.184 ON THE EARLY 



of the Indains being the inventors of these figures is only an extract from 

 the preface of a book of Arabic poems, it may be as well to mention that 

 all the Arabic and Persian books of arithmetic ascribe the invention to the 

 Indians. The following is an extract from a Persian treatise of arithme- 

 tic in my possession. 



" The Indain sages, wishing to express numbers conveniently, invent- 

 " ed these nine figures fprf'°MVA c i. The first figure on the right hand 

 " they made stand for units, the second for tens, the third for hundreds, 

 " the fourth for thousands. Thus, after the third rank, the next follow- 

 " ing is units of thousands, the second tens of thousands, the third hun- 

 " dreds of thousands, and so on. Every figure therefore in the first rank 

 " is the number of units it expresses ; every figure in the second the num- 

 " ber of tens which the figure expresses, in the third the number of hun- 

 " dreds, and so on. When in any rank a figure is wanting, write a cipher 

 " like a small circle o to preserve the rank. Thus ten is written 10, a j 

 " hundred 100 ; five thousand and twenty-five 5025/' 



Of the Indian Algebra in its full extent the Arabians seem to have been 

 ignorant ; but it is likely they had their Algebra from the same source as 

 their Arithmetic. The Arabian and Persian treatises on Algebra, like the 

 old European ones, begin with the Arithmetic, called in those treatises the 

 Arithmetic of the Indians, and have a second part on Algebra ; but no 

 notice is taken of the origin of the latter. Most likely their Algebra, be- 

 ing numeral, was considered by the authors as part of Arithmetic. 



Though part only of the Khuldsat-ul-Hisab is about Algebra, the rest, 

 relating to arithmetic and mensuration, must be thought not wholly un- j 

 connected with the subject. It is to be hoped that ere long we shall 



