. 237—243. PI. XLIV. 



