326 On the Systems of Numerical Signs 



ceUve, how the cyphers have been placed in the row of the 

 figures, and have preserved that place, when the value by 

 position was adopted. 



In reviewing once more the different methods used by the 

 different nations of both continents in computing numbers* 

 which till now have been in part so little known, we find, 

 firstly, in some only a small number of figures indicating 

 groups, and those almost only for n^, w^, w" . . . . not for 2n, 

 Sn, and 2n^, 9>n^ .... as among the Romans and ancient Tus- 

 cans*, X, C, M, and, therefore all the intermediate groups, 

 for instance, ^n or Sn^, are to be expressed by juxtaposition, 

 ^s in XX or CCCC ; we find further, in others, a great 

 number of figures of groups, not only to express n, n^, (iota 

 and rho among the Greek alphabetic figures) but also to ex- 

 press Sn or 4n^ (in X and v), by whose application a great 

 heterogeneity of the elements is produced in expressing 2 + 2n 

 +2?i^ (for instance, ax/S for i^22) ; we find lastly, that the 

 multipla of the fundamental groups and their powers (2«, 

 3n, 4n^, 5n^,) are, by others, expressed either by the addition 

 pf indicators over or under the figures of the groups (by the 



2 3 4 5 



Chinese X, X, C, O, by the Hindoos speaking the Tamul 

 language 2X, 3X, 4C, 5C,) or by placing over the figures of 

 the first nine unities a progressive number of points, that 



is a=10, a=20, a=100, a=1000, ^=40,000, as in the Gobar^ 

 figures, in the scholion of Neophytus, and in the descending 

 sexagesimal scale of the astronomers of Alexandria, for 



io, w, W\ ^^ ^° ^^' ^^" ^"^'^ '•■' ^^ ^^^^ ^^^" '^^ ^^^*, 



manner the indicators (multiplicators) used by the nations of 

 Eastern Asia, and by the inhabitants of the southern districts 

 of India within the Ganges, or, where originally figures of 

 groups did not exist, in what manner the placing of points 

 over the pythmenes in the Go6ar-system and in the scholion 

 of Neophytus ; and lastly, in what manner even the strings of 

 the suanpan, in which different value is expressed by the 



. * For brevity's sake I here take no notice of the figures of the groups of the 

 quinary system (V, L, D . . . ) which form intermediate sections. 



