APPENDIX. Ill 



Saxon, which very much coincides with that given by 

 Bede, and would appear to be taken from it 



It would be impossible, with the few materials yet 

 brought to light, to conjecture with any great probability 

 how far these Boetian contractions may have influenced 

 the introduction, or co-operated with the Arabic system 

 to the formation, of our present numerical notation. It 

 appears to me highly probable that the two systems 

 became united, because the middle age forms of the 

 figure five coincide with the Boetian mark for the same 

 numeral, and those of two others are very similar. The 

 idea of local position, again, may have had an indepen- 

 dent European origin ; the inconveniences of the abacus 

 on paper would have suggested it by destroying the 

 distinguishing boundaries, and inventing an arbitrary 

 hieroglyphic for the representation of an empty square. 



