Yol. III^ No. 7.] Note.^ on Indian Math^emctticS.-^ 481 



these num'bers wei*e read from bottom to lop, z.e,, Hvith tli^ smallei* 

 ■elements Brst. It appears tliat this method of writing is, in softie 

 waj, connected in origin with some vertical script and interesting 

 issues are suggested which* must, however, be set aside for tHe 

 present, ' ' ■ 



In many MSS. the signs of the oldlndian or Brahmi notation 

 approximate more to the forms of letters. Prinsep's idea was 

 that the figures were representatives of the initialletters of the 

 cardinal numbers, but this idea has long been given up (Ind. Antiq. 

 vi., p, 48). Pandit Bhagvantallndraji attempted to show that the 

 Kagari numerals were aksharas or syllables, and his conclusion 

 was accepted by Biihler ; but no satisfactory explanation based 

 on this principle has beeii found for the forms of the different 

 symbols. Indeed, it is now pretty certain that the more modern 

 letter forms found in manuscript are' simply developments of the 

 older numerical symbols. ■ 



in. 



209 



latest known examples of the use of the old notation or ' numeri- 



iymb 

 Circ. A- D. 



T 



f 



757 Gujarat Karachi gi^ant of Kakka. S.S, 67P 

 794 Bengal grant of, Vinayakapala. H.S. 188. / 

 822 Central India Shergadh (Kota) 



inscription of Samanta Deva- 

 datta. ... ... V.S. 879. 



. 854 A Nepal inscription. ... G.S. 535. 



But now there are known instances of the use of these 

 symbols, of a much later date. For example, we have the 

 Katmandu inscription of- the I'eign of the Rajadhiraja Mandera of 

 Newar Samvat 295, I.e., A.D. 1139. (Epigr. Ind. v. app. 76) ; and, 

 as noted above, epigraphieal examples of the thirteenth century are 

 knov^Ti and certain manuscripts have preserved this notation to 

 the present day (Biihler^ Indian Paleography ^ 11). ' 



In the twelfth century we tind examples of the old numerical 

 symbols, the word symbols, alphabetic notations and the modern 

 place value system in use in India. This period appears to have 

 been one of transition, but the evidence of such transition is 



and it is noteworthy that of these various 

 systems ilm one which afterwards predominated was not the 



mea2Te 



modem 



ha 



notation. 



Another noteworthy fact, which has often been indicated by 

 epigraphists, is the marked difference between the old symbols 

 and those of the modem system in use about this time, e.g. 

 Biihler writes : *' Occasionally the same documents combine the 

 naught and other figures of the decimal system with the ancient 

 numeral symbols. Similar mixtures occur in some later inscrip- 



