used by different Nations. 325 



Tzyphra est et vocatur id, quod cuivis litterae inde a decade 

 dt insequentibus numeris quasi oixniph inscribitur. Significat 

 autem hac Indica voce tale analogiam numerorum. Ubi igitur 

 scriptum est simile prima? litterae aX(px, pro unitate scriptae, 

 atque superimpositum habet vel punctum, vel quasi ofxiKpoVf 

 addita altera figura litterae Indicae, difFerentiam et augmentum 

 numerorum declarat. E. g. pro primo Graeco numero, a scripto, 

 apud Indos | sive linea recta perpendicularis, quando non 

 habet superimpositum punctum vel dfxixpov, ipsum hoc denotat 

 unitatem, ubi vero superimpositum sit punctum atque altera 

 littera adscripta sit, figura quidem similis priori, significat XI, 

 propter additamentum similis litterae atque superimpositum 

 unum punctum. Similiter etiam in reliquis litteris, quemad- 

 modum adspectus docet. Si vero plura habet puncta, plura 

 denotat. Quod intelligas, lector, et supputes unumquidque. 



In this system we do not find that value is expressed by position 

 any more than in the system of the Gobar figures. The number 



o 

 oo 



3006 was written 36. But in using it, it must soon have been 

 observed, that the same figures often expressed different value, 



o 

 oo oo o - 



and that (when all the groups were filled up) in 3 4 6 7, the 

 points or cyphers, by decreasing regularly in number, became 

 superfluous. The cyphers, as it were, served only to facilitate 

 the pronouncing of the number. If we now suppose that the 

 custom of writing the cyphers aside the figures instead of 

 placing them above, became prevalent, the Indian notation as 

 used at present, was introduced for the unmixed groups, as 



o o 



oo oo o 



3=3000. If further, to 3=3000 were to be added 4=40, that 

 place of the cypher was filled up which was assigned to 40 by 

 the exponent indicating the group. Thus 3040 was obtained, 

 and two of the three cyphers, which were required to express 

 the thousands, and which had previously been placed on one 

 line with tlie unities, remained there to indicate the empty 

 places. According to the scholion of Neophytus, therefore, 

 the figures of the cypher are (like the points over the Gobar 

 figures) indicators for the notation of the ascending groups. 

 From the observations made on this system it is easy to per-' 



